Category: Class 12

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3

Question 1.
Identify the type of conic section of each of the equations.
(1) 2x² – y² = 7
(2) 3x² + 3y² – 4x + 3y + 10 = 0
(3) 3x² + 2y² = 14
(4) x² + y² + x – y = 0
(5) 11x² – 25y² – 44x + 50y – 256 = 0
(6) y² + 4x + 3y + 4 = 0
Solution:
(1) 2x² – y² = 7
Comparing this equation with the general equation of the conic
Ax² + Bxy + Cy² + Dx + Ey + F = 0
We get A = 2, C = – 1
Elere A ≠ C also A and C are of opposite signs.
So the conic is a hyperbola.

(2) 3x² + 3y² – 4x + 3y + 10 = 0
A = 3, B = 0, C = 3, D = -4, E = 3, F = 10
A = C and B = 0 (No xy term)
∴ It is a circle.

(3) 3x² + 2y² = 14
A = 3, B = 0, C = 2, F = -14
A ≠ C and A & C are the same signs.
∴ It is an ellipse.

(4) x² + y² + x – y = 0
Comparing this equation with the general equation of the conic
Ax² + Bxy + Cy² + Dx + Ey + F = 0
We get A = C and B = 0
So the given conic is a circle.

(5) 11x² – 25y² – 44x + 50y – 256 = 0
A =11, B = 0, C = -25, D = -44, E = 50, F = -256
A ≠ C and A & C are the opposite signs.
∴ It is a hyperbola.

(6) y² + 4x + 3y + 4 = 0
Comparing this equation with the general equation of the conic
Ax² + Bxy + Cy² + Dx + Ey + F = 0
We get A = 0 and B = 0
So the conic is a parabola.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.5 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.5

Question 1.
A bridge has a parabolic arch that is 10 m high in the centre and 30 m wide at the bottom. Find the height of the arch 6 m from the centre, on either sides.
Solution:

PQ = 2a = 30 m
a = 15 m
Point Q be (15 , -10)
Equation of the parabola
x² = -4 ay …….. (1)
Q lies on parabola
15² = -4a( -10)
a = \(\frac {225}{40}\)
(1) ⇒ x² = -4(\(\frac {225}{40}\))y
x² = \(\frac {225}{10}\)y
Let B(6, y) lies on parabola
6² = \(\frac {225}{10}\) y₁
y₁ = –\(\frac {36×10}{225}\) = \(\frac {-8}{5}\) = \(\frac {8}{5}\) m
AB = AC – BC = 10 – \(\frac {8}{5}\)
= \(\frac {50-8}{5}\) = \(\frac {42}{5}\)
AB = 8.4 m
∴ The height of the arch 6 m from the centre is 8.4 m.

Question 2.
A tunnel through a mountain for a four lane highway is to have a elliptical opening. The total width of the highway (not the opening) is to be 16 m and the height at the edge of the road must be sufficient for a truck 4 m high to clear if the highest point of the opening is to be 5 m approximately. How wide must the opening be?
Solution:

Let the equation of the ellipse be
\(\frac {x^2}{a^2}\) + \(\frac {y^2}{b^2}\) = 1
Length of semi minor axis b = 5
i,e., \(\frac {x^2}{a^2}\) + \(\frac {y^2}{5^2}\) = 1
Let BB’ be the road width and AA’ be the end points of the opening of the tunnel.
Let CB = 8, BD = 4
∴ D is (8, 4) lies on the ellipse
\(\frac {8^2}{a^2}\) + \(\frac {4^2}{5^2}\) = 1
⇒ a² = \(\frac {25}{9}\) × 64
⇒ a = \(\frac {40}{3}\)
The width AA’ = 2a
= \(\frac {80}{3}\) = 26.66 m
The required width is 26.66 m.

Question 3.
At a water fountain, water attains a maximum height of 4 m at horizontal distance of 0.5 m from its origin. If the path of water is a parabola, find the height of water at a horizontal distance of 0.75 m from the point of origin.
Solution:

Let the equation of parabola be
(x – h)² = -4a (y – k)
Here vertex B (0.5, 4)
∴ Equation of parabola
(x – 0.5)² = -4a(y – 4)
Parabola passes through origin (0, 0)
(0 – 0.5)² = -4a(0 – 4)
(-\(\frac {1}{2}\))² = 16a
∴ \(\frac {1}{4}\) = 16a ⇒ a = \(\frac {1}{64}\)
∴ Equation of parabola
(x – 0.5)² = -4(\(\frac {1}{64}\))(y- 4)
This Parabola passes again through D(0.75, y₁)
∴ (0.75 – 0.5)² = –\(\frac {1}{16}\) (y₁ – 4)
(0.25)² = –\(\frac {1}{16}\) (y₁ – 4)
(\(\frac {1}{4}\))² = –\(\frac {1}{16}\) (y₁ – 4)
\(\frac {1}{16}\) = –\(\frac {1}{16}\) (y₁ – 4)
1 = -y₁ + 4
y₁ = 3
Height of water at a horizontal distance of 0.75 m is 3 m.

Question 4.
An engineer designs a satellite dish with a parabolic cross section. The dish is 5 m wide at the opening and the focus is placed 1.2 m from the vertex
(a) Position a co-ordinate system with the origin at the vertex and the x-axis on the parabola’s axis of symmetry and find an equation of the parabola.
(b) Find the depth of the satellite dish at the vertex.
Solution:

(a) Consider the satellite dish is open rightward parabola
y² = 4 ax ……….. (1)
Clearly a = 1.2m
(1) ⇒ y² = 4(1.2)
y² = 4.8x
(b) Use the point (x₁, 2.5) in (1)
(2.5)² = 4(1.2)x₁
\(\frac{(2.5)^{2}}{4(1.2)}\) = y₁
x₁ = 1.3 m
∴ The depth of the satellite dish at vertex is 1.3 m

Question 5.
The parabolic cable of a 60 m portion of the roadbed of a suspension bridge are positioned as shown below. Vertical cables are to be spaced every 6 m along this portion of the roadbed. Calculate; the lengths of first two of these vertical cables: from the vertex.

Solution:

From the diagram, the equation is x² = 4 ay and it passes through C(30, 13)
Equation of Parabola x² = 4ay.
30² = 4a × 13
4a = \(\frac {30^2}{13}\)
∴ Equation of the parabola is
x² = \(\frac {30^2}{13}\)y
(i) Let VG = 6 and GE = y
∴ E is (6, y) and it lies on the parabola
36 = \(\frac {30^2}{13}\)y
⇒ y = 0.52
Gable from the road = 3 + 0.52
= 3.52 m.

(ii) Let VH = 12 and HF = y
∴ F (12, y) lies on the parabola
12² = \(\frac {30^2}{13}\)y
⇒ y = \(\frac {144×13}{900}\)
= \(\frac {208}{100}\)y
y = 2.08
Cable from the road = 3 + 2.08 = 5.08
The heights of the first two vertical cables from the vertex are 3.52 m and 5.08 m

Question 6.
Cross-section of a Nuclear cooling tower is in the shape of a hyperbola with equation \(\frac {x^2}{30^2}\) – \(\frac {y^2}{44^2}\) = 1. The tower is 150 m tall and the distance from the top of the tower to the centre of the hyperbola is half the distance from the base of the tower to the centre of the hyperbola. Find the diameter of the top and base of the tower.

Solution:

Equation of hyperbola is \(\frac {x^2}{30^2}\) – \(\frac {y^2}{44^2}\) = 1
Given OC = \(\frac {1}{2}\) OD and CD = 150
∴ OC = 50 m and OD = 100 m
Let the Radius of top of the tower be x₁ and bottom of the tower be x₂.
∴ Points A(x₁, 50) and B(x₂, 100)
Hyperbola passes through A(x₁, 50)

∴ Radius of the top = 45.41 m.
Diameter of the top = 90.82 m
Also
The hyperbola again passes through B(x₂, 100)

∴ Radius of the base = 74.48 m.
Diameter of the base = 148.96 m
∴ Diameter of the top and base of the tower are 90.82 m and 148.96 m.

Question 7.
A rod of length 1.2 m moves with its ends always touching the co-ordinate axes. The locus of a point P on the rod, which is
0. 3 m from the end in contact with x axis is an ellipse. Find the eccentricity.
Solution:

Length of rod BD = 1.2 m
Let P(x, y) be any point on the Rod such
that PB = 0.3 m
∴ PD = 1.2 – 0.3 = 0.9 m
Let ΔPAB and ΔPCD are similar triangles
In ΔPAB sin θ = \(\frac {y}{0.3}\)
In A PCB cos θ = \(\frac {y}{0.9}\)
We know that sin² θ + cos² θ = 1

Question 8.
Assume that water’issuing from the end of a horizontal pipe, 7.5 m. above the ground, describes a parabolic path. The vertex of the parabolic path is at The end of the pipe. At position 2.5 in below the line of the pipe, the flow of water has curved outward 3 m beyond the vertical, line through the end of the pipe. How far beyond this vertical line will the water strike the ground?
Solution:

Equation of the water path is
x² = – 4 ay
Use the point (3, – 2.5) in (1)
(3)² = – 4a(- 2.5)
9 = 10a
a = \(\frac{9}{10}\) substituting in (1)
(1) ⇒ x² = -4\(\frac{9}{10}\)y …………. (2)
Use the point (x₁, -7.5) in (2)
(2) ⇒ x₁² = -4 \(\frac{9}{10}\)(-7.5) ⇒ x₁² = 30(\(\frac{9}{10}\))
x₁ = \(\sqrt{3 \times 9}\)
x₁ = \(3 \sqrt{3}\) m
∴ The water strikes the ground \(3 \sqrt{3}\) m beyond the vertical line.

Question 9.
On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 in when it is 6 m away from the point of projection. Finally, it reaches the ground 12 in away from the starting-point. Find the angle of! projection.
Solution:

Equation of the parabola be x² = – 4ay ……. (1)
B(6, -4) lies on parabola
6² = -4a(-4)
\(\frac {36}{16}\) = a ⇒ a = \(\frac {9}{4}\)
(1) ⇒ x² = -(\(\frac {9}{4}\))y
x² = -9y ………. (2)
Now need tofind slope at (-6, -4)
Diff (2) w.r.to x
2x = -9 \(\frac {dy}{dx}\)
\(\frac {dy}{dx}\) = \(\frac {2x}{-9}\)
At(-6, -4), \(\frac {dy}{dx}\) = \(\frac {2(-6)}{-9}\) = \(\frac {12}{9}\) = \(\frac {4}{3}\)
tan θ = \(\frac {4}{3}\)
θ = tan^-1(\(\frac {4}{3}\))

Question 10.
Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than 5. Show that the location of the explosion is restricted to a particular curve and find an equation of it.
Solution:
As shown in figure, A and B are on both sides of x-axis at Co-ordinates (-5, 0) and (5, 0)
The distance between A and B is 10. A point C is on the graph at Co-ordinates (x, y)
C is 6 km closer to A than B.

Squaring on both sides we get,
(x – 5)² + y² = 36 + (x + 5)² + y² + 12(\(\sqrt {(x+5)^2+y^2}\))
x² + 25 – 10x + y² = x² + 10x + y² + 36 + 25 + 12\(\sqrt {(x+5)^2+y^2}\)
-20x – 36 = 12\(\sqrt {(x+5)^2+y^2}\)
(÷ by 4) ⇒ -5x – 9 = 3\(\sqrt {(x+5)^2+y^2}\)
Squaring both sides we get,
25x² + 81 + 90x = 9(x² + 25 + 10x + y²)
25x² + 81 + 90x – 9x² – 90x – 9y² – 225 = 0
16x² – 9y² – 144 = 0
16x² – 9y² = 144
(÷ by 144) ⇒ \(\frac {x^2}{9}\) – \(\frac {y^2}{16}\) = 1 is the required equation of hyperbola.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 6 Applications of Vector Algebra Ex 6.2 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 6 Applications of Vector Algebra Ex 6.2

Question 1.
If \(\overline { a }\) = \(\hat { i }\) – 2\(\hat { j }\) + 3\(\hat { k }\), b = 2\(\hat { i }\) + \(\hat { j }\) – 2\(\hat { k }\), c = 3\(\hat { i }\) + 2\(\hat { j }\) + \(\hat { k }\) find \(\overline { a }\).(\(\overline { b}\) × \(\overline { c }\)).
Solution:
\(\overline { a }\).(\(\overline { b}\) × \(\overline { c }\)) = [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ] = \(\left|\begin{array}{ccc}
1 & -2 & 3 \\
2 & 1 & -2 \\
3 & 2 & 1
\end{array}\right|\)
= 1(1 + 4) + 2(2 + 6) + 3(4 – 3)
= 5 + 16 + 3 = 24

Question 2.
Find the volume of the parallelepiped whose coterminous edges are represented by the vectors -6\(\hat { i }\) + 14\(\hat { j }\) + 10\(\hat { k }\), 14\(\hat { i }\) – 10\(\hat { j }\) – 6\(\hat { k }\) and 2\(\hat { i }\) + 4\(\hat { j }\) – 2\(\hat { k }\)
Solution:
Volume of the parallelepiped = [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ]
= \(\left|\begin{array}{ccc}
-6 & 14 & 10 \\
14 & -10 & -6 \\
2 & 4 & -2
\end{array}\right|\)
= -6(20 + 24) -14(-28 + 12) + 10(56 + 20)
= -6(44) -14(-16) + 10(76)
= -264 + 224 + 760
= 720 cu. units.

Question 3.
The volume of the parallelepiped whose coterminous edges are 7\(\hat { i }\) + λ\(\hat { j }\) – 3\(\hat { k }\), \(\hat { i }\) + 2\(\hat { j }\) – \(\hat { k }\), -3\(\hat { i }\) + 7\(\hat { j }\) + 5\(\hat { k }\) is 90 cubic units. Find the value of λ
Solution:
volume of the parallelepiped = [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ]
\(\left|\begin{array}{ccc}
7 & \lambda & -3 \\
1 & 2 & -1 \\
-3 & 7 & 5
\end{array}\right|\) = 90
7(10 + 7) – λ(5 – 3) – 3(7 + 6) = 90
7(17) – λ(2) – 3(13) = 90
119 – 2λ – 39 = 90
2λ = 119 – 39 – 90
2λ = -10
λ = -5

Question 4.
If \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) are three non-coplanar vectors represented by concurrent edges of a parallelepiped of volume 4 cubic units, find the value of
(\(\overline { a }\) + \(\overline { b }\)).(\(\overline { b }\) × \(\overline { c }\)) + (\(\overline { b }\) + \(\overline { c }\)).(\(\overline { c }\) × \(\overline { a }\)) + (\(\overline { c }\) + \(\overline { a }\)).(\(\overline { a }\) × \(\overline { b }\)).
Solution:
Given [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ] = ±4.
{(\(\overline { a }\) + \(\overline { b }\)).(\(\overline { b }\) × \(\overline { c }\)) + (\(\overline { b }\) + \(\overline { c }\)).(\(\overline { c }\) × \(\overline { a }\)) + (\(\overline { c }\) + \(\overline { a }\)).(\(\overline { a }\) × \(\overline { b }\)).}
= \(\overline { a }\)(\(\overline { b }\) × \(\overline { c }\)) + \(\overline { b }\) – (\(\overline { b }\) × \(\overline { c }\)) + \(\overline { b }\) – (\(\overline { c }\) × \(\overline { a }\)) + \(\overline { c }\) – (\(\overline { c }\) × \(\overline { a }\)) + \(\overline { c }\)(\(\overline { a }\) × \(\overline { b }\)) + \(\overline { a }\) – (\(\overline { a }\) × \(\overline { b }\))
= [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ] + [ \(\overline { b }\), \(\overline { b }\), \(\overline { c }\) ] + [ \(\overline { p }\), \(\overline { c }\), \(\overline { a }\) ] + [ \(\overline { c }\), \(\overline { c }\), \(\overline { a }\) ] + [ \(\overline { c }\), \(\overline { a }\), \(\overline { b }\) ] + [ \(\overline { a }\), \(\overline { a }\), \(\overline { b }\) ]
= ± 4 + 0 ± 4 + 0 ± 4 + 0 = ± 12

Question 5.
Find the altitude of a parallelepiped determined by the vectors \(\overline { a }\) = -2\(\hat { i }\) + 5\(\hat { j }\) + 3\(\hat { k }\), \(\overline { b }\) = \(\hat { i }\) + 3\(\hat { j }\) – 2\(\hat { k }\) and \(\overline { c }\) = -3\(\hat { i }\) + \(\hat { j }\) + 4\(\hat { k }\) if the base is taken as the parallelogram determined by \(\overline { b }\) and \(\overline { c }\).
Solution:
V = \(\overline { a }\) -(\(\overline { b }\) × \(\overline { c }\)) = [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ]
= \(\left|\begin{array}{ccc}
-2 & 5 & 3 \\
1 & 3 & -2 \\
-3 & 1 & 4
\end{array}\right|\)
= -2(12 + 2) -5(4 – 6) + 3(1 + 9)
= -2(14) -5(-2) + 3(10)
= -28 + 10 + 30 = 12
Area = |\(\overline { b }\) × \(\overline { c }\)| = \(\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
1 & 3 & -2 \\
-3 & 1 & 4
\end{array}\right|\)
= \(\hat { i }\)(12 + 2) – \(\hat { j }\)(4 – 6) + \(\hat { k }\)(1 + 9)
= 14\(\hat { i }\) + 2\(\hat { j }\) + 10\(\hat { k }\)
|\(\overline { b }\) × \(\overline { c }\)| = \(\sqrt { 196+4+100 }\) = \(\sqrt { 300 }\)
= 10√3
Altitude h = \(\frac { V }{ Area }\) = \(\frac { 12 }{ 10√3 }\) = \(\frac { 12×√3 }{ 10×3 }\) = \(\frac { 2√3 }{ 5 }\)

Question 6.
Determine whether the three vectors 2\(\hat { i }\) + 3\(\hat { j }\) + \(\hat { k }\), \(\hat { i }\) – 2\(\hat { j }\) + 2\(\hat { k }\) and 3\(\hat { i }\) + \(\hat { j }\) + 3\(\hat { k }\) are coplanar.
Solution:
If vectors are coplanar, [ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ] = 0
[ \(\overline { a }\), \(\overline { b }\), \(\overline { c }\) ] = \(\left|\begin{array}{ccc}
2 & 3 & 1 \\
1 & -2 & 2 \\
3 & 1 & 3
\end{array}\right|\)
= 2(-6 – 2) -3(3 – 6) + 1(1 + 6)
= -2(-8) -3(-3) + 1(7) = -16 + 9 + 7 = 0
∴ The given vectors are coplanar

Question 7.
Let \(\overline { a }\) = \(\hat { i }\) + \(\hat { j }\) + \(\hat { k }\), \(\overline { b }\) = \(\hat { i }\) and \(\overline { c }\) = c₁\(\hat { i }\) + c₂\(\hat { j }\) + c₃\(\hat { k }\). If c₁ = 1 and c₂ = 2, find c₃ such that \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) are coplanar.
Solution:
If \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) are coplanar [ \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) ] = 0
\(\left|\begin{array}{lll}
1 & 1 & 1 \\
1 & 0 & 0 \\
c_{1} & c_{2} & c_{3}
\end{array}\right|\) = 0
1(0) – 1(c₃) + 1(c₂) = 0
-c₃ + c₂ = 0
c₃ = c₂ = 2

Question 8.
If \(\overline { a }\) = \(\hat { i }\) – \(\hat { k }\), \(\overline { b }\) = x\(\hat { i }\) + \(\hat { j }\) + (1 – x)\(\hat { k }\) c = y\(\hat { i }\) + x\(\hat { j }\) + (1 + x – y) \(\hat { k }\) Show that [ \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) ] = 0
Solution:
[ \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) ] = \(\left|\begin{array}{ccc}
1 & 0 & -1 \\
x & 1 & 1-x \\
y & x & 1+x-y
\end{array}\right|\)
= 1(1 + x – y – x + x²)-1(x² – y)
(1 + x – y – x + x² – x² + y)
= 1
There is no x and y terms
∴ [ \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) ] depends on neither x nor y.

Question 9.
If the vectors a\(\hat { i }\) + a\(\hat { j }\) + c\(\hat { k }\), \(\hat { i }\) + \(\hat { k }\) and c\(\hat { i }\) + c\(\hat { j }\) + b\(\hat { k }\) are coplanar, prove that c is the geometric mean of a and b.
Solution:
[ \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) ] = 0
\(\left|\begin{array}{lll}
a & a & c \\
1 & 0 & 1 \\
c & c & b
\end{array}\right|\) = 0
a(0 – c) – a(b – c) + c(c) = 0
-ac – ab + ac + c² = 0
c² – ab = 0
c² = ab
⇒ c in the geometric mean of a and b.

Question 10.
Let \(\overline { a }\), \(\overline { b }\) and \(\overline { c }\) be three non-zero vectors such that \(\overline { c }\) is a unit vector perpendicular to both \(\overline { a }\) and \(\overline { b }\). If the angle between \(\overline { a }\) and \(\overline { b }\) is \(\frac { π }{ 6 }\) show that [\(\overline { a }\), \(\overline { b }\) and \(\overline { c }\)]² = \(\frac { 1 }{ 4 }\) |\(\overline { a }\)|² |\(\overline { b }\)|²
Solution:

Hence proved

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Prose Chapter 3 In Celebration of Being Alive Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Prose Chapter 3 In Celebration of Being Alive

12th English Guide In Celebration of Being Alive Text Book Back Questions and Answers

Textual Questions:

1. Answer the following questions in one or two sentences based on your understanding of the lesson: (P.No. 70)(Note: IQ —> Important Questions)

Question a.
What thoughts troubled Dr. Christiaan Barnard as he neared the end of his career as a heart surgeon?
Answer:
Towards the end of his career, Dr. Christiaan Barnard was troubled by the suffering of people and especially of young children. He could not accept the fact that 12 million children are unlikely to reach the age of one and about 6 million children die annually before reaching the age of five.

Question b.
What were Dr. Barnard’s feelings when he was hospitalized after an accident?
Answer:
Dr. Barnard had a feeling about why his wife and himself had to suffer.

Question c.
When and where did the accident occur? (IQ)
Answer:
He and his wife were crossing the road after a lovely meal. A car hit him and knocked him into his wife. His wife was thrown into the other lane and was struck by a car coming in the opposite direction.

Question d.
How did the hospitalization of Dr. Barnard and his wife affect their routine?
Answer:
Dr. Barnard was not able to attend to the patients who were waiting for him to operate on them. His wife was not able to take care of her young baby.

Question e.
How was Dr. Barnard’s attitude to suffering different from that of his father’s?
Answer:
Dr. Barnard’s father accepted suffering as God’s will. He also believed that suffering ennobles humans. But Dr. Barnard found no meaning in the agony and suffering of patients and especially of the young children.

Question f.
How was the unattended trolley put to use? (IQ)
Answer:
The unattended trolley was used as a car for a race (Grand Prix of Cape Town’s Red cross children’s’ hospital) within the hospital.

Question g.
What roles did the duo take up?
Answer:

1. The two boys took the roles of a driver and a mechanic
2. The blind boy was the mechanic and the boy with on arm was the driver.

Question h.
Why did the choice of roles prove to be easy for them?
Answer:
The mechanic provided motor power by galloping along behind the trolley with his head down. The driver steered the trolley by scraping his foot on the floor. The choice of the roles was easy because the mechanic was totally blind and the driver had only one arm.

Question i.
Who encouraged them and how?
Answer:
The other patients encouraged them by laughing and shouting.

Question j.
What does Dr. Barnard compare this entertainment to?
Answer:
Dr. Barnard compared the trolley race as much better entertainment than anything anyone puts on at the Indianapolis 500 car race.

Question k.
What happened in the grand finale? (IQ)
Answer:
The grand finale led to the scattering of plates and silverware placed on the trolley.

Question l.
How does Dr. Barnard know the boy who played the trolley’s driver?
Answer:
Dr. Barnard knew the trolley’s driver better. He had successfully closed a hole in his heart a few years back.

Question m.
What was the profound lesson that Dr. Barnard learned from the boys?
Answer:
The profound lesson that Dr.Barnard learned was that the business of living in the celebration of being alive.

2. Answer the following questions in three or four sentences: (Text Book Page No. 71)

Question a.
Detail the statistics Dr. Barnard has provided in his speech.
Answer:
Of the 125 million children bom that year, 12 million are unlikely to reach the age of one. Another six million will die before the age of five. Among the rest, many will end up as mental or physical cripples.

Question b.
What happened when the doctor couple was crossing the street?
Answer:
When they were crossing the street a car hit him and knocked him into his wife. She was thrown into the
other lane and struck by a car coming from the opposite direction.

Question c.
What injuries did they sustain in the accident?
Answer:
Dr. Barnard had eleven broken ribs. A lung was profoundly perforated. His wife had a badly fractured shoulder.

Question d.
Dr. Barnard couldn’t find any nobility in suffering. Why?
Answer:
Dr.Barnard couldn’t find any nobility in suffering because a sufferer would move restlessly with his mind filled with agony.

Question e.
Why does Dr. Barnard find the suffering of children heartbreaking?
Answer:
He has always found the suffering of young children heart-breaking. Especially because they have total faith in doctors. They believe doctors will help. They don’t complain even after undergoing a mutilating surgery.

Question f.
How did the boy who played the mechanic lose his eyesight?
Answer:

1. One night his mother and father were drunk.
2. His mother threw a lantern at his father which missed and broke over the child’s head and shoulders.
3. He suffered severe third-degree burns on the upper part of his body and lost both his eyesight.

Question g.
Why does Dr. Barnard describe the blind boy as a ‘walking horror’?
Answer:
At the time of the Grand Prix, the boy was a walking horror. His face was disfigured. A long flap of skin was hanging from the side of his neck to his body. As the wound healed around his neck, his lower jaw became gripped in a mass of fibrous tissue. The only way he could open his mouth was to raise his head.

Question h.
What were the problems the trolley driver suffered from?
Answer:

1. The trolley driver had a hole in his heart which was successfully closed by Dr.Barnard.
2. He also suffered from a malignant tumour of the bone because of which his shoulder and arm were amputated.

3.Answer the following in a paragraph of 100 – 150 words each: (P.No. 71)

Question a.
Give an account of the medical problems for which the two boys were hospitalized.
Answer:
The seven years old mechanic suffered third-degree bums on the upper part of his body. He had lost both his eyes. He was literally a walking horror. He was disfigured. A long flap of skin was hanging from the side of his neck to his body. As the wound healed around his neck, his lower jaw became gripped in a mass of fibrous tissue. The trolley driver had a malignant tumour of the bone. A few days before the race, his shoulder and arm were amputated. There was little hope of his recovery. If two adults had similar ailments, they would have got dejected with life. But the boys were just happy celebrating the joy of being alive.

Question b.
“These two children had given me a profound lesson …” Elucidate.
(or)
Question c.
Describe the ‘Grand Prix’ at Cape Town’s Red Cross Children’s Hospital.
(or)
Question d.
How did a casual incident in a hospital help Dr. Barnard perceive a new dimension of life?
Answer:
The author describes the event as “the Grand Prix of Cape Town’s Red Cross Children’s’ Hospital”. A nurse had left a breakfast trolley unattended. Very soon this trolley was commandeered by a daring crew of two, a driver and a mechanic. The mechanic provided motor power by galloping along behind the trolley head down. While the driver, seated on the lower deck held on with one hand and steered it by scrapping his foot on the floor. The choice of roles wags easily because the mechanic was totally blind and the driver had only one arm. It was better than the Indianapolis 500 car race. Patients shouted and cheered the boys. There was a grand finale of scattered plates and silverware before the nurse and ward sister took control of the situation.

Question e.
Life is unjust and cruel to certain people. Do they all resign themselves to their fate? Can you think of some who have fought their disabilities heroically and remained a stellar example for others? (for e.g. the astrophysicist Stephen Hawking, a paraplegic). Give an account of one such person and his/her struggle to live a fruitful life.
Answer:
It is a true fact that life is unjust and cruel to certain people. But they all do not resign themselves to their fate. In this context it is worth mentioning Divij Shah who is a one-handed cycling champion, He lost his right hand in an accident when he was four. Determined not to define that mishap in his life, he has experienced way more than the average person with two hands. In his teens, he played for West Bengal’s U-16 cricket team. Constantly looking for challenges, he also took upcycling. After meticulous practice, he bagged silver at the Asian Para-cycling championships that took place a few months ago. At present, Divij has his eyes set on becoming a champion in the 2020 Paralympics.

Paragraph:

Introduction:
In celebration of being alive is an extract of Christiaan Barnard’s speech wherein he narrates an incident which took place in his hospital. It is this incident which made him look at the positive aspect of life. He and his wife met with an accident a few years back. They both were affected very badly. Barnard had eleven broken ribs and a perforated lung and his wife had a badly fractured shoulder. He had a bad feeling about why his wife and himself had to suffer.

4 Better person:
He remembered his father’s words who was of the view that suffering ennobles one and makes one a better person. Barnard found the suffering of children heartbreaking.

In the hospital:
A ‘Grand Prix’ of cape town’s red cross children’s hospital made him perceive a new dimension of life. A nurse had left a breakfast trolley unattended which was taken possession of by two bold and daring boys. One acted as a driver and the other a mechanic.

The mechanic who was seven years old suffered severe third-degree burns on the upper part of his body and lost both his eyes. The trolley’s driver had a hole in his heart which was successfully closed by Dr. Barnard. Later he was hospitalized again because he had a malignant tumour of the bone out of which his shoulder and arm were amputated.

Life lesson:
The patients encouraged them by their shouts and laughter. It was a much better entertainment the result of which was the scattered plates and silverware placed on the trolley. After the Grand Prix, the driver who had a little hope of recovery proudly informed Dr. Barnard that the trolley’s wheels were not properly oiled but he was a good driver and he had full confidence in the mechanic.

Conclusion:
Thus the action of the two children made Dr. Barnard realize the fact that the business of living is the celebration of being alive. He also realized that what is important is what you’ve left and not what you’ve lost.
Learn to live in the sufferings

Vocabulary:
Go through the lesson and spot the words which mean the same as the following: (Text Book Page No. 71)

Question 1.
profession (para 1)
Answer:
Career

Question 2.
sorrowful (para 2)
Answer:
Gloomy

Question 3.
decency (para 5)
Answer:
Noble

Question 4.
destiny (para 6)
Answer:
Fate

Question 5.
hijacked (para 8)
Answer:
Commandeered

Question 6.
motivation (para 9)
Answer:
Encouragement

Question 7.
serious (para 10)
Answer:
Severe

Question 8.
significant (para 13)
Answer:
Important

b) Go through the lesson and spot the words opposite to the meaning of the following:
Question 1.
rare (para 1)
Answer:
prevalent

Question 2.
primitive (para 6)
Answer:
sophisticated

Question 3.
fiction (para 7)
Answer:
witness / fact

Question 4.
fearful (para 8)
Answer:
intrepid

Question 5.
benign (para 11)
Answer:
malignant
Question 6.
diffidence (para 11)
Answer:
hope, confidence

Question 7.
boredom (para 12)
Answer:
amusement/recreation

Question 8.
criticize (para 13)
Answer:
appreciate.

c) Frame illustrative sentences to distinguish the meaning of the words in the following clusters: (Text Book Page No. 72)

1. career — carrier — courier
2. patients — patience — patents
3. accident — incident — incidence
4. scraping — scrapping — scrubbing
5. accept — except — expect
6. lesson — lessen — lesion
7. severe — sever — sewer
8. raise — rise— rice
9. quiet — quite — quit
10. final — finale — feline

Answer:

1. career	Job, Profession	she likes to pursue her career in medicine.
carrier	Transport people or goods	I will call a baggage carrier to help me.
courier	a person whose job is to carry letters, important papers urgently	A courier has arrived and there is a letter for you.
2 .patients	the person receiving medical treatment	There are many patients waiting in the hospital.
patience	remain calm and not angry	My grandfather didn’t have the patience to wait in the hospital.
patents	the document shows that this is your right ‘	An invention is not your own until it is patent.
3. accident	an unpleasant event that happens unexpectedly	A bus met with an accident yesterday.
incident	something that happens unusually	It was an incident that happened yesterday.
incidence	the number of time something happens	There is still a high incidence of Malaria in the area.
4. scraping	something you do not want any more	I heard the scraping of the spoon in the bowl.
scrapping	to get rid of something that you do not want any more	The government is scrapping the idea of collecting road tax.
scrubbing	to clean with soap and water by rubbing it hard	She started cleaning the over with the scrub sponge.
5. accept	to agree	Please accept my gift.
except	not included	All the students submitted their homework except Ram.
expect	think, belief	I expect my father to arrive at my home at this time.
6. Lesson	something should be learned	The teacher teaches her lesson in English.
lessen	to become less	The govt decided it lessen the burden of the students.
lesion	an organ that has suffered damage through injury	Her daughter suffered a brain lesion at birth.
7. severe	serious	I had severe pain in my leg yesterday.
sever	to cut into two pieces	His finger was severed in the accidents.
sewer	an underground pipe that carries human waste	The pond stank like a sewer.
8. raise	to lift	She raised her both arms above her head.
rise	to move upwards	The sun rises in the east.
rice	brown grain	I like to eat rice every day.
9. quiet	calm	Ramu is a quiet boy in the classroom.
quite	not very	It was quite impossible to do this work.
quit	give up	I want to quit my bad habits.

d) Fill in the blanks with the words given in brackets: (Text Book Page No. 72)
[profound, amusement, confidence, agony, solace, intrepid, disfigured, perforated]

Question 1.
Theatrical plays were a main source of ___________ before the advent of television.
Answer:
amusement

Question 2.
The __________ warriors of the Spartan Army marched into battle against a powerful enemy.
Answer:
intrepid

Question 3.
The ___________ of parents finally came to an end when their lost child was found with the help of police.
Answer:
agony

Question 4.
Social media has brought about a ________ impact on the lives of millennials.
Answer:
profound

Question 5.
The tires of the car got ________ when the vehicle rolled over the rusted nails scattered on the road.
Answer:
perforated

Question 6.
Thomas Alva Edison did not lose his, ________ even after facing a series of experimental failures in his quest to discover tungsten.
Answer:
confidence

Question 7.
Many victims of the pipeline explosion in an oil refinery were left permanently ________.
Answer:
disfigured

Question 8.
The old lady found ________ in the company of the children in the neighbourhood.
Answer:
solace

e) Form a phrase with each of the following pairs of nouns given below: (Text Book Page No. 72)

Here is an example from the lesson:
fibre + tissue — fibrous tissue

Question 1.
muscle + pain
Answer:
Muscular pain

Question 2.
skeleton + system
Answer:
skeletal system

Question 3.
nerve + disorder
Answer:
nervous disorder

Question 4.
digestion + enzymes
Answer:
digestive enzymes

Question 5.
surgery + instruments
Answer:
surgical instruments

Question 6.
agony + experience
Answer:
agonic experience

Question 7.
glory + victory
Answer:
glorious victory

Question 8.
fancy + idea
Answer:
fanciful idea

Question 9.
emotion + song
Answer:
emotional song

Question 10.
sense + issue
Answer:
sensible issue / sensitive issue.

f) Fill the empty boxes with suitable words under each word class: (Text Book Page No. 73)

Answer:

Noun	Verb	Adjective	Adverb
amusement	amuse	amused	amusingly
appreciation	appreciate	appreciative	appreciatively
success	succeed	successful	successfully
proud	pride	prideful	proudly
hope	hope	hopeful	hopefully

g) Spot the errors in the following sentences and rewrite them correctly: (Text Book Page No. 73) 

Question 1.
My grandfather is well-known in the village for his noble deeds.
Answer:
noble

Question 2.
I had my evening meals in a restaurant near my office.
Answer:
meal

Question 3.
The Boss had full confidence in his Manager for the successful completion of the project.
Answer:
in

Question 4.
After the complicated surgery, the patient hoped to complete recovery.
Answer:
for

Question 5.
The new health care scheme announced by the Government will bring relief to the children suffering with acute tuberculosis.
Answer:
from

Question 6.
In spite of his poverty and setbacks, was able to launch his dream carrier.
Answer:
career.

Listening: (Text Book Page No. 73)

Listen to the passage being readout. Based on your understanding, complete the statements given below with appropriate answers:

Question 1.
Boredom occurs when a person is unable to ________.
Answer:
stay attentive

Question 2.
________ and ________ are emotional consequences of boredom.
Answer:
Anger, frustration

Question 3.
Two physical signs of acute boredom are ________, ________.
Answer:

• eyelids droop
•  the frown on the face

Question 4.
How does boredom affect the quality of work a person does?
Answer:
A bored person commits a lot of errors in his work.

Question 5.
Mention two ways by which one can overcome boredom.
Answer:

• exercise
• set goals and work for them

Speaking: (Text Book Page No. 73)

Question 1.
You are rushing to attend to important work and you witness an accident on your way. Will you go to the rescue of the injured person? Share your views with the class.
Answer:
It is human nature to help the suffering. If I happen to see an accident while going on important work, I would go to the rescue of the injured person. While I was going out on important work, I happened to see an accident on the road. An old lady who was crossing the road was knocked down by a car. She fell down on the road with bleeding injuries. I immediately went to her, tied a cloth around the injured place to stop bleeding, and took her to a nearby hospital in, an auto-rickshaw. The doctors treated her injuries and her life was saved. I informed her relatives about the accident and they rushed to the hospital. They thanked me for helping the old lady.

Question 2.
Every person should take up the responsibility to serve society in his or her own way. Discuss the various ways in which you can serve society.
Answer:
Every citizen has the responsibility to serve society. There are many ways of helping the needy. Plastic has ruined the environment. The government is taking various, steps to ban the use of plastic. Awareness should be created among the public about the dangers of using plastic. I would form a small group of my friends and try to bring awareness to the public by meeting members of every household in my locality. Planting trees is very important. I will contact people, try to plant saplings wherever it is possible. I would meet the children in the locality and their parents and request them to inculcate healthy habits in their children regarding personal hygiene.

Dialogue: (Text Book Page No. 73)

Here is a conversation between a student who wishes to open an account and a bank clerk. (Text Book Page No. 74)

Student: Good morning, madam.
Bank Clerk: Good morning, what can I do for you?
Student: I would like to open an account in your bank.
Bank Clerk: Are you a student of a school or a college?
Student: I am a student of Govt. Hr. Sec. School, Tirunelveli.
Bank Clerk: Why do you want to open an account?
Student: My class teacher advised me to open an account to receive the monetary benefits from government schemes.
Bank Clerk: Here is an application form to open an account in our bank. Fill it up.
Student: Should I enclose any document with the form?
Bank Clerk: Yes. You should enclose a valid identity proof and an address proof that are approved by the government.
Student: Madam, can I submit the form and documents tomorrow?
Bank Clerk: Okay. You need to make an initial deposit of Rs. 500/- to open an account.
Student: Sure Madam, Thank you.
Bank Clerk: You are welcome.

a) Pair work: Practise the dialogue with another student. Then write a similar dialogue between a student and the class teacher regarding an educational trip: (Text Book Page No. 74)

Student: Good morning Mam.
Teacher: Yes, Good morning what about our educational trip?
Student: Yes Mam, I have come to speak about that.
Teacher: Did you inform all the students about it?
Student: Yes, Mam. I have informed all the students. But some of them are not willing to come.
Teacher: Why? Any problem?
Student: Yes Mam, Money is the only problem for them.
Teacher: OK, Give me the list of the students who are willing to participate in the educational trip.
Student: Yes Mam, I will give it at once.
Teacher: OK, see you in the classroom.

.
b) Build a conversation for the following situations with a minimum of five exchanges: (Text Book Page No. 74)

1. A passenger and a railway staff regarding the cancellation of the reserved tickets:
Passenger: Good Morning Sir.
Staff: Good morning, what can I do for you?
Passenger: Sir, I want to cancel my reserved ticket.
Staff: Why? What ¡s the reason?
Passenger: My grandfather is dead. So I am unable to go now.
Staff: 0k, It’s all right.
Passenger: Will you refund the money, Sir?
Staff: Yes, please fill the cancellation form.
Passenger: Sure sir, Thank you very much.
Staff: You are welcome.

2. Two friends about the NSS camp which they are going to attend:
Ramu: Hai Rahul, How are you?
Raghul: I am fine. How are you?
Ramu: lam fine. Are you coming to the NSS camp?
Raghul: Yes, I will come. What about you?
Ramu: Yeah! I will also come.
Raghul: Are you willing to participate in any programme?
Ramu: Yes, I will.
Raghul: Shall we speak about the danger of plastics?
Ramu: OK. It’s a good idea.
Raghul: OK, Ram we shall meet in the NSS camp.

3. A salesman and a customer at an electronic shop:
Salesman: You are welcome Sir. what do you want?
Customer: May I have a mixie?
Salesman: Yes, off course. which company do you want sir?
Customer: I want to buy preethi sir.
Salesman: Please come to this side.
Customer: what is the price of it?
Salesman: It is only Rs.3500 sir.
Customer: Does it have any warranty
Salesman: Yes, sir It has 10 years warranty.
Customer: 0K sir, I take this one.

4. A father and his daughter about the advantages of the habit of newspaper- reading:
Father: Do you read any newspaper regularly?
Daughter: Yes dad, I am reading the newspaper daily.
Father: Ws nice. Do you think reading newspaper is essential?
Daughter: Certainly. In fact, it is a storehouse of knowledge.
Father: What can you learn from it?
Daughter: I can learn about world trade, commerce, politics, films, games, and sports, etc from it.
Father Now, what is your suggestion for others?
Daughter: I want to say that everybody should read at least one newspaper daily.
Father: Okay, It is a good habit, and keeps going.
Daughter: Thank you, Dad.

c) Extend the conversation with two more relevant exchanges: (Text Book Page No. 75)

1. Receptionist: Good evening, sir. Welcome to Chennai.
Traveller: I would like to book a deluxe room in your hotel for 3 days.
Receptionist: Single room or double room?
Traveller: Double room, please
Receptionist: Sir, give me your Aadhar card.
Traveller: I have my driving license only
Receptionist: 0k. That will do sir.

2. Student: Good morning, sir. May I come in?
Teacher: Good morning, why are you late today?
Student: My bus broke down on the way. So I had to walk to school.
Teacher: Go and inform the HM.
Student: Yes sir, I will inform him.
Teacher: Get his permission and then enter the classroom

Reading:

Reading Comprehension: (Text Book Page No. 75)

Read the passage given below and answer the questions that follow:

Humans have long been fascinated by fiction. We experience the excitement in assigning supernatural power to
imaginary characters in fictional stories and so we have Spiderman, Batman, He-man, Titans, and many more. The ‘Cyborg’ was an offshoot of such wild imagination of humans to invest our species with superhuman powers. Today, the Cyborg is no more an imaginary organism. We are living in a world where a sizeable population of humans has merged their bodies with technological implants. The term Cyborg, short for ‘cybernetic organism’ was coined to describe a man, whose body is implanted with technological devices to supplement and substitute body functions.

Cyborgs include people with cardiac pacemakers, contact lenses, bionic ears and eyes, prosthetics, and so on. In other words, a cyborg is partly human and partly machine. The technological innovations in the field of medicine and healthcare augment humans with machines, producing a beta version of the human body. The advent of brain-machine interfaces is certain to blur the boundary between humans and machines. Scientists are working hard to find a technique for age reversal too. People do not want to die, so mankind is striving to get to the final frontier, which is the development of machines and devices that would accord man immortality.

The needs of humans are not limited. As time passes, food habits change, thinking patterns change, and even appearances change. We are about to travel by driverless, fully automated vehicles. Computers and smartphones have become our masters. The more we depend and merge with technological advancements, the more the humanness in us slowly erodes. Intelligence is sought to be infused into machines and robotics are designed in such a way to give the man a virtual human companion. The field of artificial intelligence is overtaking the human brain and many fear that it could even harm the human race. Despite certain limitations and potential threats, many believe that cyborgs will be the next step in the evolution of mankind. The amalgamation of man and machine is sure to add a new dimension to the life of mankind and this will prove to be the biggest evolution in Biology’ since the emergence of life, four billion years ago.

Question a.
Account for the popularity of characters with supernatural powers. (Text Book Page No. 76)
Answer:
Humans have long been fascinated by fiction. We experience the excitement in assigning supernatural power to imaginary characters in fictional stories

Question b.
Who is referred to as a ‘Cyborg’?
Answer:
The ‘Cyborg’ was an offshoot of such wild imagination of humans to invest our species with superhuman powers. Today, the Cyborg is no more an imaginary organism. We are living in a world where a sizeable population of humans have merged their bodies with technological implants.

Question c.
What is expected to happen with the advent of the brain-machine interface?
Answer:
The advent of brain-machine interfaces is certain to blur the boundary between humans and machines.

Question d.
The needs of humans are not limited. How is this statement elaborated in the passage?
Answer:
The needs of humans are not limited. As time passes, food habits change, thinking patterns change, and even appearances change. We are about to travel by driverless, fully automated vehicles. Computers and smartphones have become our masters.

Question e.
How can a machine turn into a virtual companion for humans?
Answer:
The more we depend and merge with technological advancements, the more the humanness in us slowly erodes. Intelligence is sought to be infused into machines and robotics are designed in such a way to give man a virtual human companion.

Question f.
Explain the flip side of the rapid technological advancement.
Answer:
Scientists are working hard to find a technique for age reversal too. People do not want to die, so mankind is striving to get to the final frontier, which is development of machines and devices that would accord man immortality.

Question g.
Identify the word in para 1 which means ‘everlasting life’.
Answer:
Long – immortality

Question h.
Which of the following words is synonymous with ‘amalgamation’?
Answer:
a) recreation
b) integration
c) exploration
d) proposition

Question i.
Which of the following options is the antonym of the word ‘advent’?
Answer:
a) drawback
b) dispute
c) departure
d) danger

Question j.
Find out the word which is the antonym of ‘natural’ in para 2.
Answer:
Artificial.

Active and Passive voice: (Text Book Page No. 76)

Task 1:
Change the following sentences into Passive Voice: (Text Book Page No. 77)

Question a.
Governor inaugurated the exhibition at ten o’clock.
Answer:
The exhibition was inaugurated by the Governor at ten o’clock.

Question b.
The crowd expected their leader to arrive early in the morning.
Answer:
Their leader was expected to arrive early in the morning by the crowd.

Question c.
Who taught her Computer Science?
Answer:
By whom she was taught computer science?

Question d.
They unanimously named Ravi the captain of the team.
Answer:
Ravi was named the captain of the team unanimously by them.

Question e.
The President gave the commander an award.
Answer:
The commander was given an award by the president.

Question f.
Do not tell a lie.
Answer:
Let not a fie be fold.

Question g.
Please open the door.
Answer:
Let the door be opened.

Question h.
It is time to stop work.
Answer:
Let the work be stopped by this time / It is time the work is stopped.

Question i.
They say he is a spy.
Answer:
It is said by them that he is supposed to be a spy.

Question j.
One should keep one’s promise.
Answer:
One’s promises should be kept.

Question k.
People burn a great deal of wood in winter.
Answer:
A great deal of wood is burned by people in winter.

Question l.
Where had you kept the book?
Answer:
Where had the book been kept by you?

Question m.
When did you feel the tremors?
Answer:
When was the tremors felt by you?

Question n.
How did you do the experiment?
Answer:
How was the experiment done by you?

Question o.
Whose car did someone park in front of your gate?
Answer:
Whose car was parked by someone in front of your gate?

Change the following sentences into Active Voice: (Text Book Page No. 78)

Question a.
The smuggler has been nabbed by the police.
Answer:
The police have nabbed the smuggler.

Question b.
By whom were you interviewed?
Answer:
Who interviewed you?

Question c.
Why were you scolded by your parents?
Answer:
Why did your parents scold you?

Question d.
Not a word was spoken by the convict in self¬defence.
Answer:
The convict did not speak a word in self defence.

Question e.
Good news is expected shortly.
Answer:
They expect Good news shortly.

Question f.
The mail has just been received.
Answer:
They have just received the mail.

Question g.
Sundari has been taken to the hospital by her husband.
Answer:
The husband has taken Sundari to the hospital.

Question h.
Our television is being repaired now.
Answer:
He is repairing our television now.

Question i.
Sweets have not been distributed to children by the organisers.
Answer:
The organisers have not distributed sweets to children.

Question j.
Prizes were being given by the chief guest.
Answer:
The chief guest was giving the prizes.

Question k.
Nobody has been seen in the library this week.
Answer:
I have seen nobody in the library this week.

Question l.
Nobody would have known the truth if you had not disclosed it.
Answer:
The truth would not have been known if it had not been disclosed by you.

Question m.
You are advised to help the poor and needy.
Answer:
You have to help the poor and needy.

Question n.
You are requested to make a cup of tea for the guest.
Answer:
Please make a cup of tea for the guest.

Question Tags: (Text Book Page No. 79)

Task 1:
Add suitable question tags to the following sentences and punctuate properly: (Text Book Page No.81)

Question 1.
The children are very happy today.
Answer:
Aren’t they?

Question 2.
You have not returned my books yet.
Answer:
Have you?

Question 3.
We enjoyed the trip very much.
Answer:
Didn’t we?

Question 4.
Let’s clean the shelves this weekend.
Answer:
Shall we?

Question 5.
My mother rarely travels by bus.
Answer:
Does she?

Question 6.
Somebody must bell the cat.
Answer:
Mustn’t someone?

Question 7.
Anita never comes late to the office.
Answer:
Does she?

Question 8.
I am always the winner.
Answer:
Aren’t I?

Question 9.
Don’t commit this mistake again.
Answer:
Will you?

Question 10.
There is a pharmacy near that bus stand.
Answer:
Isn’t there?

Question 11.
Bacteria can never survive in extreme weather conditions.
Answer:
Can they?

Question 12.
I am not as smart as you are.
Answer:
Am I?

Question 13.
The boys broke the windowpane last evening.
Answer:
Didn’t they?

Question 14.
Leaves wither during autumn.
Answer:
Don’t they?

Question 15.
You should add a little salt to the buttermilk.
Answer:
Shouldn’t you?

Task 2:
Correct the error found in the question tag in each of the following: (Text Book Page No.81) 

Question 1.
The evildoers cannot cross the path of truth, can’t they?
Answer:
Can they?

Question 2.
The vegetables in the fridge are still fresh, aren’t it?
Answer:
aren’t they?

Question 3.
The village head understood the intention of the politician, doesn’t he?
Answer:
didn’t he?

Question 4.
I claim to be a person of faith and prayer, aren’t I?
Answer:
don’t I?

Question 5.
The employees are seldom allowed to meet their boss, aren’t they?
Answer:
are they?

Question 6.
Let’s organize a trip to Goa, can we?
Answer:
shall we?

Question 7.
The landlady will charge me for the damage, shan’t she?
Answer:
won’t she?

Question 8.
Both the sisters have left for Canada, aren’t they?
Answer:
haven’t they?

Question 9.
That’s definitely not the right thing to do in this situation, isn’t that?
Answer:
is that?

Question 10.
We needn’t apply for a bank loan, do we?
Answer:
need we?

Question 11.
The Chief Guest spoke a few words, did he?
Answer:
didn’t he?

Question 12.
The rhinoceros has a horn made of keratin, haven’t they?
Answer:
hasn’t it?

Story writing: (Text Book Page No. 82)

Task 1:
Expand the following outlines into complete stories and supply a suitable title for each: (Text Book Page No. 83)

Exercise: (Text Book Page No. 84)

1. Big cotton merchant – owned a factory – many employees – one day a heap of cotton stolen – no due – merchant’s secretary assured to find out – asked him to host dinner – invite all workers – merchant agreed – middle of the feast – secretary suddenly shouted – cotton sticking to hair of thieves – the guilty dusted their heads – tried to clear – caught in the trap – punished.

The Clever Secretary

Once upon a time, there was a big cotton merchant. He owned a factory. Many employees were working on it. One day a bale of cotton was stolen. The merchant had no clue as to who might have stolen the baie of cotton. The merchant’s secretary assured him that she will find out the thief. She asked him to host a dinner and invite all the workers. Merchant agreed. When the feast was in progress, the secretary shouted suddenly, There is cotton sticking on to the hair of the thieves. The guilty ones dusted their heads to clear it. They ‘ .ere caught. They were punished.

2. Mr. X, a rich businessman – runs a company – always very busy with office work – one day his son – 10 years old – approaches dad and asks – how much he earns in one hour – father gets furious – boy persuades – father says Rs. 500 – immediate son asks for Rs. 300 – father shouts – wasting money on toys – son leaves to his room crying – father feels bad – thinks might need some stationery – enters boy’s room and gives money – boy becomes happy – takes some crumpled notes – under his pillow – counts everything together – total Rs.500 – gives it to dad – wants to buy – one hour of his time – father realizes his mistake – feels sorry and guilty – hugs son – closes all office files – takes him on a picnic – decides to spend more time with near and dear ones.

Sons Love for his father

Mr. X is a rich businessman. He runs a company. He is always busy with his office work. Like a snail, he carries his office workers everywhere. His young son one day asks him, “How much do you earn in an hour?”. The father gets furious and refuses to reply. But the son coaxes him to give the answer. The father grudgingly says, “Rs. 500/- an hour”. Immediately the boy asks his dad to give him three hundred rupees. He reprimands his son for trying to waste his hard-earned money. The boy cries and goes to the bedroom without dinner. The father feels guilty. He realizes that the boy might really need the money for buying some stationery. He gives him three hundred rupees. The next moment, the boy collected all the crumpled notes from under his pillow. Dad asks, “why did you ask for money when you have so much?”. Without replying the boy handed him Rs. 500/- and said, “This is the amount you earn in an hour, I have given you that money. Now will you spend an hour with me?”. The father realizes his mistake. He takes the boy out on a picnic. Then onwards he regularly spends time with him.

Task 2:
Continue and complete the following stories and suggest suitable titles for the same: (Text Book Page No. 85)

1. A rich man had a neighbour who was suffering from acute poverty. The rich man was proud of
his wealth and treated his poor neighbour with disrespect and derision. One day, a fortune-teller told the rich man that all his wealth would be possessed by his neighbour within a month. The rich man became greatly worried and spent sleepless nights. He did not know how to safeguard his wealth round the clock.

Suddenly he thought of a plan. He disposed of everything he had and with all that money, he bought a large, precious diamond. He sewed up the diamond in his turban. He proudly said to himself, “Now, there’s no way. My poor neighbour can never secure my wealth. The words of the fortune-teller will prove false.” …………………….

The rich man used to have the turban on his head securely always. One 0ay a strong wind blew the turban away. It was carried by a monkey which ran away, jumping on to trees. The rich man ran behind it. He could not keep pace with it. However, he found the turban near his house. He frantically searched for the diamond. But it was not there. The monkey searched for some food in the turban and in the process threw the diamond in the poor neighbour’s house. After many days the neighbour found the diamond, sold it, and became rich. Thus the astrologer’s prediction came true.

2. Four friends decided to go to a restaurant for dinner. They ordered an extra-large pizza with
grated cheese and other choice toppings. The next 20 minutes seemed to be too long a time. Their eyes widened and their mouth watered, when the server brought the steaming hot pizza and placed it on the table. They could barely control the drool. Simultaneously, all the four hands pulled at a slice from the plate, their faces beaming with a victorious grin. Silence prevailed as they were absorbed in the taste of their favourite food. They relished every mouthful to the core and savoured the taste of each topping with a smile of approval.

Soon, the plate was empty and clean with no trace. The boys dabbed their mouths and wiped their hands with tissues. Mission accomplished, they leaned back with immense joy and satisfaction not knowing, it would be short¬lived. The waiter arrived with the bill. Joseph, who had brought the others to the restaurant for a treat casually slipped his hand into his pocket to get his wallet. He gave a soft shriek accompanied by an expression of dismay and utter disbelief. He exclaimed, “It’s not there! Someone has pinched my wallet! What are we to do now?” ………….

Joseph tried to convince the manager of the hotel about the theft of the purse. He refused to accept their version and asked them to pay the bill. Joseph asked his friends to stay in the hotel and he went home, brought money and paid at the hotel, for the relief of all.

ஆசிரியரைப் பற்றி:

கிறிஸ்டியன் நீத்லிங் பெர்னார்டு (Christiaan Neethling Barnard) 1922ல் தென் ஆப்ரிக்காவில் ஓர் ஏழ்மையான பெற்றோருக்கு 4வது குழந்தையாகப் பிறந்தார். கல்வியில் அதிக நாட்டம் காட்டிய இவர், தனது சகோதரரை இதய நோயினால் (a cardiac ailment) இழந்த பிறகு மருத்துவம் (medicine) படிக்க தீர்மானித்தார். இவர் கல்வி உதவித்தொகை மூலமாக இதய அறுவை சிகிச்சையில் (cardiac surgery) மேற்படிப்பு பயின்றார்.

இதய அறுவை சிகிச்சை வல்லுநரான பெர்னார்டு, அக்காலத்தில் குணப்படுத்த இயலாத பிறவி மற்றும் சிக்கலான இதயக் கோளாறுகளில் கவனம் (focussed) செலுத்தினார். விலங்குகளிடம் இதயமாற்று அறுவை சிகிச்சை (heart transplantation) செய்து, பின்னர் 1967ல் உலகின் முதன்முதலில் மனிதர்களுக்கிடையே இதய மாற்று அறுவை சிகிச்சை செய்தார்.

இதனால் இவர் உலக அளவில் அடையாளங்காணப்பட்டு, இன்று வரை ஏற்றுக்கொள்ளக்கூடிய அறுவை சிகிச்சை உத்திகளை (techniques) வகுத்தார். இவர் 14 புத்தகங்களை எழுதியுள்ளார். இவரின் 235 அறிவியல் கட்டுரைகள், புகழ்பெற்ற பத்திரிக்கைகளில் பிரசுரமாகியுள்ளன. “ஒரே வாழ்க்கை ”, “ஆரோக்கியமான இதயத்திற்கு 50 வழிகள்”, “மிகச்சிறந்த மருந்து”, மற்றும் “நம்பிக்கை ‘ என்பன இவர் எழுதிய புத்தகங்களுள் சில இதய அறுவை சிகிச்சையில் முன்னோடியான இவர் கேப்டவுன் பல்கலைகழகத்தில் (University of Cape), மருத்துவத்துறையில் முனைவர் (Doctorate) பட்டம் பெற்றார்.

அதன் பிறகு உலகின் பல்வேறு பல்கலைக்கழகங்கள் இவருக்கு 11 கௌரவ டாக்டர் பட்டம் வழங்கின. இவர் 36 சர்வதேச விருதுகளைப் (International Awards) பெற்றுள்ளார். இவரின் கடைசி காலத்தில் இவர் “கிறிஸ்டியன் பெர்னார்டு அறக்கட்டளையை நிறுவி உலகம் முழுவதும் உள்ள பின்தங்கிய குழந்தைகளுக்கு (underprivileged) சேவை செய்யவும், அவர்களின் நிலையை உயர்த்த காரணமாகவும் இருந்தார். இவர் தனது 78ம் வயதில் 2001ல் மறைந்தார்.

பாடத்தைப் பற்றி:

“நாம் அனைவருக்கும் முதன் முதலில் இதய மாற்று அறுவை சிகிச்சை செய்த மருத்துவர் கிறிஸ்டியன் பெர்னான்ட் அறிவோம். இங்கே அவருடைய பேச்சின் சாரம்சம் கொடுக்கப்பட்டுள்ளது, இதில் வாழ்க்கையை குறித்து அவர் கொண்டிருந்த தோற்றத்தை மாற்றிய அவரது அனுபவத்தை விளக்குகிறார்”.

கொடுக்கப்பட்ட பாடத்தில் ஒரு மருத்துவமனையில் செவிலியர் (Nurse) ஒருவர் காலைச் சிற்றுண்டி வண்டியை கவனிக்காமல் விட்டுவிட்டனர். ஆனால் கை துண்டிக்கப்பட்ட சிறுவனும் இயந்திர வல்லுனரும் அதை நகர்த்தி நோயாளிகளுக்கு உணவு பரிமாறுகின்றனர். இருவரும் நல்ல பாடத்தை போதிக்கின்றனர். இப்படி ஒரு வியத்தகு மாற்றத்தை உண்டு பண்ணியது என்ன என்பதை இங்கே கண்டரிவோம்.

In Celebration of Being Alive Summary in Tamil

ஒரு இதய சிகிச்சை நிபுணராக என்னுடைய வேலையின் (career – பணி) இறுதியை நெருங்க நெருங்க என் மக்கள் ஏன் வேதனைப்பட வேண்டும் என்பதை நோக்கி என் எண்ணங்கள் (thoughts) திரும்பின. இன்று இவ்வுலகில் அதிகப்படியான மக்கள் மிக கொடூரமாக (cruelly) வேதனைப்படுகிறார்கள்.

இந்த ஆண்டு பிறக்கக்கூடிய 125 மில்லியன் குழந்தைகளில், 12 மில்லியன் குழந்தைகள் தங்களது ஒரு வயதை அடைவதே கடினம் மற்றும் அடுத்த 6 மில்லியன் குழந்தைகளில் 5 வயதை எட்டுவதே இல்லை என்பது உங்களுக்கு தெரியுமா! மீதமுள்ளவர்களில் நிறைய பேர் மனம் (mental) அல்லது உடல் ஊனமுற்றவர்களாகவே (physical cripples) ஆகின்றனர்.

சில வருடங்களுக்கு முன்னால் நான் சந்தித்த விபத்திலிருந்து எனக்கு இந்த இருண்ட எண்ணங்கள் (gloomy thoughts) தோன்றியிருக்கலாம் (stem). அருமையான உணவிற்கு பின் நான் என் மனைவியுடன் ஒரு நிமிடம் தெருவை தாண்டி சென்று கொண்டிருந்தேன். மறு நிமிடம் ஒரு கார் என்னை இடித்து (hit) என் மனைவியின் மீது தள்ளியது (knocked), அவளோ அடுத்த பாதையில் தூக்கி வீசப்பட்டு எதிரே வந்த காரினால் அடிப்பட்டாள் (struck).

அடுத்த சில நாட்கள் நான் மருத்துவமனையில் மிகுந்த மன வேதனையையும் (agony), பயத்தையும் (fear) மட்டும் அனுபவிக்கவில்லை கூடவே கோபத்தையும் (anger) உணர்ந்தேன். நானும் என் மனைவியும் ஏன் வேதனைப்பட வேண்டும் என என்னால் புரிந்து கொள்ள முடியவில்லை . என்னுடைய 11 விலா எலும்புகள் (ribs) உடைந்தன மற்றும் எனது நுரையீரலிலும் (lung) அடிபட்டு துளைகள் விழுந்தன. எனது மனைவியின் தோல்பட்டையும் நொறுங்கியது. ஏன் எங்களுக்கு இவ்வாறு நடக்க வேண்டும்? என மீண்டும் மீண்டும் நான் எனக்குள்ளே கேட்டுக்கொண்டேன்.

எல்லாவற்றிற்கும் மேலாக நான் எனது வேலையையும் பார்க்க வேண்டியதிருந்தது. என்னிடம் சிகிச்சை பெற நோயாளிகள் (patients) காத்து கொண்டிருந்தனர். எங்களின் சிறு வயது குழந்தைக்கு என் மனைவியின் அரவணைப்பு தேவைப்பட்டது.
எனது தந்தை இப்போது உயிரோடிருந்தால் அவர் இவ்வாறு தான் கூறியிருப்பார். “மகனே, இது கடவுளின் விருப்பம், அவர் இவ்வாறு தான் உன்னை சோதிப்பார். சோதனைகளே உன்னை மேன்மையாக்கி, ஒரு சிறந்த மனிதனாக உன்னை உருவாக்கும் (ennobles)”.

ஆனால், ஒரு மருத்துவராக வேர்வையால் நனைந்த படுக்கையில் (sweatsoaked bed) வலியால் துடித்துக் கொண்டும், மனம் நிறைய கடுந்துயராலும் நிரப்பப்பட்ட நோயாளிடம் எந்தவொரு பெருந்தன்மையையும் (noble) என்னால் காண இயலவில்லை. இரவில் மருத்துவமனையில் தனிமையில் படுக்கையில் அழுது கொண்டிருக்கும் குழந்தையிடமும் என்னால் எந்தவொரு பெருந்தன்மையையும் (nobility) காண இயலவில்லை.

அக்காலத்தில் அதிநவீன (sophisticated) இதய அறுவை சிகிச்சை முறைகள் கிடையாது. குழந்தைகள் வேதனையடைவதைக் கண்டுநான் மனமுடைந்து போயிருக்கிறேன். ஏனென்றால் அவர்கள் தங்களின் முழு நம்பிக்கையையும் (trust) மருத்துவர்கள் மற்றும் செவிலியர்கள் மீது வைப்பார்கள். நீங்கள் அவர்களுக்கு உதவுவீர்கள் என்று அவர்கள் நம்புவார்கள்.

உங்களால் முடியவில்லை என்றால் அவர்கள் தங்கள் விதியைக் கூட ஏற்றுக் கொள்ள (believe) மாட்டார்கள். உருவச்சிதைவு அடையக்கூடிய அறுவைச்சிகிச்சை (mutilating surgery) செய்த பிறகு கூட அவர்கள் குறைகூற மாட்டார்கள்.

பல வருடங்களுக்கு முன்னால் ஒரு நாள் காலையில் நான் கண்டதை கேட்டவுடன் நகரின் செஞ்சிலுவை (Red cross) சிறுவர் மருத்துவமனையில் மோட்டார் வாகன ஓட்டப் பந்தயம் (Grand Prix) என்றே அழைப்பேன். அந்நிகழ்வு வேதனையைக் குறித்து நான் எண்ணிவந்ததில், ஒரு உண்மையை நான் விட்டிருந்ததை குறித்து அது என் கண்களைத் திறந்தது. அது எனக்கு ஒரு பெரிய ஆறுதலாக (solace) இருந்தது.

அந்த காலை அங்கு என்ன நடந்தது என்றால், காலை உணவு தள்ளுவண்டியை (breakfast trolley) செவிலியர் எடுக்கவில்லை. அடுத்தகணமே அந்த தள்ளுவண்டியானது இரு துணிச்சலான (intrepid), தைரியமான ஓட்டுநர் மற்றும் இயந்திர வல்லுநரால் வழி நடத்தப்பட்டது.

இயந்திர வல்லுநரோ தலையை குனிந்தவாறு தள்ளுவண்டியை பின்புறமிருந்து விரைந்து தள்ளி அதற்கு இயந்திர சக்தியளித்தனர் (provided), அதே வேளையில் ஓட்டுநரோ, தள்ளுவண்டியின் முன்புறம் அமர்ந்து கொண்டு ஒருகையால் வண்டியைப் பிடித்து காலால் தரையை உரசி (scraping) தள்ளுவண்டியை ஓட்டினார். அவர்கள் தேர்ந்தெடுத்த வேடங்கள் மிக எளிது ஏனென்றால் இயந்திர வல்லுநரோ கண்ணிழந்தவன் (blind), ஓட்டுநரோ ஒரு கை (arm) மட்டுமே கொண்டவன்.

அன்று அவர்கள் ஒரு பெரிய நிகழ்ச்சியையே நடத்தினார்கள். மீதமிருந்த நோயாளிகளிடமிருந்து அவர்களுக்கு கிடைத்த உற்சாகத்தையும் (encouragement) சிரிப்பையும் பார்த்த போது இண்டியானா போலிஸில் (Indiana Polis) நடைபெறும் 500 கார்களின் ஓட்டப்பந்தயத்தை (race) விட இவர்களின் நிகழ்ச்சி மிகச்சிறந்தது என தோன்றியது. அவர்களை செவிலியர்கள் பிடித்து, திட்டி, படுக்கைக்கு திரும்ப அனுப்பும் வரை, அங்கு சிதறிய தட்டுகள் மற்றும் சில்வர் பாத்திரங்களின் இறுதிச் சுற்று (grand finale) நடந்தது.

அவ்விருவர்களைப் பற்றி நான் கூறுகிறேன். இயந்திர வல்லுநரோ 7 வயதானவன். ஒரு நாள் அவனது தாயும் தந்தையும் குடித்து விட்டு சண்டையில், அவனது தாய் விளக்கை (lantern) எடுத்து தந்தை மீது எறியும் போது அது தவறி குழந்தையின் தலை மற்றும் தோள் பகுதியின் மீது விழுந்தது. இதனால் அதிகப்படியான மூன்றாம் நிலை காயங்களால் அவனது மேலுடல் பாதிக்கப்பட்டது, அவனது இரண்டு கண்களும் பார்வை இழந்தன.

வாகன ஓட்டப்பந்தயத்தின் போது அவன் ஒரு நடமாடும், பயமூட்டும் (horror) பொருளாக, அதாவது உருக்குலைந்த (disfigured) முகத்தோடும், ஒரு நீண்ட சதை மடிப்பு கழுத்திலிருந்து தொங்கிய வண்ணமும் காணப்பட்டான்.

அவனது கழுத்தைச் சுற்றி காயம் ஆறிக்கொண்டிருந்த வேளையில், அவனுடைய கீழ்த்தாடை நரம்புத் திசுக்களினால் (tissue) இறுகப்பற்றிக் கொள்ளப்பட்டது. அவன் தனது தலையை உயர்த்தினால் (raise) மட்டுமே அவனால் தனது வாயைத் திறக்க முடியும். அந்த பந்தயம் முடிந்து நான் அவளை சந்தித்த போது “நாங்கள் வென்று விட்டோம். உங்களுக்கு தெரியுமா?” என்று சிரித்துக்கொண்டே கூறினான்.

அந்த தள்ளுவண்டியின் ஓட்டுநரை (trolley’s driver) எனக்கு நன்றாக தெரியும். சில வருடங்களுக்கு முன்னால். அவன் இதயத்தில் இருந்த ஓட்டையை நான் வெற்றிகரமாக அடைத்தேன். அவன் எலும்பில் இருந்த வீரியமான (malignant tumour) கட்டியின் காரணமாக அவன் மறுபடியும் மருத்துவமனைக்கு அழைத்து வரப்பட்டான். பந்தயத்திற்கு சில நாட்கள் முன்னதாக அவனது தோள்பட்டையும், கையும் சிகிச்சையின் மூலம் வெட்டி எடுக்கப்பட்டது (amputated).

அவன் குணமடைவதற்கான (recovery) நம்பிக்கை குறைவாகவே காணப்பட்டது. பந்தயத்திற்குப் பின் அவன் என்னிடம், தள்ளுவண்டியின் சக்கரங்கள் சரியாக எண்ணெய் இடப்படவில்லை என்றும், அவன் ஒரு சிறந்த ஓட்டுநர் என்றும், தான் இயந்திர வல்லுநரிடம் முழு நம்பிக்கை கொண்டிருந்ததாகவும் கூறினான்.

திடீரென, வாழ்க்கையை வாழ்வதற்கான ஒரு ஆழமான பாடத்தை (profound lesson) இவர்கள் இருவரும் எனக்கு கற்று கொடுத்ததாகவே உணர்ந்தேன் (realized). ஏனென்றால் வாழ்வது என்பது இனிமைக்காவோ, பொழுது போக்கிற்காகவோ, மனமகிழ்ச்சிக்காகவோ நாம் செய்யும் ஏதோ ஒன்று அல்ல, மாறாக மகிழ்ச்சி என்ற வார்த்தையின் உண்மையான உணர்வே ஆகும். வாழ்வதென்பது உயிரோடிருப்பதின் கொண்டாட்டமே (celebration).

நான் வேதனைப்படுவதை தவறான (wrong) முறையிலிருந்தே பார்த்து கொண்டிருந்தேன். நீங்கள் வேதனை அடைவதால் மட்டும் சிறந்த மனிதராக முடியாது. ஆனால் வேதனையை அனுபவித்து (experience) இருக்கிறீர்கள் என்றால் உங்களால் ஒரு சிறந்த மனிதனாக முடியும். இருளைப் பற்றி அறியாவிட்டால், நம்மால் ஒளியைப் பாராட்ட இயலாது.

கடுங்குளிரால் பாதிக்கப்படாமல் நம்மால் வெதுவெதுப்பை பாராட்ட இயலாது. நீங்கள் இழந்தது எதுவோ அது முக்கியமில்லை (important), உங்களிடம் மீதமிருப்பது (left) எதுவோ அதுவே மிக முக்கியம் என்று இச்சிறுவர்கள் எனக்கு உணர்த்தி விட்டார்கள்.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.4

Question 1.
Find the equations of the two tangents that can be drawn from (5, 2) to the ellipse 2x² + 7y² = 14.
Solution:
2x² + 7y² = 14
(÷ by 14) ⇒ \(\frac{x^{2}}{7}+\frac{y^{2}}{2}\) = 1
comparing this equation with \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1
we get a² = 7 and b² = 2
The equation of tangent to the above ellipse will be of the form
y = mx + \(\sqrt{a^{2} m^{2}+b^{2}}\) ⇒ y = mx + \(\sqrt{7 m^{2}+2}\)
Here the tangents are drawn from the point (5, 2)
⇒ 2 = 5m + \(\sqrt{7 m^{2}+2}\) ⇒ 2 – 5m = \(\sqrt{7 m^{2}+2}\)
Squaring on both sides we get
(2 – 5m)² = 7m² + 2
25m² + 4 – 20m – 7m² – 2 = 0
18m² – 20m + 2 = 0
(÷ by 2) ⇒ 9m² – 10m + 1 = 0
(9m – 1) (m – 1) = 0
‘ m = 1 (or) m = 1/9
When m = 1, the equation of tangent is
y = x + 3 or x – y + 3 = 0
When m = \(\frac{1}{9}\) the equation of tangent is 9
y = \(=\frac{x}{9}+\sqrt{\frac{7}{81}+2}\) (i.e.) y = \(\frac{x}{9}+\frac{13}{9}\)
9y = x + 13 or x – 9y + 13 = 0

Question 2.
Find the equations of tangents to the hyperbola \(\frac {x^2}{16}\) – \(\frac {y^2}{64}\) = 1 which are parallel to 10x – 3y + 9 = 0.
Solution:
Equation of Hyperbola \(\frac {x^2}{16}\) – \(\frac {y^2}{64}\) = 1
∴ a² = 16, b² = 64
Tangent is parallel to the line
10x – 3y + 9 = 0 is
10x – 3y + k = 0
∴ 3y = 10x + k
y = \(\frac {10}{3}\)x + \(\frac {k}{3}\)
∴ m = \(\frac {10}{3}\) c = \(\frac {k}{3}\)
Condition that the line y = mx + c to be tangent to the hyperbola is
c² = a²m² – b²

k² = 1024
k = ±32
∴ Equation of tangent
⇒ 10x – 3y ± 32 = 0

Question 3.
Show that the line x – y + 4 = 0 is a tangent to the ellipse x² + 3y² = 12. Also find the co-ordinates of the point of contact.
Solution:
The given ellipse is x² + 3y² = 12
(÷ by 12) ⇒ \(\frac{x^{2}}{12}+\frac{y^{2}}{4}\) = 1
(ie.,) Here a² = 12 and b² = 4
The given line is x – y + 4 = 0
(ie.,) y = x + 4
Comparing this line with y = mx + c
We get m = 1 and c = 4
The condition for the line y = mx + c
To be a tangent to the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1 is c² = a²m² + b²
LHS = c² = 4² = 16
RHS: a²m² + b² = 12( 1 )² + 4 = 16
LHS = RHS The given line is a tangent to the ellipse. Also the point of contact is
\(\left(\frac{-a^{2} m}{c}, \frac{b^{2}}{c}\right)=\left[-\left(\frac{12(1)}{4}\right), \frac{4}{4}\right]\) (i.e.,) (-3, 1)

Question 4.
Find the equation of the tangent to the parabola y² = 16x perpendicular to 2x + 2y + 3 = 0.
Solution:
Equation of the parabola
y² = 16x
4 a = 16
a = 4
Tangent is perpendicular to the line
2x + 2y + 3 = 0 is 2x – 2y + k = 0
2x – 2y + k = 0
2y = 2x + k
y = x + \(\frac {k}{2}\)
m = 1 c = \(\frac {k}{2}\)
Condition that the line y = mx + c to be tangent to the parabola is
c = \(\frac {a}{m}\)
\(\frac {k}{2}\) = \(\frac {4}{1}\)
k = 8
Equation of the tangent
2x – 2y + 8 = 0
÷ by 2 ⇒ x – y + 4 = 0

Question 5.
Find the equation of the tangent at t = 2 to the parabola y² = 8x (Hint: use parametric form).
Solution:
y² = 8x
Comparing this equation with y² = 4ax
we get 4a = 8 ⇒ a = 2
Now, the parametric form for y² = 4ax is x = at², y = 2at
Here a = 2 and t = 2
⇒ x = 2(2)² = 8 and y = 2(2) (2) = 8
So the point is (8, 8)
Now eqution of tangent to y² = 4 ax at (x₁, y₁) is yy₁ = 2a(x + x₁)
Here (x₁, y₁) = (8, 8) and a = 2
So equation of tangent is y(8) = 2(2) (x + 8)
(ie.,) 8y = 4 (x + 8)
(÷ by 4) ⇒ 2y = x + 8 ⇒ x – 2y + 8 = 0
Aliter
The equation of tangent to the parabola y² = 4ax at ‘t’ is
yt = x + at²
Here t = 2 and a = 2
So equation of tangent is
(i.e.,) y(2) = x + 2(2)²
2y = x + 8 ⇒ x – 2y + 8 = 0

Question 6.
Find the equations of the tangent and normal to hyperbola 12x² – 9y² = 108 at θ = \(\frac {π}{3}\) .
(Hint: use parametric form)
Solution:
(i) Equation of the tangent to hyperbola be

⇒ 4x – 3y = 6
⇒ 4x – 3y – 6 = 0

(ii) Equation of the normal to hyperbola be

⇒ 3x + 4y – 42 = 0

Question 7.
Prove that the point of intersection of the tangents at ‘t₁‘ and ‘t₂‘ on the parabola y² = 4ax is [at₁t₂, a(t₁ + t₂)].
Solution:
Equation of the tangent of parabola y² = 4ax be
at t₁ yt₁ = x + at₁² ……….. (1)
at t₂ yt₂ yt = x + at₂² ……….. (2)
(1) – (2) ⇒ y(t₁ – t₂) = a(t₁² – t₂²)
y(t₁ – t₂) = a(t₁ + t₂)(t₁ – t₂)
y = a(t₁ + t₂)
(1) ⇒ t₁a(t₁ + t₂) = x + at₁²
x = at₁² + at₁t₂ – at₁²
x = at₁t₂
Point of intersection be [at₁t₂, a(t₁ + t₂)]

Question 8.
If the normal at the point ‘t₁‘ on the parabola y² = 4ax meets the parabola again at the point t₂ then prove that t₂ = -(t₁ + \(\frac {2}{t_1}\))
Solution:
Equation of normal to y² = 4at’ t’ is y + xt = 2at + at³.
So equation of normal at ‘t₁’ is y + xt₁ = 2at₁ + at₁³
The normal meets the parabola y² = 4ax at ‘t₂’ (ie.,) at (at₂², 2at₂)
⇒ 2at₂ + at₁t₂² = 2at₁ + at₁³
So 2a(t₂ – t₁) = at₁³ – at₁t₂²
⇒ 2a(t₂ – t₁) = at₁(t₁² – t₂²)
⇒ 2(t₂ – t₁) = t₁(t₁ + t₂)(t₁ – t₂)
⇒ 2= -t₁(t₁ + t₂)
⇒ t₁ + t₂ = \(\frac{-2}{t_{1}}\)
⇒ t₂ = \(-t_{1}-\frac{2}{t_{1}}=-\left(t_{1}+\frac{2}{t_{1}}\right)\)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.2 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.2

Question 1.
Find the equation of the parabola in each of the cases given below:
(i) focus (4, 0) and directrix x = -4.
(ii) passes through (2, – 3) and symmetric about y axis.
(iii) vertex (1,-2) and focus (4, – 2).
(iv) end points of latus rectum (4, -8) and (4, 8).
Solution:
(i) focus (4, 0) and directrix x = -4
Parabola is open rightwards vertex (0, 0)

a = 4
(Distance AS = 4 unit)
f² = 4(4) x
Equation of parabola
y² = 16x.

(ii) passes through (2, – 3) and symmetric about y-axis

x² = 4ay
It passes through (2, -3)
⇒ 2² = 4a(-3)
4 = -12a ⇒ a = \(-\frac{1}{3}\) ⇒ 4a = \(-\frac{4}{3}\)
∴ Equation of parabola is x² = \(-\frac{4}{3}\) y
3x²= – 4y.

(iii) vertex (1,-2) and focus (4, – 2)

In given data the parabola is open rightwards and symmetric about the line parallel to x-axis.
Equation of parabola
(y – k)² = 4a(x – h)
Vertex (h, k) = (1, -2)
(y + 2)² = 4a(x – 1)
a = AS = 3
Equation of parabola
(y + 2)² = 4(3)(x – 1)
(y + 2)² = 12(x – 1)

(iv) end points of latus rectum (4, -8) and (4, 8)

Focus = (4, 0)
Equation of the parabola will be of the form y² = 4ax
Here a = 4
⇒ y² = 16x

Question 2.
Find the equation of the ellipse in each of the cases given below:
(i) foci (± 3, 0), e = \(\frac {1}{2}\)
(ii) foci (0, ±4) and end points of major axis are (0, ±5).
(iii) length of latus rectum 8, eccentricity = \(\frac {3}{5}\) and major axis on x-axis.
(iv) length of latus rectum 4, distance between foci and major axis as y axis.
Solution:
(i) foci (± 3, 0), e = \(\frac {1}{2}\)
foci (± c, 0) = (± 3, 0)

e = \(\frac {1}{2}\)
c = ae = 3
a(\(\frac {1}{2}\)) = 3
a = 6 ⇒ a² = 36
b² = a² – c²
b² = 36 – 9 = 27
b² = 27
Equation of the ellipse be \(\frac {x^2}{a^2}\) + \(\frac {y^2}{b^2}\) = 1
\(\frac {x^2}{36}\) + \(\frac {y^2}{27}\) = 1

(ii) foci (0, ±4) and end points of major axis are (0, ±5)

foci (0, ±c) = (0, +4)
vertex (0, ±a) = (0, ±5)
∴ c = 4, a = 5
ae = 4
5e = 4
e = \(\frac {4}{5}\)
b² = a² – c²
= 25 – 16
b² = 9
Equation of the ellipse be \(\frac {x^2}{b^2}\) + \(\frac {y^2}{a^2}\) = 1
\(\frac {x^2}{9}\) + \(\frac {y^2}{25}\) = 1

(iii) length of latus rectum 8, eccentricity = \(\frac {3}{5}\) and major axis on x-axis.
e = \(\frac {3}{5}\)
Latus rectum \(\frac {2b^2}{a}\) = 8

(iv) length of latus rectum 4, distance between foci 4√2 and major axis as y-axis

Given \(\frac{2 b^{2}}{a}\) = 4 and 2ae = \(4 \sqrt{2}\)
Now \(\frac{2 b^{2}}{a}\) = 4 2b² = 4a
⇒ b² = 2a
2ae = \(4 \sqrt{2}\) ae = \(2 \sqrt{2}\)
So a²e² = 4(2) = 8
We know b² = a²(1 – e²) = a² – a²e²
⇒ 2a = a² – 8 ⇒ a² – 2a -8 = 0
⇒ (a – 4) (a +2) = 0 ⇒a = 4 or -2
As a cannot be negative
a = 4 So a² = 16 and b² = 2(4) = 8
Also major axis is along j-axis
So equation of ellipse is \(\frac{x^{2}}{8}+\frac{y^{2}}{16}\) = 1

Question 3.
Find the equation of the hyperbola in each of the cases given below:
(i) foci (± 2, 0), eccentricity = \(\frac {3}{2}\)
(ii) centre (2, 1) one of the foci (8, 1) and corresponding directrix x = 4.
(iii) passing through (5, -2) and length of the transverse axis along x axis and length 8 units.
Solution:
(i) foci (± 2, 0), eccentricity = \(\frac {3}{2}\)

(ii) centre (2, 1) one of the foci (8, 1) and corresponding directrix x = 4.
Distance CS = ae = 6 …….. (1)
Directrix \(\frac {a}{e}\) = 4 ……… (2)
(1) × (2) ⇒ ae × \(\frac {a}{e}\) = 24
a² = 24

∴ c = ae = 6
b² = c² – a²
= 36 – 24 = 12
The transverse axis is parallel to x-axis
∴ \(\frac {(x-h)^2}{a^2}\) – \(\frac {(y – k)^2}{b^2}\) = 1 (h, k) = (2, 1)
\(\frac {(x-2)^2}{24}\) – \(\frac {(y – 1)^2}{12}\) = 1

(iii) passing through (5,-2) and length of the transverse axis along x axis and of length 8 units.
Transverse axis along x-axis
\(\frac {x^2}{a^2}\) – \(\frac {y^2}{b^2}\) = 1
Length of transverse axis 2a = 8
⇒ a = 4

Question 4.
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
(i) y² = 16x
(ii) x² = 24y
(iii) y² = -8x
(iv) x² – 2x + 8y + 17 = 0
(v) y² – 4y – 8x + 12 = 0
Solution:
(i) y² = 16x

4a = 16
a = 4
(a) Vertex V (0, 0)
(b) Focus S(a, 0) = S(4, 0)
(c) Equation of the directrix x = – a
x = -4 ⇒ x + 4 = 0
(d) Length of the latus rectum = 4a = 4(4)
= 16

(ii) x² = 24y

(a) Vertex V (0, 0),
(b) Focus S (0, a) = S(0, 6)
(c) Equation of the directrix y = -a = -6
⇒ y + 6 = 0
(d) Length of the latus rectum = 4a
= 4 (6) = 24

(iii) y² = -8x
4a = 8,
a = 2

(a) Vertex V(0, 0) = ( 0, 0)
(b) Focus S(-a, 0) = (-2, 0)
(c) Equation of the directrix x = a = 2
x – 2 = 0
(d) Length of the latus rectum 4a = 8
(iv) x² – 2x + 8y + 17 = 0
x² – 2x = -8y – 17
(x – 1)² = -8y – 17 + 1
(x – 1)² = -8y – 16
(x – 1)² = -8(y + 2)
It is form of (x – h)² = -4a(y – k)
4a = 8 ⇒ a = 2
(a) Vertex be (h, k) = (1, -2)

(b) Foeus = (0 +h, -a + k) = (0 + 1, -2 – 2) = (1, -4)
(c) Equation of the directrix is y + k + a = 0
y – 2 + 2= 0
y = 0
(d) Length of latus rectum is 4a = 4 × 2 = 8 units,

(v) y² – 4y – 8x + 12 = 0

y² – 4y = 8x – 12
(y – 2)² = 8x – 12 + 4
= 8x – 8
= 8 (x – 1)
(y – 2)² = 8 (x – 1)
It is form of (y – k)² = Aa(x – h)
4a = 8 ⇒ a = 2
(a) Vertex (h, k) = (1, 2)
(b) Focus = (a+h, 0 + k) = (2 + 1, 0 + 2) = (3, 2)
(c) Equation of the directrix x = -a + h
= -2 + 1
= -1
x + 1 = 0
(d) Length of latus rectum is
4a = 4 × 2 = 8 units.

Question 5.
Identify the type of conic and find centre, foci, vertices and directrices of each of the following:
(i) \(\frac {x^2}{25}\) + \(\frac {y^2}{9}\) = 1
(ii) \(\frac {x^2}{3}\) + \(\frac {y^2}{10}\) = 1
(iii) \(\frac {x^2}{25}\) – \(\frac {y^2}{144}\) = 1
(iv) \(\frac {y^2}{16}\) – \(\frac {x^2}{9}\) = 1
Solution:
(i) \(\frac{x^{2}}{25}+\frac{y^{2}}{9}\) = 1
It is of the form \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1, which is an ellipse
Here a² = 25, b² = 9
a = 5, b = 3
e² = \(\frac{a^{2}-b^{2}}{a^{2}}=\frac{25-9}{25}=\frac{16}{25}\) ⇒ e = \(\frac{4}{5}\)
Now e = \(\frac{4}{5}\) and a = 5 ⇒ ae = 4 and \(\frac{a}{e}=\frac{5}{4 / 5}=\frac{25}{4}\)
Here the major axis is along x axis
∴ Centre = (0, 0)
Foci = (± ae, 0) = (± 4, 0)
Vertices = (± a, 0) = (±5, 0)
Equation of directrix x = ± \(\frac{a}{e}\) (ie.,) x = ± \(\frac{25}{4}\)

(ii) \(\frac {x^2}{3}\) + \(\frac {y^2}{10}\) = 1
It is an ellipse. The major axis is along y axis

a² = 10 b² = 3
a = \(\sqrt {10}\) b = √3
c² = a² – b²
= 10 – 3 = 7
c = √7
ae = √7 .
\(\sqrt {10}\) = √7
e = \(\sqrt {\frac{7}{10}}\)
(a) Centre (0, 0)
(b) Vertex (0, ±a) = (0, ±\(\sqrt {10}\))
(c) Foci (0, ±c) – (0, ±√7)
(d) Equation of the directrix a
y = ±\(\frac{a}{e}\)
= ±\(\frac{\sqrt {10}}{√7}\).\(\sqrt {10}\) = ±\(\frac {10}{√7}\)
y = ±\(\frac {10}{√7}\)

(iii) \(\frac {x^2}{25}\) – \(\frac {y^2}{144}\) = 1
It is Hyperbola. The transverse axis the x axis.

a² = 25; b² = 144
a = 5; b = 12
c² = a² + b²
= 25 + 144 = 169
c = 13
ae = 13
5e = 13
e = \(\frac {13}{5}\)
(a) Centre (0, 0)
(b) Vertex (± a, 0) = (± 5, 0)
(c) Foci (± c, 0) = (± 13, 0)
(d) Equation of the directrix
x = ±\(\frac {a}{e}\) = ±\(\frac {5}{\frac{13}{5}}\) = ±\(\frac {25}{13}\)
x = ±\(\frac {25}{13}\)

(iv) \(\frac {y^2}{16}\) – \(\frac {x^2}{9}\) = 1
It is Hyperbola. The transverse axis the y axis.

a² = 16; b² = 9
a = 4; b = 3
c² = a² + b²
= 16 + 6 = 25
c = 5
ae = 5
4e = 5
e = \(\frac {5}{4}\)
(a) Centre (0, 0)
(b) Vertex (0, ±a) = (0, ±4)
(c) Foci (0, ±ae) = (0, ±5)
(d) Equation of the directrix
y = ±\(\frac {a}{e}\) = ±\(\frac {4}{\frac{5}{4}}\) = ±\(\frac {16}{5}\)
y = ±\(\frac {16}{5}\)

Question 6.
Prove that the length of the latns rectum of the hyperbola \(\frac {x^2}{a^2}\) – \(\frac {y^2}{b^2}\) = 1 is \(\frac {2b^2}{a}\)
Solution:
The latus rectum LL’ of an hyperbola \(\frac {x^2}{a^2}\) – \(\frac {y^2}{b^2}\) = 1 passes through S(ae, 0)
Hence L is (ae, y₁)

Hence proved

Question 7.
Show that the absolute value of the difference of the focal distances of any point P on the hyperbola is the length of its transverse axis.
Solution:

Let P be a point on the hyperbola.
Definition of conic
\(\frac {SP}{PM}\) = e; \(\frac {S’P}{PM’}\) = e
SP = e(PM) ……..(1)
S’P = e (PM’) ……….(2)
(2) – (1) ⇒ S’P – SP = e PM’- e PM
= e(PM’ – PM)
= e MM’
= e ZZ’
[∵ MM’ = ZZ’ = \(\frac {2a}{e}\) ]
= e(\(\frac {2a}{e}\))
S’P – SP = 2a (constant)
= length of the transverse axis.

Question 8.
Identify the type of conic and find centre, foci, vertices and directrices of each of the following:

(v) 18x² + 12y² – 144x + 48y + 120 = 0
(vi) 9x² – y² – 36x – 6y + 18 = 0
Solution:
(i) \(\frac {(x-3)^2}{225}\) + \(\frac {(y-4)^2}{289}\) = 1

It is an ellipse. The major axis is parallel to y axis
a² = 289, b² = 225
a = 17, b = 15
c² = a² – b²
= 289 – 225 = 64
c = 8
ae = 8
17e = 8
e = \(\frac {8}{17}\)
Centre (h, k) = (3, 4)
Vertices (h, ±a + k) = (3, 17 + 4) & (3, -17 + 4)!
= (3, 21) and (3, -13)
Foci (h + 0, ± c + k) = (3, 8 + 4) & (3, -8 + 4)
= (3, 12) and (3, -4)

(ii) \(\frac {(x+1)^2}{100}\) + \(\frac {(y-2)^2}{64}\) = 1
It is an ellipse. The major axis is parallel to the x-axis.
a² = 100, b² = 64
a = 10, b = 8
c² = a² – b²
= 100 – 64 = 36
c = 6
ae = 6
10 e = 6
e = \(\frac {6}{10}\) = \(\frac {3}{5}\)
centre (h, k) = (-1, 2)
vertices (h±a, k) = (-1±10, 2)
= (-1+10, 2) & (-1-10, 2)
= (9, 2) & (-11, 2)
foci (h±c, k) = (-1±6, 2)
= (-1+6, 2) & (-1-6, 2)
= (5, 2) & (-7, 2)
directrix x = ±\(\frac {a}{e}\) + h

(iii) \(\frac {(x+3)^2}{225}\) + \(\frac {(y-4)^2}{64}\) = 1
It is an hyperbola. The transverse axis is parallell to x axis.
a² = 225, b² = 64
a = 15, b = 8
c² = a² – b²
= 225 + 64
c² = 289
c = 17
ae = 17
5e = 17
e = \(\frac {17}{15}\)
centre (h, k) = (-3, 4)
vertices (h±a, k) = (-3±15, 4)
= (-3+15, 4) & (-3-15, 4)
= (12, 4) & (-18, 4)
foci (h±c, k) = (-3±17, 4)
= (-3+17, 4) & (-3-17, 4)
= (14, 4) & (-20, 4)
directrix x = ±\(\frac {a}{e}\) + h

(iv) \(\frac {(y-2)^2}{25}\) + \(\frac {(x+1)^2}{16}\) = 1
It is an hyperbola. The transverse axis is parallell to y axis.
a² = 25, b² = 16
a = ±5, b = 4
c² = a² + b²
= 25 + 16
= 41
c = \(\sqrt {41}\)
ae = \(\sqrt {41}\)
5 e = \(\sqrt {41}\)
e = \(\frac {\sqrt {41}}{5}\)
centre (h, k) = (-1, 2)
vertices (h, ±a + k) = (-1, ±5 + 2)
= (-1, 5 + 2) & (-1, -5 + 2)
= (-1, 7) & (-1, -3)
foci (h, ±c + k) = (-1, ±\(\sqrt {41}\) + 2)
= (-1, \(\sqrt {41}\) + 2) & (-1, –\(\sqrt {41}\) + 2)
directrix x = ±\(\frac {a}{e}\) + k

(v) 18x² + 12y² – 144x + 48y + 120 = 0
18x² – 144x + 12y² + 48y = -120
18 (x² – 8x) + 12 (y² + 4y) = -120
18 (x – 4)² + 12 (y + 2)² = -120 + 288 + 48
18(x – 4)² + 12 (y + 2)² = 216
\(\frac {18(x-4)^2}{216}\) + \(\frac {12(y+2)^2}{216}\) = 1
\(\frac {(x-4)^2}{12}\) + \(\frac {(y+2)^2}{18}\) = 1
It is an ellipse. The major axis is parallell to y axis.
a² = 18, b² = 12
a = \(\sqrt {18}\), b = 2√3
= 3 √2
c² = a² + b²
= 18 – 12
= 6
c = √6
ae = √6
3√2 e = √6
e = \(\frac {√6}{3√2}\) = \(\frac {√3}{3}\) = \(\frac {1}{√3}\)
centre (h, k) = (4, -2)
vertices (h, ±a + k) = (4, ±3√2 – 2)
= (4, 3√2 – 2) & (4, -3√2 – 2)
foci (h, ±c + k) = (4, ±√6 – 2)
= (4, ±√6 – 2) & (4, -√6 – 2)
directrix y = ±\(\frac {a}{e}\) + k
= ±\(\frac {3√2}{1}\) – 2
= ±3√6 – 2
y = 3√6 – 2 & y = -3√6 – 2

(vi) 9x² – y² – 36x – 6y + 18 = 0
9x² – 36x – y² – 6y = – 18
9(x² – 4x) – (y² + 6y) = -18
9(x – 2)² – (y + 3)² = -18 + 36 – 9
9(x – 2)² – (y + 3)² = 9
\(\frac {(x-2)^2}{1}\) – \(\frac {(y+3)^2}{9}\) = 1
It is hyperbola. The transverse axis is parallel to x axis.
a² = 1; b² = 9
a = 1; b = 3
c² = a² + b²
= 1 + 9
= 10
c = \(\sqrt {10}\)
ae = \(\sqrt {10}\)
e = \(\sqrt {10}\)
centre (h, k) = (2, -3)
vertices (h ± a, k) = (2 ± 1, -3)
= (2 + 1, -3) & (2 – 1, -3)
= (3, -3) & (1, -3)
foci (h ± c, k) = (2 ±\(\sqrt {10}\), -3)
= (2 + \(\sqrt {10}\), -3) & (2 –\(\sqrt {10}\), -3)
directrix x = ±\(\frac {a}{e}\) + h
= ±\(\frac {1}{\sqrt {10}}\) + 2 & x = –\(\frac {1}{\sqrt {10}}\) + 2

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.5 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.5

Question 1.
Find the value, if it exists. If not, give the reason for non-existence.
(i) sin^-1 (cos π)
(ii) tan^-1(sin(\(\frac {-5π}{2}\)))
(iii) sin^-1 [sin 5]
Solution:
(i) sin^-1 (cos π) = sin^-1 (-1) = -sin^-1 (1) = –\(\frac {π}{2}\) [∵ cos π = -1]

(iii) sin^-1 [sin 5]
–\(\frac {π}{2}\) ≤ sin^-1 5 ≤ \(\frac {π}{2}\)
-3\(\frac {π}{2}\) ≤ 5 ≤ 2π
–\(\frac {π}{2}\) ≤ 5 – 2π ≤ 0 ≤ \(\frac {π}{2}\)
sin(5 – 2π) = sin 5
sin^-1 (sin 5) = 5 – 2π

Question 2.
Find the value of the expression in terms of x, with the help of a reference triangle.
(i) sin (cos^-1(1 – x))
(ii) cos (tan^-1 (3x – 1))
(iii) tan (sin^-1(x + \(\frac {π}{2}\)))
Solution:
(i) sin (cos^-1(1 – x)) = sin [cos^-1(adj/hyp)]

(ii) cos (tan^-1(3x – 1)) = cos [opp/adj]
Let θ = tan^-1(3x – 1)
tan θ = 3x- 1
1 + tan² θ = 1 +(3x – 1)²
sec² θ = 9x² – 6x + 2
sec θ = \(\sqrt{9x² – 6x + 2}\)
cos θ = \(\frac{1}{\sqrt{9x² – 6x + 2}}\)
⇒ cos (tan^-1(3x – 1)) = \(\frac{1}{\sqrt{9x² – 6x + 2}}\)

Question 3.
Find the value of
(i) sin^-1(cos(sin^-1(\(\frac {√3}{2}\))))
(ii) cot(sin^-1 \(\frac {3}{5}\) + sin^-1\(\frac {4}{5}\))
(iii) tan(sin^-1 \(\frac {3}{5}\) + cot^-1\(\frac {3}{2}\))
Solution:

Question 4.
(i) tan^-1\(\frac {2}{11}\) + tan^-1 \(\frac {7}{24}\) = tan^-1 \(\frac {1}{2}\)
(i) tan^-1\(\frac {3}{5}\) + cos^-1 \(\frac {12}{13}\) = sin^-1 \(\frac {16}{65}\)
Solution:

Question 5.
Prove that
tan^-1 x + tan^-1 y + tan^-1 z = tan^-1 (\(\frac {x+y+z-xyz}{1-xy-yz-zx}\))
Solution:
tan^-1 x + tan^-1 y + tan^-1 z

Question 6.
tan^-1 x + tan^-1 y + tan^-1 z = π, show that x + y + z = xyz
Solution:
tan^-1 x + tan^-1 y + tan^-1 z = π

x + y + z – xyz = 0
x + y + z = xyz

Question 7.
Prove that
tan^-1 x + tan^-1 \(\frac {2x}{1-x^2}\) = tan^-1 \(\frac {3x-x^3}{1-3x^2}\), |x| < \(\frac {1}{√3}\)
Solution:

Question 8.
Simplify
tan^-1 \(\frac {x}{y}\) – tan^-1 \(\frac {x-y}{x+y}\)
Solution:

Question 9.
(i) sin^-1 \(\frac {5}{x}\) + sin^-1 \(\frac {12}{x}\) = \(\frac {π}{2}\)
(ii) 2 tan^-1 x = cos^-1 \(\frac {1-a^2}{1+a^2}\) – cos^-1 \(\frac {1-b^2}{1+b^2}\), a > 0, b > 0
(iii) 2 tan^-1 (cos x) = tan^-1 (2 cosec x)
(iv) cot^-1 x – cot^-1 (x + 2) = \(\frac {π}{12}\), x > 0
Solution:

sin² x = sin x cos x
⇒ sin x cos x – sin² x = 0
⇒ sin x(cos x – sin x) = 0
sin x = 0 (or) cos x – sin x = 0
⇒ x = nπ, n ∈ Z, (or) cos x = sin x
tan x = 1 = tan \(\frac {π}{4}\)
⇒ x = nπ + \(\frac {π}{4}\), n ∈ Z

⇒ (x + 1)² = 4 + 2√3
⇒ (x + 1)² = 1 + 3 + 2√3
⇒ (x + 1)² = (1 + √3)²
⇒ x + 1 = 1 + √3
∴ x = √3

Question 10.
Find the number of the solutions of the equations
tan^-1(x – 1) + tan^-1 x + tan^-1(x + 1) = tan^-13x
Solution:
tan^-1(x – 1) + tan^-1 x + tan^-1(x + 1)
= tan^-1(x – 1) + tan^-1(x + 1) + tan^-1x

4x – x³ = 6x – 9x³
8x³ = 2x
8x³ – 2x = 0
2x(x² – 1) = 0
x = 0, x² = 1
x = ±1
Number of solutions are three (0, 1 -1)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.1 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.1

Question 1.
Obtain the equation of the circles with a radius of 5 cm and touching the x-axis at the origin in a general form.
Solution:

Given radius = 5 cm and the circle is touching x axis
So centre will be (0, ± 5) and radius = 5
The equation of the circle with centre (0, ± 5) and radius 5 units is
(x – 0)² + (y ± 5)² = 5²
(i.e) x² + y² ± 10 y + 25 – 25 = 0
(i.e) x² + y² ± 10y = 0

Question 2.
Find the equation of the circle with centre (2, – 1) and passing through the point (3, 6) in standard form.
Solution:
Centre = (2, -1) = (h, k)
Passing through the point (3, 6)
Equation of the circle (x – h)² + (y – k)² = r² ………. (1)
(3 – 2)² + (6 + 1)² = r²
1² + 7² = r²
1 + 49 = r²
r² = 50
(1) ⇒ (x – 2)² + (y + 1)² = 50

Question 3.
Find the equation of circles that touch both the axes and pass-through (-4, -2) in a general form.
Solution:

Since the circle touches both the axes, its centre will be (r, r) and the radius will be r.
Here centre = C = (r, r) and point on the circle is A = (-4, -2)
CA = r ⇒ CA² = r²
(i.e) (r + 4)² + (r + 2)² = r²
⇒ r² + 8r +16 + r² + 4r + 4 – r² = 0
(i.e) r² + 12r + 20 = 0
(r + 2) (r + 10) = 0
⇒ r = -2 or -10
When r = -2, the equation of the circle will be (x + 2)² + (y + 2)² = 2²
(i.e) x² + y² + 4x + 4y + 4 = 0
When r = -10, the equation of the circle will be (x + 10)² + (y + 10)² = 10²
(i.e) x² + y² + 20x + 20y + 100 = 0

Question 4.
Find the equation of the circles with centre (2, 3) and passing through the intersection of the lines 3x – 2y – 1 =0 and 4x + y – 27 = 0.
Solution:
centre (2, 3) = (h, k)
Point of intersection
Solve 3x – 2y – 1 = 0 ………. (1)
4x + y – 27 = 0 ……… (2)
(1) ⇒ 3x – 2y = 1
(2) × 2 ⇒ 8x + 2y = 54
11x = 55
x = 5
put in (1)
15 – 2y – 1 = 0
14 = 2y
y = 7
Passing-through point is (5, 7)
Equation of circle be (x – h)² + (y – k)² = r² ……….(3)
(5 – 2)² + (7 – 3)² = r²
3² + 4² = r²
r² = 25
∴ (3) ⇒ (x – 2)² + (y – 3)² = 25
x² – 4x + 4 + y² – 6y + 9 – 25 = 0
x² + y² – 4x – 6y – 12 = 0

Question 5.
Obtain the equation of the circle for which (3, 4) and (2, -7) are the ends of a diameter.
Solution:
The equation of a circle with (x₁ , y₁) and (x₂ , y₂ ) as end points of a diameter is
(x – x₁ )(x – x₂) + (y – y₁ )(y – y₂) = 0
Here the end points of a diameter are (3, 4) and (2, -7)
So equation of the circle is (x – 3 )(x – 2 ) + (y – 4) (y + 7.) = 0
x² + y² – 5x + 37 – 22 = 0

Question 6.
Find the equation of the circle through the points (1, 0), (-1, 0) and (0, 1).
Solution:
Let the general equation of the circle be
x² + y² + 2gx + 2fy + c = 0
It passes through the points (1, 0), (-1, 0) and (0,1)
1 + 0 + 2g + c = 0
2g + c = -1 ………(1)
1 + 0 – 2g + c = 0
-2g + c = -1 …………(2)
0 + 1 + 0 + 2f + c = 0
2f + c = -1
(1) + (2) ⇒ 2c = -2
c = -1
substitute in eqn (1)
2g – 1 = -1
2g = 0
g = 0
substitute in eqn (3)
2f – 1 = -1
2f = -1 + 1
2f = 0
f = 0
Therefore, the required equation of the circle
x² + y² – 1 = 0

Question 7.
A circle of area 9π square units has two of its diameters along the lines x + y = 5 and: x – y = 1. Find the equation of the circle.
Solution:

Area of the circle = 9π
(i.e) πr² = 9π
⇒ r² = 9 ⇒ r = 3
(i.e) radius of the circle = r = 3
The two diameters are x + y = 5 and x – y = 1
The point of intersection of the diameter is the centre of the circle = C
To find C: Solving x + y = 5 ……… (1)
x – y = 1 ………. (2)
(1) + (2) ⇒ 2x = 6 ⇒ x = 3
Substituting x = 3 in (1) we get
3 + y = 5 ⇒ y = 5 – 3 = 2
∴ Centre = (3, 2) and radius = 3
So equation of the circle is (x – 3)² + (y – 2)² = 3²
(i.e) x² + y² – 6x – 4y + 4 = 0

Question 8.
If y = 2√2 x + c is a tangent to the circle x² + y² = 16, find the value of c.
Solution:
The condition of the line y = mx + c to be a tangent to the circle x² + y² = a² is
c² = a²( 1 + m²)
a² = 16; m = 2√2 ⇒ m² = 4 × 2 = 8
c² = 16(1+8)
c² = 16(9)
c = ±4 × 3 = ±12
∴ c = ± 12.

Question 9.
Find the equation of the tangent and normal to the circle x² + y² – 6x + 6y – 8 = 0 at (2, 2).
Solution:
The equation of the tangent to the circle x² + y² + 2 gx + 2fy + c = 0 at (x₁, y₁) is
xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 9
So the equation of the tangent to the circle
x² + y² – 6x + 6y – 8 = 0 at (x₁, y₁) is
xx₁ + yy₁ – \(\frac{6\left(x+x_{1}\right)}{2}+\frac{6\left(y+y_{1}\right)}{2}\) – 8 = 0
(i.e) xx₁ + yy₁ – 3(x + x₁) + 3(y + y₁) – 8 = 0
Here (x₁, y₁) = (2, 2)
So equation of the tangent is
x(2) + y(2) – 3(x + 2) + 3(y + 2) – 8 = 0
(.i.e) 2x + 2y – 3x – 6 + 3y + 6 – 8 = 0
(i.e) -x + 5y – 8 = 0 or x – 5y + 8=0
Normal is a line ⊥r to the tangent
So equation of normal circle be of the form 5x + y + k = 0
The normal is drawn at (2, 2)
⇒ 10 + 2 + k = 0 ⇒ k = -12
So equation of normal is 5x + y – 12 = 0

Question 10.
Determine whether the points (- 2, 1), (0, 0) and s (- 4, – 3) lie outside, on or inside the circle x² + y² – 5x + 2y – 5 = 0.
Solution:
x² + y² – 5x + 2y – 5 = 0
(i) At (-2, 1) ⇒ (-2)² + 1² – 5(-2) + 2(1) – 5
= 4 + 1 + 10 + 2 – 5 = 12 > 0
∴ (-2, 1) lies outside the circle.

(ii) At(0, 0) ⇒ 0 + 0 – 0 + 0 – 5 = -5 < 0
(0, 0) lies inside the circle.

(iii) At (-4, -3) ⇒ (-4)² + (- 3)² – 5(-4) + 2(-3) – 5 = 16 + 9 + 20 – 6 – 5 = 34 > 0
(-4, -3) lies outside the circle.

Question 11.
Find the centre and radius of the following circles.
(i) x² + (y + 2)² = 0
(ii) x² + y² + 6x – 4y + 4 = 0
(iii) x² + y² – x + 2y – 3 = 0
(iv) 2x² + 2y² – 6x + 4y + 2 = 0
Solution:
(i) x² + (y + 2)² = 0
(i.e) x² + y² + 4y + 4 = 0
Comparing this equation with the general form x² + y² + 2gx + 2fy + c = 0
we get 2g = 0 ⇒ g = 0
2f = 4 ⇒ f= 2 and c = 4
Now centre = (-g, -f) = (0, -2)
Radius = r = \(\sqrt{g^{2}+f^{2}-c}=\sqrt{0+4-4}\)
∴ Centre = (0, -2) and radius = 0

(ii) x² + y² + 6x – 4y + 4 = 0
Comparing with the general form we get
2g = 6, 2f = -4
⇒ g = 3, /= -2 and c = 4
Centre = (-g, -f) = (-3, 2)
Radius = \(\sqrt{g^{2}+f^{2}-c}=\sqrt{9+4-4}\)= 3
∴ Centre = (-3, 2) and radius = 3

(iii) x² + y² – x + 2y – 3 = 0
2g = -1; 2f = 2; c = -3
g = \(\frac{-1}{2}\) f = 1
Centre (-g, -f) = (\(\frac{1}{2}\), -1)
Radius = \(\sqrt{g^2+f^2-c}\) = \(\sqrt{\frac{1}{4}+1+3}\)
\(\sqrt{\frac{1+4+12}{4}}\)
\(\sqrt{\frac{17}{4}}\) = \(\frac{\sqrt{17}}{2}\)

(iv) 2x² + 2y² – 6x + 4y + 2 = 0
(÷ by 2) ⇒ x² + y² – 3x + 2y + 1 =0
Comparing this equation with the general form of the circle we get
2g = -3, 2f= 2
g = \(-\frac{3}{2}\), g= 1 and c = 1
So centre = (-g, -f) = (\(\frac{3}{2}\), -1)
and radius = \(\sqrt{g^{2}+f^{2}-c}=\sqrt{\frac{9}{4}+1-1}=\frac{3}{2}\)
∴ Centre = (\(\frac{3}{2}\), -1) and radius = \(\frac{3}{2}\)

Question 12.
If the equation 3x² + (3 – p) xy + qy² – 2px = 8pq represents a circle, find p and q. Also determine the centre and radius of the circle.
Solution:
3x² + (3 – p) xy + qy² – 2px = 8pq represent a circle means,
Co-efficient of x² = co-efficient of y²
3 = q ⇒ q = 3
Co-efficient of xy = 0
3 – p = 0 ⇒ p = 3
3x² + 3y² – 6x = 8 (3)(3)
3x² + 3y² – 6x – 72 = 0
(÷3) x² + y² – 2x – 24 = 0
2g = -2; 2f = 0; c = -24
g = -1 f = 0
Centre (-g, -f) = (1, 0)
Radius = \(\sqrt{g^2+f^2-c}\) = \(\sqrt{1+0+24}\)
= \(\sqrt{25}\) = 5

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Prose Chapter 1 Two Gentlemen of Verona Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Prose Chapter 1 Two Gentlemen of Verona

12th English Guide Two Gentlemen of Verona Text Book Back Questions and Answers

Textual Questions:

I. Answer the following questions in one or two sentences each based on your understanding of the story:
(Note: IQ Important Questions)

Question a.
Who did the narrator meet at the outskirts of Verona? (IQ)
Answer:
The Narrator met Nicola and Jacopo at the outskirts of Verona.

Question b.
Why did the driver not approve of the narrator buying fruits from the boys?
Answer:
The driver did not approve of the narrator buying fruits from the boys because of their shabby appearance.

Question c.
The boys did not spend much on clothes and food, why?
Answer:
The boys had to save every penny towards the weekly medical bill of their sister Lucia. So, they did not spend much on clothes and food.

Question d.
Were the boys saving money to go to the states? How do you know?
Answer:

1. The boys had the commitment to saving the life of their sister.
2. So they were not saving money to go to the states.

Question e.
Why did the author avoid going to Lucia’s room?
Answer:

1. The author did not like to disturb the happy family party.
2. So he avoided going to Lucia’s room.

Question f.
What was Lucia suffering from? (IQ)
Answer:
Lucia was suffering from tuberculosis of the spine.

Question g.
What made the boys join the resistance movement against the Germans?
Answer:

1. The Germans killed the boy’s father and made them homeless.
2. This made the boys join the resistance movement.

Question h.
What made the boys work so hard? (IQ)
Answer:
They did not want charity from the hospital. The determination to save the life of their sister made the boys work hard.

Question i.
Why didn’t the boys disclose their problem to the author?
Answer:

1. The boys didn’t like to gain sympathy.
2. So they did not disclose their problem to the author.

2. Answer the following questions in three or four sentences each: (Text Book Page No. 5)

Question a.
Describe the appearance of Nicola and Jacopo.
Answer:
One boy had worn Jersey and cut-off khaki pants. The other had a shortened army tunic gathered in loose folds about his skinny frame. They had tangled hair and dark earnest eyes.

Question b.
What were the various jobs undertaken by the little boys? (IQ)
Answer:
They shined shoes, sold fruits, hawked newspapers, conducted tourists round the town, and ran errands.

Question c.
How did the narrator help the boys on Sunday? (IQ)
Answer:
The author took the boys in his car to a tiny village called Poleta, set high upon a hill. He drove the car up to a large red-roofed villa. The boys asked the author to come thereafter for an hour and went inside.

Question d.
Who took the author to the cubicle? (IQ)
Answer:
The nurse who was taking care of the boy’s sister Lucia took the author to the cubicle.

Question e.
Describe the girl with whom the boys were talking to in the cubicle.
Answer:

1. The girl seemed to be about twenty.
2. She wore a pretty lace jacket.
3. Propping up on pillows, she was listening to the chatter of the boys.
4. Her eyes were soft and tender.

Question f.
Recount the untold sufferings undergone by the siblings after they were rendered homeless.
Answer:
The boys and their sister were thrown in the streets. Lucia had to give up her singing lessons. They had suffered horribly from near starvation and exposure to the cold winter. Lucia developed tuberculosis of the spine. The boys built a home from the rubbles. They had to admit Lucia to a nursing home. To pay the weekly medical bill, they worked from dawn to midnight doing odd jobs eating very little.

Question g.
The narrator did not utter a word and preferred to keep the secret to himself. Why? Substantiate the statement with reference to the story.
Answer:

1. The narrator kept the secret to himself because he knew that the boys did not like to reveal their secret to anyone.
2. When the narrator asked them what did they do with the money they earned, they were not ready to give a prompt reply for it.

3. Answer the following in a paragraph of 100-150 words each: (Text Book Page No. 5)

Question a.
What was the driving force that made the boys do various jobs?
Answer:
In the war-hit Verona, everything was difficult. Food had become scarce and dear. The hospital which offered to treat Lucia was forced to charge a weekly fee. Work was scarce. But the boys were determined to save the life of their beloved sister.

After the untimely death of the father in the war, the two little boys Nicola and Jacopo took the responsibility of earning money by doing all odd jobs for defraying the medical expenses for their sister on their tender shoulders. They spent very little on their food and clothes. The driving force behind their selfless sacrifice and hard work from dawn to midnight was the love they had for their elder sister. They wanted her to get well soon and become an accomplished singer in life. Once you set a goal far above your capacity but work hard ceaselessly, you are bound to achieve it.

Question b.
How was the family affected by the war?
Answer:
The family was terribly affected by the war. Their father, a well-known singer had been killed in the early part of the war. After some time a bomb had destroyed their home and so the three children Nicola, Jacopo, and Lucia were thrown out into the streets. Their comfortable and cultured life got destroyed by the war. In fact, they suffered horribly from near starvation and exposure to the cold winter.

For many months they lived in a shelter made of broken building walls and bricks. In the meantime, the two boys get separated from their sister. They were under German rule for nearly three years. The boys grew to hate the Germans just because they suffered a lot because of them. In fact, they were the first to join the resistance movement against the Germans.

Question c.
Write a character sketch of Nicola and Jacopo.
Answer:
Nicola was 13 and Jacopo only 12. They were brothers. They were tanned, had tangled hair and dark earnest eyes. Though they were just kids, they were serious about their work. They did hundreds of errands for the tourists. They were found doing brisk business shining shoes or selling wild berries. They had the skill to find seats in the theater for the tourists and also guide the tourists through many important sites of the city of Verona such as Juliet’s tomb. Jacopo was lively as a squirrel.

Nicola’s smile was steady and engaging yet in their innocent faces, one could find seriousness far beyond their years. What struck one was the extreme willingness of both the boys to work. Under the scorching Sun, they hawked newspapers. When the narrator enquired what they did with the money they earned as they were not spending it on clothes or food or saving it for emigrating to America, Nicola coloured but he did not reveal the secret family adversity. Both are gentlemen because they did not want anyone’s sympathy.

Question d.
What message is conveyed through the story “Two Gentlemen of Verona”
Answer:
The message conveyed through the story is one can overcome one’s adversities with strong will and determination. Nothing is impossible in this world. It is one’s hard work and dedication which can help one to achieve one’s goal. The boys in the story were badly affected by the war. In spite of it they were ready to do many odd jobs to save their sister.

This action of the boys throws light on the fact that family is the true demonstration of love, affection, and faith. Yet another message which gets conveyed is that it is the situation and circumstance which one faces in one’s life that makes one shoulder responsibilities with strong determination. In simple words, we can say that Nature is the best teacher who teaches us many lessons in our life.

Question e.
Justify the title of the story “Two Gentlemen of Verona”.
Answer:
In the story ‘Two Gentlemen of Verona’, the two orphan boys Jacopo and Nicola work immensely and exhaustively. They shine shoes, sell newspapers, run errands, and show tourists round the city. They take only figs and black tea as food. They save every penny for the medical treatment of their sister Lucia who is suffering from tuberculosis of the spine. The narrator himself admits that their willingness to work impressed him. They demonstrate an unusual devotion to their work.

The objective of their hard work and purpose behind their half-starved daily routine is not known to many in Verona. Anyone may polish shoes or hawk newspapers but it is the magnanimity of heart and nobleness of purpose that actually determines whether one is a real gentleman or a hypocrite. Hence the title ‘‘Two Gentlemen of Verona” is justified.

Question f.
Adversity brings out the best as well as the worst in people. Elucidate this statement with reference to the story.
Answer:
No human life is possible without adversities. In fact, it is these adversities that bring out the qualities of self-confidence and endeavor in a person. It depends upon the mentality of a man to make it the worst or brings out the best out of it. In this story, the two boys faced the great disaster of losing their father and their home because of the war. To add fuel to it their sister suffered from tuberculosis of the spine.

This was the worst adversity in their life as they lost almost everything at a young age. but they did not lose hope. They had a strong determination to work hard and earn money for the treatment of their sister. Many good qualities like love, devotion, sacrifice, sincerity, and maturity get revealed just because of the adversities they face in their life. Thus the statement “Adversity brings out the best as well as the worst in people” is justified.

Question g.
Which character do you like the most in the story and why?
Answer:
Of all the characters, I like Nicola who is a 13-year-old boy (i.e.) one of the two gentlemen of Verona. Though he is small, he is mature beyond his years. Like John Keets, he hated sympathy and self-pity. He does not want any favour except for the opportunity to work. He has an engaging smile. He and his brother Jacopo were hardworking and devoted to their sister Lucia. He has seriousness far beyond his years.

Even when kindly enquired by the narrator as to why he was spending little on clothes and food, he doesn’t open up. He colours deeply and grows pale. He even avoided the eyes of the narrator. When his squirrel-like brother requested the narrator to send them in his car to Poleta on Sunday, Nicola doesn’t like it. He glares at his brother in vexation and says, “we couldn’t think of troubling you, sir.” He wins the respect of all readers because of his maturity, willingness to work, and devotion to his sister.

Paragraph:

Introduction:
A.J. Cronin has explained the importance of dedication towards a relationship in the story, “Two Gentlemen of Verona”.

About the story:
The story is about the two boys named Nicola and Jacopo, who do numerous things to earn money only to pay for their sister’s treatment who suffers from tuberculosis of the spine. The narrator was driving down the foothills of the Alps along with his companion. At that time, two young boys who sold wild strawberries stopped their car.

Two gentlemen of Verona:
‘The small boys appeared to be quite shabby. The boys were brothers, The elder one Nicola was 13 and the younger Jacopo was 12 years old. The narrator and his companion bought the biggest basket of strawberries from the boys. They came to know that the boys did many kinds of jobs like selling fruits, polishing shoes, selling newspapers, etc., to earn money. During the time of their stay in the town, the young boys were very helpful.

Lucia’s Suffering:
The boys earned money but they spent only a little. The boys earned the money to cure their sister who was hospitalised for tuberculosis of spine. They had a decent life before the war and the war made them orphans. They tried their best to make the payments regularly to the hospital, The narrator drove them to the hospital one Sunday and knew everything about the boys and he did not reveal it to the boys. He drove them back in silence.

Conclusion:
Their selfless action brought nobility to human life, they were really two gentlemen of Verona.

Vocabulary:
a) Read the following words taken from the story. Give two synonyms and one antonym for each of these words. Use a dictionary, if required: O(Text Book Page No. 6)

Answer:

Word	Synonyms	Antonym
cautious	careful/watchful	careless
disapprove	condemn / criticise / refuse	approve
brisk	quick / hurried / active	idle / inactive
engaging	attractive / appealing / interesting	boring.
humble	courteous / polite / modest	impolite
eager	keen / willing / craving	uninterested
resistance	opposition	compliance
persuade	induce / encourage	dissuade
scarce	rare	adequate
nobility	honour / dignity	dishonour

b) Homophones and Confusables: (Text Book Page No. 6, 72, 148)
Homophones are two or more words with the same sound but with different spellings and meanings. You have already learned that homophones are words that sound alike but are different in spelling and
meaning.
E.g. feet – feat / face – phase / sort – sought / hair – heir/

Question 1.
What are confusables?
Answer:
Confusables /confusables are words that are commonly confused with one another in meaning or usage
because of slight similarities in spelling, pronunciation, or meaning.
e.g. moment – movement / except – expect / human – humane / discover – invent.

(i) Given below is a list of common confusables. Distinguish the meaning of each pair of words by framing your own sentences: (Text Book Page No. 6)

a) emigrate – leave one’s country/move abroad (my friend wants to emigrate from Asia)
immigrate – come to live permanently in a foreign country (He wants to immigrate to India)

b) beside – near (He stands beside me)
besides – in addition to (Besides having a car, he also has a bike)

c) judicial – legal (The court ordered judicial custody of the convict)
judicious – wise (The lawyer argued in a judicious manner)

d) eligible – qualified (He ¡s an eligible hand)
illegible – not clear (Mostly doctor’s prescriptions are illegible)

e) conscience – moral sense (His conscience promoted him to know his mistakes)
conscious – awareness (He has consciously abused his teacher)

f) industrial – commercial (The industrial chemicals are polluting the river)
industrious – hard-working (Sathish is an industrious student)

g) eminent – famous (Ramesh is an eminent scientist)
imminent – about to happen (There is an imminent danger of corona virus)

h) illicit – illegal (Ten people were arrested for brewing illicit liquor)
elicit – bring out (The teacher elicited answers from the student)

i) prescribed – advised (The doctor prescribed powerful medicines to me)
proscribed – remove (The police proscribed the striking students)

j) affect – change (The place is affected by the flood)
effect – the result of a change (The effect of the flood in very heavy)

k) aural – related to hearing
oral – related to speaking

l) born – related to birth (Raji was born on 2nd January 2020)
borne – carry (The people near the border borne the brunt of the attack.)

(ii) Fill in the blanks using suitable homophones or confusables:

Answer:

wallet	valet	hoard	horde
fairy	faerie	desert	dessert
medal	meddle	night	knight
wait	weight	sweet	suite
yoke	yolk	plain	plane
grown	groan	might	mite
earn	erne/urn	quite	quiet

c) Give the meanings of the following phrasal verbs and frame sentences using them: (Text Book Page No. 7)

Question 1.
cut off
Answer:

• to remove something by cutting
• The branch was cut off from the tree

Question 2.
come upon
Answer:

• meet someone by chance
• I came upon my Maths teacher in Chennai

Question 3.
put out
Answer:

• stop something burning
• The firefighters put out the fire

Question 4.
draw up
Answer:

• stop
• A taxi drew up outside the hotel

Question 5.
pass out
Answer:

• become unconscious/faint
• The politician passed out when the income tax officials quizzed him.

Question 6.
take off
Answer:

• Start flying/remove clothing
• The flight took off at the right time.

Question 7.
turn away
Answer:

• refuse permission
• The reporters who came to interview the Prime Minister were turned away.

Question 8.
stand by
Answer:

• help someone who ¡s in difficult to be ready.
• My friend stood by me all the time.

Question 9.
bank on
Answer:

• depend on
• The whole team is banking on him to win the match.

d) Read the list of words formed by adding suffixes: (Text Book Page No. 7)
frequently, satisfaction, willingness, inevitable, preparation, government, periodic, management,
population, department, announcement, comfortable, resemblance, nobility.

Form two derivatives from each of the following words by adding prefixes and suffixes: (Text Book Page No. 7)

Answer:

Word	Prefix	Suffix
patient	impatient	patiently
honour	dishonour	honourable
respect	disrespect	respectful
manage	mismanage	management, manageable
fertile	infertile	fertility
different	indifferent	differentiate / difference
friend	befriend	friendship, friendly
obey	disobey	obedience

Listening:

Floods are an inevitable natural disaster which can occur in any part of the world. Floods can prove all the more
disastrous in localities, where population density is high. Preparation for Disaster Management has become imperative for any city, town, or village during monsoons. The Government Department entrusted with Disaster Management makes periodic announcements about the precautions to be taken whenever floods are anticipated.

Now, you are going to listen to the cautionary instructions that are given to the general public living in flood-prone areas. Listen carefully and complete the following sentences:

Question a.
The announcement was made by the Department of _______.
Answer:
Disaster Management.

Question b.
Widespread heavy rains are expected from the early hours of _______.
Answer:
Sunday.

Question c.
The public is asked to find out the locations of _______.
Answer:
the closest flood shelters available and routes to reach them

Question d.
An emergency kit should contain water bottles, biscuit packets, and a _______.
Answer:
whistle to signal for help

Question e.
A list of__________ should be displayed on the wall.
Answer:
emergency telephone numbers

Question f.
Important documents can be secured by keeping them in a ___________case.
Answer:
waterproof

Question g.
Damage to refrigerators can be avoided by _______.
Answer:
leaving their door open

Question h.
Mobile phones should be charged to enable the marooned to contact their friends, relatives, and _______.
Answer:
emergency services

Question i.
___________ should be placed in the toilet bowls to prevent sewage inflow.
Answer:
Sandbags

Question j.
Listen to the_________ and follow the instructions implicitly.
Answer:
periodic news updates

Speaking: (Text Book Page No. 8)

Drafting a Speech:

Task 1:
On the occasion of World Environment Day, you have been asked to deliver a speech during the morning assembly on the importance of tree planting. Write the speech in about 100 – 150 words:

1. Introduction
2. Suggested value points:
   Pollution control – Medicine – Necessary for wildlife – Cause rainfall
3. Conclusion

Respected Principal, the chief guest

Good evening. I am immensely delighted to speak to you on World Environment Day. All of you know that
we celebrate Environment Day on 5th June, every year. Let me explain why we celebrate World Environment
Day. The relationship between humanity and the environment is a delicate balance. Since the industrial revolution,
the world’s population has increased exponentially.

With the population growth, the environment has been profoundly affected Deforestation, pollution and global climatic changes are amongst the adverse effect the explosive population and technological expansion have introduced. The main objective of Environment Day is to gain a greater understanding of the environment.

This enhanced awareness, I believe, will help the country reduce its carbon footprint, increase the use of solar power, reduce and recycle non-biodegradable waste and evolve alternative technologies which would reduce our dependence on fossil fuels.

Moreover, tree planting will be done on a mission mode by school children and college students representing
NCC and NSS wings. This would spread the forest cover and give shelter to the wildlife and also ensure
plentiful rainfall sustaining life on this lovely planet. The student community shall disseminate the urgent need to
conserve water and other natural resources appeal to the younger generation, I mean my friends to be socially
responsive and do their part to preserve the environment.

Task 2:
Prepare a speech on “The importance of a reading habit” in about 100—150 words as using the hints given below together with your own ideas: (Text Book Page No. 9)

1. Introduction
2. Suggested value points
   Knowledge enrichment — Skill development — Meaningful usage of time — Overall development
3. Conclusion

The most distinguished chief guest, revered Principal, dignitaries on the Dias and off the dais, my beloved teachers and friends. This morning I wish to share my views on a man-making habit called ‘Reading’.

Books are the quietest and most constant of friends. They are the most accessible and wisest of counsellors and the most patient of teachers. Some schools do focus on developing a flair for reading by keeping a library period. Children are allowed to borrow books and also share their observations with their peers after the library hour is over. Such sharing introduces children to the wonderful world of books.

The art of reading is in great part that of acquiring a better understanding of life from one’s encounter with it in a book. Through reading, one exposes oneself to new things, new ways to solve a problem. Reading is a very useful hobby. Wiseman has lauded the importance of reading and the hobby of reading. Kofi Annan said, “Literacy is a bridge from misery to hope”.

William James said, “So it is with children who learn to read fluently and well. They begin to take flight into whole new worlds as effortlessly as young birds take to the sky”. Dear friends let us read books and conquer the world.

Reading – Note Making: (Text Book Page No. 9)

Read the passage given below and make notes:

To match the best cities across the world, the Government of India initiated ‘smart cities’ to drive economic growth and improve the quality of life of people. The agenda under smart city promises to resolve urban sustainability problems. Urban forests provide a range of important ecosystem services that are critical for the sustainability of cities. Urban forestry, which is defined more as ‘Management of Trees’ contributes to the physiological, sociological, and economic well-being of the society.

Mangroves, lakes, grasslands, and forests in and around our cities, act as sponges that absorb the air and noise pollution and they present themselves as our cultural and recreational hotspots. However, these spots are rapidly being reclaimed and replaced in the name of development. The presence of urban green has shown to increase the economic value of the place.

Urban forests contribute to reducing the cost of building stormwater drain systems for municipalities and neutralizing the urban heat island effect. Plants not only provide shade but also help in regulating the micro-climate. They help regulate energy budgets, improve air quality, and curtail noise pollution. Trees, herbs, shrubs, and grasses arrest sedimentation and prevent other pollutants from entering our water systems, This will give a chance for our urban lakes and rivers to recover and help improve aquatic ecosystems.

Biodiversity also gets a boost through the urban forests and helps create corridors connecting the forest areas, High biodiversity areas can also help to build resilient ecosystems. The availability of forests within our urban areas gives an opportunity for children to connect to the natural environment and learn about native species.
Answer:
Smart city:
1. Initiation by Indian Government

• Economic growth
• Urban sustainability.

2. Urban forestry

• management of trees
• Act as sponges to absorb pollution.

3. Benefits of urban forestry

• Regulated micro-climate
• Arrests sedimentation and pollutants.

Grammar:

Task 1:
Tick the correct options and complete the dialogue:

A: Hello. What do you watch/are you watching?

B: A programme about the Jillian Wala Bagh massacre, which I recorded last night. I study /I’m studying about it this term.

A: All that I know / I’ve known about it is that hundreds of people died /had died in it.

B: Yes, it was much, much worse than anyone has expected/had expected. It went on / has gone off for hours. Do you want / Have you wanted to watch the programme with me?

A: No, thanks. I’ve got to do some veena practice. I’ve just remembered / I just remembered that we’ve got a concert tomorrow, and I don’t have/haven’t had time to practice my new piece this week.

B: OK. I’ve already done / I already did my practice, so I’ve got time to watch TV. See you later.

Task 2:
Complete the sentences with the correct tense form of the verbs in brackets: (Text Book Page No. 11)

Question a.
(tell) me exactly what (happen) last night!
Answer:
Tell me exactly what happened last night.

Question b.
Mrs. Mageswari is my Maths teacher. She (teach) me for four years.
Answer:
Mrs. Mageswari is my maths teacher She has been teaching me for four years.

Question c.
I (never /think) of a career ¡n medicine before I spoke to my Biology teacher but now I (seriously! consider) it.
Answer:
I had never thought of a career in medicine before I spoke to my biology teacher but now I seriously consider it.

Question d.
Oh no! I (forget) to bring my assignment! What am I going to do? This is the second time I (do) this!
Answer:
Oh no I forgot to bring my assignment! what am I going to do? This is the second time I am doing this.

Question e.
I can’t remember what my teacher (say) yesterday about our homework. I (not listen) properly because Hussain (talk) to me at the same time.
Answer:
I can’t remember what my teacher said yesterday about our homework. I did not listen properly because Hussian was talking to me at the same time.

Question f.
Last year we (go) on a school trip to Kanyakumari. We (have) a very interesting time.
Answer:
Last year we went on a school trip to Kanyakumari. We had a very interesting time.

Question g.
At the moment I (think) about what course to pursue next year but I (not make) a final decision yet.
Answer:
At the moment I am thinking about what course to pursue next year but I have not made a final decision yet.

Question h.
I (get) up at 7 every morning but this morning I (sleep) for a long time and I (not get) up until 8.
Answer:
I get up at 7 every morning but this morning I slept for a long time and I did not get up until 8.

Task 3:
Fill in the blanks with the correct form of the verbs given in the brackets:

Question a.
Everyone _________ when the earthquake hit the small town. (sleep)
Answer:
was sleeping

Question b.
Evangeline _______ her job a couple of years ago. (quit)
Answer:
quit

Question c.
Where ___________ your last holidays? (you spend)
Answer:
did you spend

Question d.
I think Suresh _________ for Tiruvallur next morning. (leave)
Answer:
will leave

Question e.
I was angry that I _______ such a mistake (make).
Answer:
had made

Question f.
My mother was tired yesterday because she __________ well the night before (not sleep).
Answer:
did not sleep

Question g.
Her parents ___________ in Coimbatore for two weeks from today (be).
Answer:
havebeen

Question h.
Nothing much ________ when I got to the meeting (happen).
Answer:
had happened

Question i.
Scientists predict that by 2050, man ________ on Mars. (land)
Answer:
will land

Question j.
Sh! Someone ___________ to our conversation! (listen)
Answer:
is listening

Question k.
The plane ________ off in a few minutes. (take)
Answer:
will take

Question l.
They _________ about me when I interrupted their conversation. (talk)
Answer:
were talking

Question m.
Justin and his parents _________ in an apartment right now because they can’t find a cheap house. (live)
Answer:
are living

Question n.
Rajini Prem’s family _________ in Chengalpet now. (be)
Answer:
is
Question o.
Yusuf_________ to the movies once in a while. (go)
Answer:
goes

Question p.
This _________ an easy quiz so far (be).
Answer:
has been

Question q.
Our team _________ any games last year. (not win)
Answer:
did not win

Question r.
We _________ a wonderful film at the cinema last night. (see)
Answer:
saw

Question s.
Hurry up! The movie ________ (already begin)
Answer:
has already begun.

Modal Auxiliaries: (Text Book Page No. 12)

Modal Auxiliary is a special auxiliary that is used to denote a particular mood or expression of the subject.
There are 13 Modal Auxiliaries (four of which are quasi-modals/ margins).

Task 1:
Fill in the blanks with modal auxiliaries: (Text Book Page No. 14)

Question a.
The candidates _______ answer five out of ten questions.
Answer:
must

Question b.
How _______ you open my bag?
Answer:
dare/can

Question c.
Tajudeen ________ finish this work by Monday.
Answer:
will

Question d.
_______ I go to school today?
Answer:
Shall

Question e.
I wish you ________ tell me the truth.
Answer:
would

Question f.
Poonam __________ not catch the bus yesterday.
Answer:
could

Question g.
People who live in glass houses ______ not throw stones.
Answer:
should/must

Question h.
You ________ not go to the market as I have brought vegetables.
Answer:
need

Question i.
_______ you have taken all this trouble?
Answer:
Must

Question j.
You ______ be joking.
Answer:
must

Question k.
I tried to climb up the tree, but _____ not.
Answer:
could

Question l.
Hima Das ran so fast that she ______ win the medal.
Answer:
could

Question m.
You ________ lead a horse to water, but you _______ make it drink.
Answer:
can, cannot

Question n.
I ________ like to have a cup of coffee.
Answer:
would

Question o.
My grandfather _____ visit this temple when he was young.
Answer:
used to/would

Task 2:
Complete the following sentences with modals using the clues given:

Question a.
You _________ help the needy. (moral obligation)
Answer:
must/ought to

Question b.
If I were you, I ________ not behave like that. (conditional sentence)
Answer:
would

Question c.
I _______ never tell a lie. (determination)
Answer:
will

Question d.
My uncle _______ have reached by now. (possibility)
Answer:
may

Question e.
The patient is critical. He __________be taken to the hospital.(compulsion)
Answer:
must

Question f.
I ________ to play hockey when I was a student. (past habit)
Answer:
used to

Question g.
You _______ not attend my class. (order)
Answer:
must

Question h.
He ___________ come today. (remote possibility)
Answer:
might

Question i.
You ___________ follow the traffic rules. (regulation)
Answer:
must

Question j.
He play the match. (willingness)
Answer:
will

Question k.
You __________ not waste time on it. (necessity)
Answer:
need

Question l.
Had the doctor come in time, he _______ have saved the patient.(probability)
Answer:
would

Reported Speech:

Task 1:
Read what these people say and rewrite as sentences: (Text Book Page No. 15)underlines

Question 1.
I am very busy.
Answer:
Raja said that he was very busy.

Question 2.
I have completed my work.
Answer:
Satya said that he had completed his work.

Question 3.
I don’t like to go out.
Answer:
Johnson said that he didn’t like to go out.

Question 4.
I have just come back from Chennai.
Answer:
Akshita said that she had just come back from Chennai.

Question 5.
I am learning English.
Answer:
Jayan said that he was learning English.

Question 6.
I bought a pen yesterday.
Answer:
Madhu said that she had bought a pen the previous day.

Question 7.
We will go shopping tomorrow.
Answer:
Joseph and Mary said that they would go shopping the next day.

Question 8.
We can’t attend the party.
Answer:
Afsar and Ayesha said that they could not attend the party.

Question 9.
How are you?
Answer:
Satish asked how he was.

Question 10.
I am fine. Thank you
Answer:
Victor said that he was fine and thanked him.

Task 2:
Read the following dialogue and complete the report in the space provided:

Priya: Where are you going to?
Vijay: I am going to the railway station.
Priya: Why are you going there?
Vijay: I want to receive my uncle who is coming from Bangalore.

Question 1.
Priya asked Vijay ___________
Answer:
Priya asked Vijay where he was going.

Question 2.
Vijay replied __________
Answer:
Vijay replied that he was going to the railway station.

Question 3.
Priya further inquired ___________
Answer:
Priya further enquired why he was going there.

Question 4.
Vijay stated that ___________
Answer:
Vijay stated that he wanted to receive his uncle who was coming from Bangalore.

b) Teacher: Why are you late?
Divya: I missed the bus.
Teacher: You should have reached the bus stop on time.
Divya: My grandmother is ill. So, I had to take her to the doctor.
Teacher: I am sorry. What ails her?
Divya: She has a high fever.

Question 1.
The teacher asked Divya why she was late. Divya replied that (a) ________.The teacher told her that (b) _____. Divya said that her grandmother was ill so she had to take her to the doctor. The teacher felt sorry and further asked her (c) _____. Divya explained that she (c)_________ high fever.
Answers:
(a) She had missed the bus
(b) She should have reached the bus stop on time.
(c) what ailed her?
(d) had

Task 3:
Rewrite the following passage in indirect speech: (Text Book Page No. 16)

Question 1.
Pradeep got out of bed with much excitement. “It is going to be a lovely sunny day,” he remarked
to his sister Varshini. “Just let me sleep a bit longer, Pradeep,” Varshini begged, “and since you are feeling so
enthusiastic, “she suggested, “Why don’t you go and help a mother in cooking?” Sure, I will say Pradeep.
“Can I help you, mum?’ he said to his mother. “Yes, of course. There are idlis and vadas on the dining table.
Have your breakfast.” “Thank you, mum; I’ll surely help you by eating them.”
Answer:
Pradeep got out of bed with much excitement. He told his sister Varshini that it was going to be a lovely sunny day. Varshini begged him to let her sleep a bit longer and since he was feeling so enthusiastic she asked him why not go and help a mother in cooking. Pradeep said that he would. He asked his mother if he could help her. The mother replied positively and added that there were idlis and vadas on the dining table and told him to have his breakfast. Pradeep thanked his mother and said that he would surely help her by eating them.

Writing:
Read the following letter carefully, discuss with your partner, and answer the questions:

Sir,
I request you to publish the following letter in your daily to address an important issue which needs immediate redressal.

During weekends motorcyclists are seen racing on the East Coast Road and the Old Mahabalipuram road of Chennai. The amateur racers are risking their own lives and of the public as well. They are fearless and irresponsible, not knowing the price of human lives. Risking others and their lives for their pleasure is highly condemnable.

Even school students indulge in such activities and cause fatal accidents. The racers have started
occupying the lanes and streets of busy localities. As such, the violation of traffic rules often results in the loss of young lives. Such reckless riders who violate traffic rules should be punished severely. As a responsible citizen of society, I request the authorities concerned to take appropriate measures to put an end to this menace.
Yours truly,
xxxxx.

Questions:

Question a)
Who is the sender of the letter?
Answer:
Srivastava is the sender of the letter.

Question b)
Who is the receiver?
Answer:
The editor of a daily is the receiver.

Question c)
What is the issue?
Answer:
Motorcycle racing is the issue.

Question d)
What is the request of the sender?
Answer:
The request of the sender to the authorities concerned is to take appropriate measures to put an end to the motorcycle racing.

Question e)
Who will take steps after reading it?
Answer:
The traffic police will take steps after reading it.

b) You have chosen Computer Science in the Higher Secondary Course. Write a letter to your friend giving reasons for your choice. Read the clues given in brackets to complete the letter.

Dear Arjun (Greeting),

Hope you are well (enquire about his well-being). I would like to say that I have chosen computer science in Hr. Sec course. Firstly I want you to help me with my future (the reason for your choice of group). I wish to become an Engineer (state your ambition). We come to hear a lot of instances of misusing social media. (discuss recent unhealthy happenings in social media and society). These have made me select the course so that after knowing the system well. I will be able to find out something to stop such things (demand or need of this profession). I have plans to pursue M.S in the US (higher studies or specialization).

All the best for your CA preparation. Convey my regards to all at home.

Yours lovingly,
(your name)

Task: (Text Book Page No. 18)
a) You had been to your Grandma’s house during the summer holidays. You enjoyed your stay in her company. Write a letter to your Grandma stating how much you miss her after returning to your home.

My dear Grandma,

I hope, you are quite well. But I am not fine here, because I miss you a lot. I enjoyed your company during my summer holidays. I feel very sad after returning to my home. I am expecting my next vacation to come. I felt very happy when I stayed with you. Take care of your health. See you on your next vacation.

Yours lovingly,
Arjun S.

Address on the envelope
To

STAMP

Mrs. R.Vasantha,
No.75, West Street,
Trichy – 627032.

b) You are the head of the English department in a renowned institution. You are invited to preside over the inauguration of the English Literary club in your alma mater. Respond to the letter you have received either accepting the invitation or expressing your inability to attend the function.

From
M Ravi Kumar,
Head of the Department of English,
Joseph College of Arts and Science,
Madurai – 627035

To
The Principal,
ABC College of Arts and Science
Trichy – 620177

Sir,

Sub: Accepting your invitation – reg.

This is to kindly inform you that I have received your invitation to the inauguration of the English Literary club. I am really happy to preside over the function in my alma mater. I am sure that I will be at the function on time.
Thanking you,

Yours faithfully,
M Ravikumar.

Madurai,
10.04.2020.

Address on the envelope
To

STAMP

The Principal
ABC College of Arts and Science
Trichy-620177

c. Write a letter to the Headmaster of your school requesting him to help you obtain a duplicate mark sheet of class XII, which you lost while traveling.

From
S. Anand,
No. 12, West Street,
Virudhunagar.

To
The Headmaster,
TCS. Hr. Sec. School,
Virudhunagar.

Sir,
Sub: Requesting to obtain a duplicate mark sheet of class XH-reg.

I would like to bring to your kind notice that I had missed my mark sheet for class XII while traveling. Therefore, I kindly request you to help me to obtain a duplicate mark sheet.

Thanking you,

Yours faithfully,
B. Anand.

Virudhunagar,
15.04.2020.

Address on the envelope
To

STAMP

The Headmaster,
TCS. Hr. Sec. School,
Virudhunagar.

d) Write a letter to AZ Company requesting them to replace the defective juicer that you bought recently. Include the following details: the problem, date of purchase, receipt number, model, and warranty.

From
S. Rahul,
No.2, North Street,
Kovilpatti.

To
The manager,
AZ company,
Chennai-627201

Sir,

Sub: Requesting to replace the defective juicer-reg.

I would like to bring to your kind notice that I had bought a juicer in your company a week ago. Now it is not working but properly due to magnetic sensors. I have also mentioned the date of purchase and receipt number. So, kindly replace the defective juices as early as possible.
Thanking you,

Yours faithfully,
S. Raghul.

Kovilpatti,
20.05.2020.

Address on the envelope

To

Stamp

The manager,
AZ company,
Chennai-627201

e) You wish to become a pilot. Write a letter to a college enquiring about the details of the pilot training course offered by the college. Include the following details in your inquiry: duration of the course, fee structure, scholarships, hostel facilities, and placement details.

From
D.Kumar,
No.75, East street,
Tenkasi.

To
The principal,
ABC College of Technology,
Coimbatore.

Sir.

Sub: Enquiring about the details of the pilot training course offered-reg.
This is to inform you that I would like to know about the pilot training course offered at your college. Please let me know the duration of the course, fee structure, scholarships, hostel facilities, and placement details as soon as possible.

Thanking you,

Yours faithfully,
D. Kumar.

Tenkasi,
25.04.2020.

Address on the envelope

To

STAMP

The principal,
ABC College of Technology,
Coimbatore.

f) Write a letter to the manager of Waves Furniture Company ordering furniture for a coaching center. Include the following details: description of the furniture, number of pieces, mode of payment, time, and delivery options.

From
S. Ramesh,
No.72, Anbu Nagar, Palayamkottai.

To
The manager,
The waves furniture company,
Chennai.

Sir,

Sub: Ordering some furniture-reg.

We are in need of some furniture for our coaching center. Kindly send the goods by train to the above address.

Items	Quantity
Chair	50 nos
Tables	10 nos
Boards	5 nos

Thanking you,

Yours faithfully,
S. Ramesh.

Palayamkottai,
20.06.2020.

Address on the envelope
To

STAMP

The manager,
The waves furniture company,
Chennai.

g. Write an application for the post of Personal Secretary to the Managing Director of a company. Include the following details: Educational qualification, experience, various other qualifications required for the post.

From
XXX
YYY
ZZZ.

To
The Managing Director,
Software solution,
Chennai-28

Sir,

Sub: Application for the post of personal secretary -reg.

Ref: Advertisement in The Hindu dated 8th June 2020.

I read your advertisement in “The Hindu” dated 8th June 2020.1 wish to apply for the post of personal secretary. I have given below my bio-data. If I am appointed, I assure you that I will discharge my duties to your entire satisfaction.

Bio – Data

1. Name of the applicant: xxx
2. Residential Address: yyy
3. Father’s name: A.Jeyaraj
4. Date of birth and age: 27th Dec 1990
5. Age: 28 years old
6. Sex: Male/Female
7. Educational Qualification: M.A. English
8. Experience: 3 years
9. Languages Known: Tamil, English, and Hindi
10. Special Talent: Fluency in English, good knowledge of computer, a good athlete
11. Salary expected: 15,000/- per month

Thanking you,

Declaration:

I, XXX hereby declare that the information which I have furnished is true to the best of my knowledge.

Yours faithfully,
Place: yyy, XXX
Date: 10.06.2020.

Address on the envelope

To

STAMP

The Managing Director,
Software solution,
Chennai-28

h) Write a letter to the editor of a newspaper about the nuisance created by the roadside vendors blocking the pavements and occupying the parking zone.

From
K. Ashok,
No.7, West Mambalam st,
Villupuram.

To
The Editor,
The Indian Express,
Villupuram-27.

Sir,

Sub: Publishing the nuisance created by the roadside vendors in your newspaper -reg.

This is to bring to your kind attention that the roadside vendors are blocking the pavements and occupying the parking zone and thereby creating a nuisance to the public. So, please bring the news to the government by publishing this in your newspaper.

Thanking you,

Yours faithfully,
K.Ashok.

Villupuram,
05.07.2020.

Address on the envelope

To

STAMP

The Editor,
The Indian Express,
Villupuram-27.

j) Write a letter to your relative or friend who is admitted in the hospital for treatment of jaundice. Advise him/her not to worry about the illness and be positive. Assure him/her of your psychological and financial help during the crisis.

My dear Friend,

I heard that you are admitted to the hospital for the treatment of jaundice. It is only a common disease, especially in summer days. So, you take rest and always think positive which will enable you to recover from it soon. If you need any financial help, please inform me at once, So that I will help and be with you.

Yours lovingly,
Arun S

Address on the envelope
To

STAMP

Mrs. M. Karthick,
No.45, North street,
Tirunelveli

ஆசிரியரைப் பற்றி:

ஆர்ச்சிபால்டு ஜோசப் க்ரோனின் (Archibald Joseph Cronin) (1896-1981) ஸ்காட்டிஷை சார்ந்த நாவலாசிரியர், நாடக ஆசிரியர் மற்றும் இயற்பியலாளர் ஆவார். மருத்துவப் பயிற்சிப் பெற்ற க்ரோனின் இருபதாம் நூற்றாண்டின் புகழ் பெற்ற கதை சொல்லுபவரில் ஒருவர், அவரின் பல கதைகள் இவரின் மருத்துவ பணியிலிருந்து வெளிப்பட்டதாகவும் (emerged) அவைகளின் கதைப்பாணி, சமூக அக்கறையுடையதாகவும், அமைக்கப்பட்டிருக்கும்.

க்ரோனின் புத்தகங்கள் அதிகமாக விற்பனையாவது மட்டுமல்லாமல் சில படைப்புகள் (The Citadel and The Keys of the Kingdom) வெற்றிகரமான படங்களாகவும், வானொலி மற்றும் தொலைகாட்சிகளிலும் ஒளிபரப்பப்பட்டன. இவரின் “Novella country doctor” என்னும் படைப்பு தேர்ந்தெடுக்கப்பட்டு BBC வானொலியிலும், தொலைக்காட்சி தொடரிலும் அதிக நாட்களாக ஒளிபரப்பப்பட்டது.

பாடத்தைப் பற்றி:

கொடுக்கப்பட்டுள்ள இந்த பாடத்தின் ஆசிரியர் A.J.Cronin இரு சிறுவர்களின் வாழ்க்கைப்பற்றியும், அவர்கள் தங்களின் சிறுவயதிலேயே அனுபவிக்கின்ற துன்பங்களைப் பற்றியும் விவரிக்கிறார். பெற்றோரை தங்களின் சிறு வயதிலேயே இழந்த முதுகெலும்பு காசநோயால் பாதிக்கப்பட்ட (Tuberculosis of the spine) சகோதரியைக் காப்பாற்ற போராடும் இரு சகோதரர்களின் செயல்களில் வெளிப்படும் அன்பு, அர்ப்பணிப்பு, தியாகம், நேர்மை மற்றும் முதிர்ச்சி ஆகியவை குறித்த ஒரு கதை கொடுக்கப்பட்டுள்ளது. அவர்களுடைய செயல்கள் எவ்வாறு மனிதநேயத்திற்கு ஒரு புதிய நம்பிக்கையை ஊட்டுகிறது என்பதை அறிய தொடர்ந்து வாசிப்போம்.

Two Gentlemen Of Verona Summary in Tamil

நாங்கள் மகிழுந்தில் (Car) வெரோனா புறநகர்பகுதியில் ஆல்ப்ஸ் (Alps) மலையின் அடிவாரம் வழியாக பயணித்த போது இரு சிறுவர்கள் எங்களை நிறுத்தினர். அவர்கள் காட்டு ஸ்ட்ராபெரி (strawberry) பழங்களை விற்றுக் கொண்டிருந்தனர். ”வாங்காதீர்கள்” என்று, எங்களின் எச்சரிக்கையான (Cautious) வாகன ஓட்டுநர் லூகி (Luigi) கூறினான். “வெரோனா நகரின் உட்பகுதியில் இதை விட சிறந்த பழங்களை நீங்கள் பெறலாம். மேலும் இந்தப் பையன்கள்….” என்று அவர்களின் அழுக்குத் தோற்றத்தை ஏற்றுக்கொள்ளாத வகையில் அவரது தோளை அழுத்தினார். ஒரு சிறுவன் மேலாடையையும், வெட்டப்பட்ட காக்கி காற்சட்டையையும் அணிந்திருந்தான்.

மற்றொருவன் சிறியதாக்கப்பட்ட, முழங்கால் வரை அணியக்கூடிய உடையை அவனது மெல்லிய உடம்பில் தொளதொளவென் அணிந்திருந்தான். பழுப்பு நிறத்தையும், கலைந்த முடியையும், ஊக்கமான கண்களையும் உடைய அந்த இரு சிறிய உருவங்களை இன்னும் கூர்ந்து நோக்கியபடியே, நாங்கள் அவர்களால் கவரப்பட்டதை உணர்ந்தோம். என்னுடன் வந்தவர் (companion), அச்சிறுவர்களிடம் பேச்சுக்கொடுத்து அவர்களிருவரும் சகோதரர்கள் என்று அறிந்தார். மூத்தவன் பெயர் நிக்கோலா (Nicola), வயது 13; எங்கள் காரின் கதவின் அருகே வந்து நின்றவன் பெயர் ஜாகோபா (Jacopo), வயது 12-யை நெருங்கும். நாங்கள் அவர்களின் பெரிய கூடை முழுவதையும் வாங்கிக்கொண்டு (bought) நகரத்தை நோக்கிப் புறப்பட்டோம்.

அடுத்த நாள் காலையில் நாங்கள் எங்கள் விடுதியில் இருந்து வெளியே வந்தபோது, எங்களின் அந்த நண்பர்கள் காலணிகளை பளபளப்பாக்கும் பெட்டியில் (shoe shine box) குணிந்தவாறு, நகரின் பொது சதுக்கத்தின் (public square) நீர்வீழ்ச்சி அருகில் சுறுசுறுப்பாக வேலை செய்வதைக் கண்டோம்.

சிறிது நேரம் அவர்களைக் கவனித்தோம் (watched). அவர்களின் தொழில் மந்தமான (slackened) போது நாங்கள் அவர்களிடம் சென்றோம். அவர்கள் எங்களை இன்முகத்தோடுவரவேற்றார்கள் “நீங்கள் வாழ்வாதாரத்திற்கு தான் பழங்களை விற்றீர்கள் என்று நினைத்தேன்” என்றேன்.

“நாங்கள் நிறைய வேலைகள் பார்ப்போம்” ஐயா என்றான் நிக்கோலா. அவன் நம்பிக்கையுடன் (hopefully) எங்களை நோக்கினான். “நாங்கள் இங்கு வரும் பார்வையாளர்களுக்கு இந்த நகரத்தையும், ஜீலியட்டின் கல்லறையையும் மற்றும் அவர்கள் விரும்பும் இடங்களையும் சுற்றிக்காண்பிப்போம்’, என்றான்.

நான் புன்னகையுடன் “சரி எங்களுக்கும் சுற்றிக் காண்பி” என்றேன். நாங்கள் சுற்றிப்பார்த்து கொண்டிருந்த போது, அவர்களின் குறிப்பிடத்தக்க நடத்தை (demeanour) என் ஆர்வத்தை மேலும் தூண்டியது. அவர்கள் குழந்தைத்தனத்துடன் பல செயல்களில் கள்ளக்கபடமில்லாமல் (artless) இருந்தார்கள். ஜாகோபா அணிற்பிள்ளைப் (squirrel) போன்று மிகவும் சுறுசுறுப்புடன் இருந்தான். நிக்கோலா எப்பொழுதும் சிரித்த முகத்தோடு இருந்தான். இருந்தாலும் அச்சிறுவர்களின் குழந்தை முகங்களில், அவர்களின் வயதுக்கு அப்பாற்பட்ட தீவிரம் (seriousness) காணப்பட்டது.

அதற்கு அடுத்த வாரத்தில் அவர்களை நாங்கள் அடிக்கடி (frequently) பார்த்தோம். அவர்கள் எங்களுக்கு மிகவும் உபயோகமாக (useful) இருந்தார்கள். எங்களுக்கு அமெரிக்க சிகரெட்டுகள் வேண்டுமென்றாலும், இசை நிகழ்ச்சிக்கு சீட்டு வேண்டுமென்றாலும், நல்ல உணவகத்திற்கு செல்ல வேண்டுமென்றாலும் எங்களின் தேவைகளை நிறைவேற்ற நாங்கள் நிக்கோலா மற்றும் ஜாகோபாவை நம்பினோம். அவர்களின் வேலை செய்யும் ஆர்வம் எங்களை வெகுவாக ஈர்த்தது. இந்த கடுமையான வெயிலிலும் அவர்கள், காலணிகளை பளபளப்பாக்குதல், பழங்கள் விற்றல், ஓர் இடத்திலிருந்து இன்னொரு இடத்திற்கு எடுத்துச் சென்று செய்தித்தாள்களை விற்றல், பார்வையாளர்களை சுற்றிக் காண்பித்தல் என அனைத்து வேலைகளையும் ஒரே நேரத்தில் செய்தனர்.

ஒரு நாள் இரவு அவர்களை காற்றோட்டமான, ஆள் நடமாட்டமில்லாத (deserted), சதுக்கத்தின், விளக்குகளுக்கு கீழே, கல் நடைபாதையில் (pavement) ஓய்வெடுப்பதை கண்டோம். நிக்கோலா கலைப்புடன் அமர்ந்திருந்தான். விற்காத ஒரு கட்டு செய்தித்தாள்கள் அவன் காலடியில் கிடந்தன. ஜாகோபா, அவனது சகோதரரின் தோளின் மேல் தலைவைத்து தூங்கி கொண்டிருந்தான். நேரம் நள்ளிரவை நெருங்கியது.

“ஏன் இவ்வளவு நேரம் இங்கே இருக்கிறீர்கள், நிக்கோலா?”

“பதுவாவிலிருந்து (Padua) வரும் கடைசி பேருந்துக்காக காத்துக் கொண்டிருக்கிறோம். அது வந்தவுடன் எங்களின் அனைத்து செய்தித்தாள்களையும் விற்று விடுவோம்”. என்றான்.

“நீங்கள் இவ்வளவு கடினமாக உழைக்க வேண்டுமா? பார்பதற்கு மிகவும் களைப்பாக (tired) இருக்கிறீர்கள்”. என்று நான் கேட்டேன்.

“நாங்கள் அதனை குறையாக தெரிவிக்கவில்லை ஐயா”, என்றான்.

மறுநாள் காலை நான் காலணிகளை பளபளப்பாக்க சதுக்கத்தின் நீர்வீழ்ச்சி அருகே சென்றபோது, “நிக்கோலா, நீங்கள் உழைப்பதைப் பார்த்தால் நீங்கள் நிறைய சம்பாதிக்க வேண்டும். நீங்கள் ஆடைகளில் செலவலிப்பதில்லை. மிகக் குறைவாகவே சாப்பிடுகிறீர்கள், வழக்கமாக நீ கருத்த ரொட்டித்துண்டு (blackbread) மற்றும் அத்திப்பழங்களை (figs) மட்டுமே சாப்பிடுவதை நான் கண்டிருக்கிறேன். உங்கள் பணத்தை வைத்து நீங்கள் என்ன செய்கிறீர்கள்? என்று என்னிடம் சொல்”.

அவன் உடனே குழம்பிப்போய் மிகுந்த வருத்தமுற்றான். பின்பு தரையைப் பார்த்துக் குணிந்தான்.
”அமெரிக்காவிற்கு புலம் பெயர்வதற்காகவா (emigrate) பணத்தை சேமிக்கிறீர்கள்?” என்று கேட்டேன். அவன் என்னை பக்கவாட்டில் பார்த்து பேசினான். “எங்களுக்கும் அமெரிக்கா போக வேண்டும் என்று பெரிய ஆசை உண்டு” ஆனால், இங்கே, இப்போது நாங்கள் வேறு திட்டங்கள் வைத்திருக்கிறோம்”.

“என்ன திட்டங்கள்?” (plans)
அவன் சங்கடத்துடன் (uncomfortably) புன்னகைத்தான். “சாதரணமான திட்டங்கள் தான்”, என்றான் மெதுவான குரலில்.

“நல்லது,” “நாங்கள் வரும் திங்கட்கிழமை புறப்படுகிறோம். நாங்கள் புறப்படுவதற்குள் உனக்கு ஏதாவது செய்ய வேண்டுமா?” என்றேன். வேண்டாமென் நிக்கோலா தலையை அசைத்தான். ஆனால் திடிரென ஜாகோபா, ஐயா நாங்கள் ஒவ்வொரு ஞாயிற்றுகிழமையும் முப்பது கிலோமீட்டர் அப்பால் இருக்கக்கூடிய ‘பொலேடா (Poleta) என்ற இடத்திற்கு வாடகை மிதிவண்டியில் (hire bicycles) செல்வோம். நீங்கள் எங்களிடம் மிக கனிவுடன் நடந்து கொள்வதால், நாளை எங்களை உங்கள் காரில் அங்கு அழைத்து செல்லலாம் என்றான். நான் லூகியிடம் ஞாயிற்றுகிழமை ஓய்வு. இருந்தபோதும் உங்களுக்காக கார் ஓட்டுகிறேன்” என்று பதிலளித்தேன்.

சிறிய இடைவெளிக்குப்பின், நிக்கோலா அவனது சகோதரனை எரிச்சலுடன் (Vexation) முறைத்தான். “உங்களுக்கு தொந்தரவு வேண்டாம் என்று நினைத்தோம் ஐயா”
“இது ஒன்றும் தொந்தரவு இல்லை”.

தனது உதட்டை கடித்தபடியே மெல்லிய குரலில் சரி நல்லது’ என்றான். அடுத்த கிராமத்திற்கு காரில் பயணமானோம். நாங்கள் அங்கு வசிக்கக் கூடிய இடம் மிகச்சாதரணமாகத்தான் இருக்கும் என கற்பனை செய்திருந்தேன். ஆனால், ஜாகாபாவோ எங்களை பெரிய சிவப்புக் கூரையிட்ட, பெரிய கல் சுவரால் சூழப்பட்ட கிராமப்புற வீட்டுக்கு அழைத்துச் சென்றான். என்னால் என் கண்களையே நம்பமுடியாமல் திகைத்திருந்த வேளையில், என்னுடன் வந்த இரு பயணிகளும் காரில் இருந்து குதித்து இறங்கினர்.

“நாங்கள் அதிக நேரம் எடுத்துக்கொள்ள மாட்டோம் ஐயா, ஒரு மணி நேரம் மட்டுமே. நீங்கள் இங்கே உள்ள தேநீர் கடையில் ஏதேனும் அருந்த விரும்புகிறீர்களா?”. அவர்கள் இருவரும் சுவரின் பின்னால் மறைய (disappear) ஆரம்பித்தனர்.

சில நிமிடங்களுக்கு பிறகு, நானும் அவர்களை பின்தொடர்ந்தேன். நான் கம்பியினால் ஆன ஒரு வாசலைக் கண்டேன். தீர்மானமாக (determinedly) அழைப்பு மணியை அடித்தேன்.

இரும்பு வளையத்தினால் (steel-rimmed) ஆன கண்ணாடியை அணிந்த ஒரு கனிவான பெண்மணி வந்தாள். அந்த பெண்மணி வெள்ளை நிற செவிலியர் உடையுடன் வந்தாள். நான் வியந்து பார்த்தேன்.

“நான் இங்கே இரு சிறுவர்களை அழைத்து வந்தேன்”. ஓ! அப்படியா! என்று அவர் முகம் பிரகாசமானது. அவள் கதவை திறந்து என்னை உள்ளே அனுமதித்தாள். நிக்கோலா, ஜாகோபாவிடம், நான் உங்களை அழைத்துச் செல்கிறேன்” என்றேன்.

அவள் என்னை குளிர்ந்த, பளிங்கினால் ஆன தாழ்வாரம் (vestibule) வழியே ஒரு மருத்துவமனைக்கு அழைத்துச்சென்றாள். (அந்த கிராமத்து வீடே இப்போது மருத்துவமனையாகி இருந்தது. ஒரு சிறிய படுக்கை அறையின் வாசலில் அவள் நின்று, தன் வாயில் அவள் கையை வைத்து புன்னகைத்தப்படி, கண்ணாடி பிளவின் (glass partition) வழியே என்னைப் பார்க்கச் சொன்னாள்.

அந்த இரு பையன்களும், 20 வயது மதிக்கத்தக்க அழகான பின்னலாடை அணிந்திருந்த தலையணைகளால் தாங்கப்பட்டு படுக்கையிலிருந்த பெண்ணின் அருகில் கட்டிலில் அமர்ந்திருந்தனர். அந்த பெண் அவர்கள் பேசுவதைக் (chatter) கேட்டுக் கொண்டிருந்தாள். அவளது கண்கள் இளமையாகவும், மென்மையாகவும் இருந்தது. பார்த்தவுடன் அவளது தோற்றம் அவளுடைய சகோதரர்களை ஒத்திருப்பதை யாராலும் சொல்ல முடியும். அவளது மேசையில் ஒரு ஜாடி நிறைய காட்டு மலர்களும், கூடவே பழங்களும், நிறைய புத்தகங்களும் இருந்தன.

“நீங்கள் உள்ளே போகவில்லையா?” என்று முனுமுனுத்தாள் அந்த செவிலியப் பெண். “உங்களைப் பார்த்தால் ‘லூசியா (Lucia) மகிழ்வாள்” என்றாள் செவிலி.

நான் தலையை அசைத்து மறுத்த படியே அங்கிருந்து நகர்ந்தேன். அவர்களின் மகிழ்ச்சியான குடும்ப சந்திப்பின் போது உள்ளே நுழைய வேண்டாம் என்று நான் நினைத்தேன். ஆனால் படிகட்டுகளின் கீழே நின்று அவளிடம் அந்த இரு சிறுவர்களைப் பற்றி நீ அறிந்ததை கூறு என்று கெஞ்சி (begged) கேட்டேன். அவளும் சம்மதித்தாள்.

“அவர்கள் இருவருக்கும் அவர்களின் அக்கா லூசியாவைத் தவிர இவ்வுலகில் யாரும் கிடையாது” என்று விவரித்தாள் (explained). மனைவியை இழந்த அவர்களின் தந்தை ஒரு நல்ல பாடகர் (singer), அவர் போர்காலத்தில் கொல்லப்பட்டார்.

பின் சிறிது காலத்தில் அவர்கள் வீட்டின் மீது ஒரு குண்டு விழுந்து, இம்மூன்று சிறுவர்களையும் வீதிக்கு தூக்கி எறிந்தது. அவர்கள் எப்போதும் சுகமான (comfortable) வாழ்வை வாழ்ந்து வந்தார்கள். லூசியாவோ ஒரு பாடகராக பயிற்சி செய்து கொண்டிருந்தாள். மேலும் அவர்கள் கடுங்குளிரினாலும், பசியினாலும் கடுமையாகப் பாதிக்கப்பட்டார்கள்.

பல மாதங்கள், அவர்கள் பழைய செங்கல் மற்றும் சிறந்த பொருள்களினால், அவர்களே செய்த கூடாரத்தில் வாழ்ந்து வந்தார்கள். அதன்பின் 3 வருடங்கள் ஜெர்மனியர்கள் இந்த நகரை ஆண்டார்கள் ஜெர்மானியர்களை (Germans) வெறுத்தபடியே (hate) இச்சிறுவர்கள் வளர்ந்த னர்.

“ஜெர்மானியர்களை எதிர்த்து எதிர்ப்பு இயக்கம் (resistance movement) தோன்றிய போது இவர்கள் முதலில் போய் அதில் இணைந்தனர். போர் முடிவடைந்து அமைதி திரும்பியபோது, அவர்கள் தங்கள் அன்பிற்குரிய சகோதரியிடம் திரும்பி வந்தார்கள். மேலும் தங்களது சகோதரி முதுகெலும்பு காசநோயால் (tuberculosis) பாதிக்கப்பட்டிருப்பதை கண்டறிந்தார்கள்”, என்று அவள் ஒரு கணம் நிறுத்தி மூச்சை உள்ளிளுத்தாள்.

“அவர்கள் அவளை கை விட்டு (give up) விட்டார்களா? என்ற கேள்விக்கு நான் பதில் கூற வேண்டியதில்லை. அவர்களே அவளை இங்கு கொண்டு வந்து எங்களிடம் அவளை இந்த மருத்துவமனையில் சேர்த்துக் கொள்ளும் படி வேண்டி கேட்டுக் கொண்டார்கள், இந்த 12 மாதங்கள் அவள் எங்கள் நோயாளியாகவே (patient) இருக்கிறாள், மேலும் அவளது நிலையில் முன்னேற்றம் இருக்கிறது. அவள் மீண்டும் எழுந்து வந்து பாடுவாள் என்ற நம்பிக்கை எங்களுக்கு உள்ளது”.

“இங்கு எல்லாமே இப்போது மிக கடினமாக (difficult) உள்ளது. எனவே உணவு, தங்குமிடம் என அனைத்திற்கும் நாங்கள் பணம் வசூலிக்கவில்லையென்றால் எங்களால் மருத்துவமனையை நடத்த இயலாது. ஆனால் ஒவ்வொரு வாரமும் லூசியாவின் சகோதரர்கள் அவளுக்கான கட்டணத்தை (payment) செலுத்திவிடுவார்கள்.

அவர்கள் என்ன வேலை செய்கிறார்கள் என்று தெரியவில்லை, நானும் கேட்பதில்லை. வெரோனா நகரில் வேலைக் கிடைப்பது மிகக் கடினம். என்னவாக இருந்தாலும் சரி, அவர்கள் நன்றாக செய்கிறார்கள் என்று எனக்குத் தெரியும்”.

“ஆமாம், இதைவிடச் சிறப்பாக அவர்களால் செய்ய இயலாது” என்று நானும் சம்மதித்தேன் (agreed). அவர்கள் என்னிடம் வரும் வரையில் நான் வெளியே காத்திருந்தேன். வந்ததும் மீண்டும் நகருக்கு திரும்பினோம். அவர்கள் என்னிடம் எதுவும் பேசாமல் அமர்ந்திருந்தார்கள். நானும் அவர்களிடம் ஒரு வார்த்தைக்கூட கேட்கவில்லை. அவர்கள் தங்கள் சகோதரி குறித்த இரகசியத்தை (secret) தங்களுடன் மட்டுமே வைத்துக் கொள்ள விரும்புவார்கள் என்று எனக்குத் தெரியும்.

போர் (war) அவர்களது மனநிலையை உடைக்கமுடியவில்லை . அவர்களின் தன்னலமற்ற செயல், மனித வாழ்க்கைக்கு ஒரு புதிய பெருந்தன்மையையும் (nobility), மனித சமுதாயத்திற்கு ஒரு பெரிய நம்பிக்கையைத் (hope) தரக்கூடிய உறுதியையும் அளித்துள்ளன.

Glossary:

WORDS	SYNONYMS	ANTONYMS
1. Shrug	raise one’s shoulders slightly	concur
2. tunic	a loose outer garment without sleeves
3. slackened	reduced	grow/increase
4. demeanor	appearance and behaviour	rudeness
5. artless	innocent	artful
6. hawk	sell things crying out loudly, going from place to place	–
7. deserted	uninhabited, unoccupied	crowded, populous
8. emigrate	take up citizenship of another country	immigrate
9. vexation	annoyance	delight, contentment
10. vestibule	lobby	wayout
11. chatter	a series of short, quick, high- pitched sounds	quiet
12. intrude	enter without permission	abandon
13. rubble	debris, broken bricks	treasure, valuable
14. glaring	staring fiercely	soft
15. destination	end, terminal	start, beginning
16. dwelling	habitat, residence	–
17. scarcely	rarely, seldom	frequently
18. leaped	jumped	descended
19. blink	wink of an eye, flutter	be aware
20. propped up	to support	let down
21. resemblance	similarity, affinity	contrast, difference
22. exposure	subjection, risk	safety, cover
23. starvation	malnutrition, need	supply, plenty
24. barely	scarcely, hardly	often
25. persuaded	convinced, induced	dissuaded
26. devotion	attachment, fondness	aversion, dislike
27. nobility	greatness, honor	dishonour, humiliation
28. cautious	careful	reckless
29. disapprove	criticize	approve
30. brisk	energetic / fast / quick	idle / slow
31.engaging	amicable / charming / captivating	hateful / boring
32. humble	courteous / poor / inferior	intricate / superior
33. eager	craving / anxious / enthusiastic	apathetic/unenthusiastic
34. resistance	defiance / fighting / struggle	assistance / cooperation
35. persuade	induce / prompt	dissuade / discourage
36. scarce	insufficient, deficient	frequent / adequate
37. nobility	honour / dignity / virtue	dishonour

Additional:

WORDS	SYNONYMS	ANTONYMS
1. outskirts	border	interior
2. cautious	careful	reckless / careless
3. disapproved	criticize	approval/permit
4. shabby	ill-dressed	smart
5. angled	entwined	plain
6. set off	to start on a journey	–
7. glance	glimpse, look	examine
8. provoke	evoke, cause, kindle	allay
9. frequently	regularly, often	rarely
10. relied upon	depended on	distrusted
11. errands	odd jobs	–
12. pale	ill or tired	healthy
13. burst out	explode, begin suddenly	dull

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.3

Question 1.
Find the domain of the following functions
(i) tan^-1 (\(\sqrt {9-x^2}\))
(ii) \(\frac {1}{2}\) tan^-1 (1 – x²) – \(\frac {π}{4}\)
Solution:
(i) f(x) = \(\tan ^{-1}(\sqrt{9-x^{2}})\)
We know the domain of tan^-1 x is (-∞, ∞) and range is \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
So, the domain of f(x) = \(\tan ^{-1}(\sqrt{9-x^{2}})\) is the set of values of x satisfying the inequality
\(-\infty \leq \sqrt{9-x^{2}} \leq \infty\)
⇒ 9 – x² ≥ 0
⇒ x² ≤ 9
⇒ |x| ≤ 3

(ii) Range of tan^-1 x is R
-∞ < 1 – x² < ∞
-∞ < -x² < ∞
-∞ < x < ∞
x ∈ R
Domain = R

Question 2.
Find the value of
(i) tan^-1(tan\(\frac {5π}{4}\))
(ii) tan^-1(tan(-\(\frac {π}{6}\)))
Solution:

Question 3.
Find the value of
(i) tan(tan^-1(\(\frac {7π}{4}\)))
(ii) tan(tan^-1(1947))
(iii) tan(tan^-1(-0.2021))
solution:
We know that tan(tan^-1 x) = x
(i) \(\tan \left(\tan ^{-1} \frac{7 \pi}{4}\right)=\frac{7 \pi}{4}\)
(ii) tan(tan^-1(1947))= 1947
(iii) tan(tan^-1 (-0.2021)) = -0.2021

Question 4.
Find the value of
(i) tan(cos^-1(\(\frac {1}{2}\)) – sin^-1(-\(\frac {1}{2}\)))
(ii) sin(tan^-1(\(\frac {1}{2}\)) – cos^-1(\(\frac {4}{5}\)))
(iii) cos(sin^-1(\(\frac {4}{5}\)) – tan^-1(\(\frac {3}{4}\)))
solution: