{"id":1790,"date":"2024-04-27T13:11:08","date_gmt":"2024-04-27T07:41:08","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=1790"},"modified":"2024-04-27T17:13:20","modified_gmt":"2024-04-27T11:43:20","slug":"tamil-nadu-12th-maths-model-question-paper-2-english-medium","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/tamil-nadu-12th-maths-model-question-paper-2-english-medium\/","title":{"rendered":"Tamil Nadu 12th Maths Model Question Paper 2 English Medium"},"content":{"rendered":"

Students can Download Tamil Nadu 12th Maths Model Question Paper 2 English Medium Pdf, Tamil Nadu 12th Maths Model Question Papers<\/a> helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.<\/p>\n

TN State Board 12th Maths Model Question Paper 2 English Medium<\/h2>\n

Instructions:<\/p>\n

    \n
  1. \u00a0The question paper comprises of\u00a0four<\/span>\u00a0parts.<\/li>\n
  2. \u00a0You are to attempt all the parts. An internal choice of questions is provided wherever applicable.<\/li>\n
  3. questions of Part I, II. III and IV are to be attempted separately<\/li>\n
  4. Question numbers\u00a01 to 20 in Part I\u00a0<\/span>are objective type questions of\u00a0one -mark<\/span>\u00a0each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer<\/li>\n
  5. Question numbers\u00a021 to 30 in Part II\u00a0<\/span>are\u00a0two-marks<\/span>\u00a0questions. These are to be answered in about one or two sentences.<\/li>\n
  6. Question numbers\u00a031 to 40 in Parr III<\/span>\u00a0are\u00a0three-marks<\/span>\u00a0questions, These are to be answered in about three to five short sentences.<\/li>\n
  7. Question numbers\u00a041 to 47 in Part IV<\/span>\u00a0are\u00a0five-marks<\/span>\u00a0questions. These are to be answered) in detail. Draw diagrams wherever necessary.<\/li>\n<\/ol>\n

    Time: 3 Hours
    \nMaximum Marks: 90<\/p>\n

    Part – I<\/span><\/p>\n

    I. Choose the correct answer. Answer all the questions. [20 \u00d7 1 = 20]<\/span><\/p>\n

    Question 1.
    \nIf A = \\(\\left[\\begin{array}{cc}
    \n2 & 3 \\\\
    \n5 & -2
    \n\\end{array}\\right]\\) be such that \u03bbA-1<\/sup> = A, then \u03bb is _______.
    \n(a) 17
    \n(b) 14
    \n(c) 19
    \n(d) 21
    \nAnswer:
    \n(c) 19<\/p>\n

    Question 2.
    \nIf \u03c9 \u2260 1 is a cubic root of unity and (1+ \u03c9)7<\/sup> = A+ B \u03c9, then (A, B) equals to _______.
    \n(a) (1,0)
    \n(b) (-1, 1)
    \n(c) (0, 1)
    \n(d) (1, 1)
    \nAnswer:
    \n(d) (1, 1)<\/p>\n

    \"Tamil<\/p>\n

    Question 3.
    \nThe value of z – \\(\\bar{Z}\\) is ______.
    \n(a) 2 Im (z)
    \n(b) 2 i Im (z)
    \n(c) Im (z)
    \n(d) i Im (z)
    \nAnswer:
    \n(b) 2 i Im (z)<\/p>\n

    Question 4.
    \nIf x3<\/sup> + 12x2<\/sup> + 10ax + 1999 definitely has a positive zero, if and only if ________.
    \n(a) a \u2265 0
    \n(b) a > 0
    \n(c) a < 0
    \n(d) a < 0
    \nAnswer:
    \n(c) a < 0<\/p>\n

    Question 5.
    \nsin(tan-1<\/sup> x), |x| < 1 is equal to _______.
    \n\"Tamil
    \nAnswer:
    \n(d) \\(\\frac{x}{\\sqrt{1+x^{2}}}\\)<\/p>\n

    Question 6.
    \nThe centre of the circle inscribed in a square formed by the lines x2<\/sup> – 8x – 12 = 0 and y2<\/sup> – 14y + 45 = 0 is _____.
    \n(a) (4, 7)
    \n(b) (7, 4)
    \n(c) (9, 4)
    \n(d) (4, 9)
    \nAnswer:
    \n(a) (4, 7)<\/p>\n

    \"Tamil<\/p>\n

    Question 7.
    \nThe axis of the parabola x2<\/sup> = – 4y is ______.
    \n(a) y= 1
    \n(b) x = 0
    \n(c) y = 0
    \n(d) x = 1
    \nAnswer:
    \n(b) x = 0<\/p>\n

    Question 8.
    \nThe coordinates of the point where the line \\(\\vec{r}=(6 \\hat{i}-\\hat{j}-3 \\hat{k})+t(-\\hat{i}+4 \\hat{k})\\) meets the plane \\(\\vec{r} \\cdot(\\hat{i}+\\hat{j}-\\hat{k})=3\\) are _______.
    \n(a) (2, 1, 0)
    \n(b) (7, -1, -7)
    \n(c) (1, 2, -6)
    \n(d) (5, -1, 1)
    \nAnswer:
    \n(d) (5, -1, 1)<\/p>\n

    Question 9.
    \nIf the vectors \\(\\vec{a}=3 \\vec{i}+2 \\vec{j}+9 \\vec{k}\\) and \\(\\vec{b}=\\vec{i}+m \\vec{j}+3 \\vec{k}\\) are parallel then m is _________.
    \n\"Tamil
    \nAnswer:
    \n(b) \\(\\frac{2}{3}\\)<\/p>\n

    Question 10.
    \nThe minimum value of the function |3 – x | + 9 is ________.
    \n(a) 0
    \n(b) 3
    \n(c) 6
    \n(d) 9
    \nAnswer:
    \n(d) 9<\/p>\n

    Question 11.
    \nThe curve y2<\/sup> = x2<\/sup> (1 – x2<\/sup>) has ______.
    \n(a) an asymptote x = -1
    \n(b) an asymptote x = 1
    \n(c) two asymptotes x = 1 and x = -1
    \n(d) no asymptote
    \nAnswer:
    \n(d) no asymptote<\/p>\n

    \"Tamil<\/p>\n

    Question 12.
    \nIf \/(x, y, z) = xy + yz + zx, then fx<\/sub> – fz<\/sub> is equal to _______.
    \n(a) z – x
    \n(b) y – z
    \n(c) x – z
    \n(d) y – x
    \nAnswer:
    \n(a) z – x<\/p>\n

    Question 13.
    \nA circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is _______.
    \n(a) 0.2%
    \n(b) 0.4%
    \n(c) 0.04%
    \n(d) 0.08%
    \nAnswer:
    \n(b) 0.4%<\/p>\n

    Question 14.
    \nThe value of \\(\\int_{0}^{\\pi} \\sin ^{4} x d x\\) is _______.
    \n\"Tamil
    \nAnswer:
    \n(b) \\(\\frac{3 \\pi}{8}\\)<\/p>\n

    Question 15.
    \n\\(\\int_{a}^{b} f(x) d x\\) is _______.
    \n\"Tamil
    \nAnswer:
    \n(d) \\(\\int_{a}^{b} f(a+b-x) d x\\)<\/p>\n

    Question 16.
    \nThe degree of the differential equation \\(y(x)=1+\\frac{d y}{d x}+\\frac{1}{1.2}\\left(\\frac{d y}{d x}\\right)^{2}+\\frac{1}{1.2 .3}\\left(\\frac{d y}{d x}\\right)^{3}+\\ldots\\) is ________.
    \n(a) 2
    \n(b) 3
    \n(c) 1
    \n(d) 4
    \nAnswer:
    \n(c) 1<\/p>\n

    \"Tamil<\/p>\n

    Question 17.
    \nIn finding the differential equation corresponding toy = emx<\/sup> where m is the arbitrary constant, then m is ____.
    \n(a) \\(\\frac{y}{y^{\\prime}}\\)
    \n(b) \\(\\frac{y^{\\prime}}{y}\\)
    \n(c) y’
    \n(d) y
    \nAnswer:
    \n(b) \\(\\frac{y^{\\prime}}{y}\\)<\/p>\n

    Question 18.
    \nLet X be random variable with probability density function f(x) = \\(\\left\\{\\begin{array}{ll}
    \n2 \/ x^{3} & x \\geq 1 \\\\
    \n0 & x<1
    \n\\end{array}\\right.\\)
    \nWhich of the following statement is correct
    \n(a) both mean and variance exist
    \n(b) mean exists but variance does not exist
    \n(c) both mean and variance do not exist
    \n(d) variance exists but mean does not exist
    \nAnswer:
    \n(b) mean exists but variance does not exist<\/p>\n

    Question 19.
    \nThe random variable X has the probability density function f(x) = \\(\\left\\{\\begin{array}{cc}
    \na x+b, & 0<x<1 \\\\
    \n0, & \\text { otherwise }
    \n\\end{array}\\right.\\)
    \nand E(X) = \\(\\frac{7}{12}\\), then a and b are respectively _______.
    \n(a) 1 and \\(\\frac{1}{2}\\)
    \n(b) \\(\\frac{1}{2}\\) and 1
    \n(c) 2 and 1
    \n(d) 1 and 2
    \nAnswer:
    \n(a) 1 and \\(\\frac{1}{2}\\)<\/p>\n

    \"Tamil<\/p>\n

    Question 20.
    \nA binary operation on a set S is a function from ________.
    \n(a) S \u2192 S
    \n(b)(S x S) \u2192 S
    \n(c) S \u2192 (S x S)
    \n(d) (S x S) \u2192 (S x S)
    \nAnswer:
    \n(b)( S x S) \u2192 S<\/p>\n

    Part – II<\/span><\/p>\n

    II. Answer any seven questions. Question No. 30 is compulsory. [7 \u00d7 2 = 14]<\/span><\/p>\n

    Question 21.
    \nSolve the following system of homogeneous equations.
    \n3x + 2y + 7z = 0, 4x – 3y – 2z = 0, 5x + 9y + 23z = 0
    \nAnswer:
    \nThe matrix form of the above equation is
    \n\"Tamil
    \nThe augmented matrix [A, B] is
    \n\"Tamil
    \nThe above matrix is in echelon form. Here \u03c1(A, B) = \u03c1( A) < number of unknowns.
    \n\u21d2 The system is consistent with infinite number of solutions. To find the solutions.
    \nWriting the equivalent equations.
    \nWe get 3x + 2y + 7z = 0 ……..(1)
    \n-17y – 34z = 0 …….(2)
    \nTaking z = t in (2) we get -17y – 34t = 0
    \n\u21d2 -17y = 34t
    \n\u21d2 y= \\(\\frac{34 t}{-17}\\) = -2t
    \nTaking z = t; y = -2t in (1) we get
    \n3x + 2 (-2t) + 7t = 0
    \n3x – 4t + 7t = 0
    \n\u21d2 3x = -3t \u21d2 x = -t
    \nSo the solution is x = -t; y = -2t; and z = t, t\u2208R<\/p>\n

    \"Tamil<\/p>\n

    Question 22.
    \nShow that |3z – 5 + i| = 4 represents a circle, and, find its centre and radius.
    \nAnswer:
    \nThe given equation |3z – 5 + i| = 4 can be written as
    \n\"Tamil
    \nIt is of the form |z – z| = r and so it represents a circle, whose center and radius are \\(\\left(\\frac{5}{3},-\\frac{1}{3}\\right)\\) and 4\/3 respectively.
    \n\"Tamil<\/p>\n

    Question 23.
    \nFind the equation of the circle whose centre is (2, -3) and passing through the intersection of the line 3x – 2y = 1 and 4x + y = 27.
    \nAnswer:
    \nSolving 3x – 2y = 1 and 4x + y = 27
    \nSimultaneously, we get x = 5 and y = 7
    \n\u2234 The point of intersection of the lines is (5, 7)
    \nNow we have to find the equation of a circle whose centre is
    \n(2, -3) and which passes through (5, 7)
    \n\"Tamil
    \n\u2234 Required equation of the circle is
    \n(x – 2)2<\/sup> + (y + 3)2<\/sup> = \\((\\sqrt{109})^{2}\\)
    \n\u21d2 x2<\/sup> + y2<\/sup> – 4x + 6y – 96 = 0
    \n\"Tamil<\/p>\n

    Question 24.
    \nFind the intercepts cut off by the plane \\(\\vec{r} \\cdot(6 \\hat{i}+4 \\hat{j}-3 \\hat{k})=12\\) on the coordinate axes.
    \nAnswer:
    \n\\(\\vec{r} \\cdot(6 \\vec{i}+4 \\vec{j}-3 \\vec{k})=12\\)
    \nCompare the above equations into \\(\\vec{r} \\cdot \\vec{n}=q\\) so q = 12
    \nLet a, b, c are intercepts of x-axis, y-axis and z-axis respectively.
    \nClearly
    \n\"Tamil
    \nx – intercept = 2; y – intercept = 3; z – intercept = -4<\/p>\n

    Question 25.
    \nFind the values in the interval (1, 2) of the mean value theorem satisfied by the function f(x) = x – x2<\/sup> for 1 \u2264 x \u2264 2.
    \nAnswer:
    \nf(1) = 0 and f(2) = -2. Clearly f(x) is defined and differentiable in 1 < x < 2. Therefore, by the Mean Value Theorem, there exists a c \u2208(1, 2) such that
    \nf'(c) = \\(\\frac{f(2)-f(1)}{2-1}\\) = 1 – 2c
    \nThat is, 1 – 2c = -2 \u21d2 c = \\(\\frac{3}{2}\\)<\/p>\n

    \"Tamil<\/p>\n

    Question 26.
    \nShow that the percentage error in the nth<\/sup> root of a number is approximately \\(\\frac{1}{n}\\) times the percentage error in the number.
    \nAnswer:
    \n\"Tamil<\/p>\n

    Question 27.
    \nSolve the differential equation: tany \\(\\frac{d y}{d x}\\) = cos (x + y) + cos (x -y)
    \nAnswer:
    \ntan y \\(\\frac{d y}{d x}\\) = cos (x + y) + cos(x – y)
    \ntan y \\(\\frac{d y}{d x}\\) = cos x cos y – sin x sin y + cos x cos y + sin x sin y
    \ntan y \\(\\frac{d y}{d x}\\) = 2 cos x cos y
    \nseperating the variables
    \n\\(\\int \\frac{\\tan y}{\\cos y}\\) dy = 2\u222bcos x dx \u21d2 \u222bsec y tan y dy = 2\u222bcos x dx
    \nsec y = 2 sin x + c<\/p>\n

    Question 28.
    \nThe probability density function of X is given by \\(f(x)=\\left\\{\\begin{array}{cc}
    \nk e^{-\\frac{x}{3}} & \\text { for } x>0 \\\\
    \n0 & \\text { for } x \\leq 0
    \n\\end{array}\\right.\\)
    \nFind the value of k.
    \nAnswer:
    \n\"Tamil<\/p>\n

    Question 29.
    \nConstruct the truth table for the following statement. \\(\\neg(p \\wedge \\neg q)\\).
    \nAnswer:
    \n\"Tamil<\/p>\n

    \"Tamil<\/p>\n

    Question 30.
    \nFind an approximate value of \\(\\int_{1}^{1.5} x^{2} d x\\) by applying the right-hand rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}.
    \nAnswer:
    \nHere a = 1; b = 1.5; n = 5; f(x) = x2<\/sup>
    \nSo, the width of each subinterval is
    \n\"Tamil
    \nx0 <\/sub>= 1; x1<\/sub> = 1.1; x2 <\/sub>= 1.2; x3 <\/sub>= 1.3; x4 <\/sub>= 1.4; x5 <\/sub>= 1.5
    \nThe Right hand rule for Riemann sum,
    \nS = [f(x1<\/sub>) + f(x2<\/sub>) + f(x3<\/sub>) + f(x4<\/sub>) + f(x5<\/sub>)] \u0394x
    \n= [f(1.1) + f(1.2) + f(1.3) + f(1.4) + f(1.5)] (0.1)
    \n= [1.21 + 1.44 + 1.69 + 1.96 + 2.25] (0.1)
    \n= [8.55] (0.1)
    \n= 0.855.<\/p>\n

    Part – III<\/span><\/p>\n

    III. Answer any seven questions. Question No. 40 is compulsory. [7 \u00d7 3 = 21]<\/span><\/p>\n

    Question 31.
    \nFind a matrix A if adj (A) = \\(\\left[\\begin{array}{ccc}
    \n7 & 7 & -7 \\\\
    \n-1 & 11 & 7 \\\\
    \n11 & 5 & 7
    \n\\end{array}\\right]\\)<\/p>\n

    Question 32.
    \nObtain the Cartesian form of the locus of z = x + iy in the following case Im[(1 – i)z +1] = 0<\/p>\n

    \"Tamil<\/p>\n

    Question 33.
    \nIf \\(\\vec{a}=\\hat{i}-\\hat{k}, \\vec{b}=x \\hat{i}+\\hat{j}+(1-x) \\hat{k}, \\vec{c}=y \\hat{i}+x \\hat{j}+(1+x-y) \\hat{k}\\), show that \\([\\vec{a} \\vec{b} \\vec{c}]\\) depends on neither x nor y.<\/p>\n

    Question 34.
    \nThe Taylor\u2019s series expansion of f(x) = sin x about x = \\(\\frac{\\pi}{2}\\) is obtained by the following way.<\/p>\n

    Question 35.
    \nThe edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error in computing (i) the volume of the cube and (ii) the surface area of cube.<\/p>\n

    Question 36.
    \nEvaluate \\(\\int_{0}^{1} \\frac{\\sin \\left(3 \\tan ^{-1} x\\right) \\tan ^{-1} x}{1+x^{2}} d x\\)<\/p>\n

    Question 37.
    \nFind the particular solution of (1 + x3<\/sup>) dy – x2<\/sup> ydx = 0 satisfying the condition y(1) = 2.<\/p>\n

    Question 38.
    \nIf X is the random variable with distribution function F(x) given by,
    \n\\(\\mathrm{F}(x)=\\left\\{\\begin{array}{ll}
    \n0, & x<0 \\\\
    \nx, & 0 \\leq x<1 \\\\
    \n1, & 1 \\leq x
    \n\\end{array}\\right.\\)
    \nthen find (z) the Probability density function f(x)<\/p>\n

    \"Tamil<\/p>\n

    Question 39.
    \nShow that \\(((\\neg q) \\wedge p) \\wedge q\\) is a contradiction.<\/p>\n

    Question 40.
    \nShow that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis.<\/p>\n

    Part – IV<\/span><\/p>\n

    IV. Answer all the questions. [7 \u00d7 5 = 35]<\/span><\/p>\n

    Question 41.
    \n(a) By using Gaussian elimination method, balance the chemical reaction equation:
    \nC2<\/sub>H6<\/sub> + O2<\/sub> \u2192 H2<\/sub>O + CO2<\/sub>.
    \n[OR]
    \n(b) \\(\\frac{d y}{d x}+\\frac{3 y}{x}=\\frac{1}{x^{2}}\\), given that y = 2 when x = 1<\/p>\n

    \"Tamil<\/p>\n

    Question 42.
    \n(a) Find the real values of x and y for the equation \\(\\frac{(1+i) x-2 i}{3+i}+\\frac{(2-3 i) y+i}{3-i}=i\\)
    \n[OR]
    \n(b) Find the area between the line y = x + 1 and the curve y = x2<\/sup> – 1.<\/p>\n

    Question 43.
    \n(a) Determine k and solve the equation 2x3<\/sup> – 6x2<\/sup> + 3x + k = 0 if one of its roots is twice the sum of the other two roots.
    \n[OR]
    \n(b) Evaluate: \\(\\int_{0}^{\\frac{\\pi}{2}} \\frac{d x}{5+4 \\sin ^{2} x}\\)<\/p>\n

    Question 44.
    \n(a) 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?
    \n[OR]
    \n(b) Using truth table check whether the statements \\(\\neg(p \\vee q) \\vee(\\neg p \\wedge q)\\) and \\(\\neg p\\) are logically equivalent.<\/p>\n

    Question 45.
    \n(a) Find the value of cot-1 <\/sup>x – cot-1<\/sup> (x + 2) = \\(\\frac{\\pi}{12}\\), x > 0
    \n[OR]
    \n(b) Verify Euler\u2019s theorem for f(x, y) = \\(\\frac{1}{\\sqrt{x^{2}+y^{2}}}\\)<\/p>\n

    \"Tamil<\/p>\n

    Question 46.
    \n(a) Find the points where the straight line passes through (6, 7, 4) and (8, 4, 9) cuts the xz and yz planes.
    \n[OR]
    \n(b) If X is the random variable with probability density function f(x) given by,
    \n\\(f(x)=\\left\\{\\begin{array}{rc}
    \nx+1, & -1 \\leq x<0 \\\\
    \n-x+1, & 0 \\leq x<1 \\\\
    \n0, & \\text { otherwise }
    \n\\end{array}\\right.\\)
    \nthen find (z) the distribution function f(x) (ii) P (-0.5 \u2264 X \u2264 0.5)<\/p>\n

    \"Tamil<\/p>\n

    Question 47.
    \n(a) Sketch the graph of the function: y = \\(x \\sqrt{4-x}\\)
    \n(b) The velocity v, of a parachute falling vertically satisfies the equation, \\(v \\frac{d v}{d x}=g\\left(1-\\frac{v^{2}}{k^{2}}\\right)\\)
    \nwhere g and k are constants. If v and x are both initially zero, find v in terms of x.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Students can Download Tamil Nadu 12th Maths Model Question Paper 2 English Medium Pdf, Tamil Nadu 12th Maths Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. TN State Board 12th Maths Model Question Paper 2 English …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-1790","post","type-post","status-publish","format-standard","hentry","category-class-12"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1790"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=1790"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1790\/revisions"}],"predecessor-version":[{"id":40028,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1790\/revisions\/40028"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=1790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=1790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=1790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}