Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 9 Limits and Continuity Ex 9.6 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.6

Choose the correct or the most suitable answer

Question 1.

(1) 1

(2) 0

(3) ∞

(4) -∞

Answer:

(2) 0

Explaination:

Question 2.

(1) 2

(2) 1

(3) -2

(4) 0

Answer:

(3) -2

Explaination:

Question 3.

(1) 0

(2) 1

(3) √2

(4) does not exist

Answer:

(3) √2

Explaination:

Question 4.

(1) 1

(2) -1

(3) 0

(4) 2

Answer:

(1) 1

Explaination:

Question 5.

(1) e^{4}

(2) e^{2}

(3) e^{3}

(4) 1

Answer:

(1) e^{4}

Explaination:

Question 6.

(1) 1

(2) 0

(3) -1

(4) \(\frac{1}{2}\)

Answer:

(4) \(\frac{1}{2}\)

Explaination:

Question 7.

(1) log ab

(2) log \(\left(\frac{\mathbf{a}}{\mathbf{b}}\right)\)

(3) log \(\left(\frac{\mathbf{b}}{\mathbf{a}}\right)\)

(4) \(\frac{\mathbf{a}}{\mathbf{b}}\)

Answer:

(2) log \(\left(\frac{\mathbf{a}}{\mathbf{b}}\right)\)

Explaination:

Question 8.

(1) 2 log 2

(2) 2(log 2)^{2}

(3) log 2

(4) 3 log 2

Answer:

(2) 2(log 2)^{2}

Explaination:

= (log 2) × (log 4)

= log 2 × log 2^{2}

= log 2 × 2 log 2

= 2 (log 2)^{2}

Question 9.

(1) -1

(2) 0

(3) 2

(4) 4

Answer:

(2) 0

Explaination:

Question 10.

(1) 2

(2) 3

(3) does not exist

(4) 0

Answer:

(3) does not exist

Explaination:

Question 11.

Let the function f be defined by

(1)

(2)

(3)

(4)

Answer:

(4)

Explaination:

Question 12.

(1) -2

(2) -1

(3) 0

(4) 1

Answer:

(3) 0

Explaination:

Question 13.

(1) 1

(2) 2

(3) 3

(4) 0

Answer:

(4) 0

Explaination:

Question 14.

(1) 6

(2) 9

(3) 12

(4) 4

Answer:

(3) 12

Explaination:

Question 15.

(1) \(\sqrt{2}\)

(2) \(\frac{1}{\sqrt{2}}\)

(3) 1

(4) 2

Answer:

(1) \(\sqrt{2}\)

Explaination:

Question 16.

(1) \(\frac{1}{2}\)

(2) 0

(3) 1

(4) ∞

Answer:

(1) \(\frac{1}{2}\)

Explaination:

Question 17.

(1) 1

(2) e

(3) \(\frac{1}{\mathrm{e}}\)

(4) 0

Answer:

(1) 1

Explaination:

Question 18.

(1) 1

(2) e

(3) \(\frac{1}{2}\)

(4) 0

Answer:

(1) 1

Explaination:

Put tan x – x = y

When x = 0, tan 0 – 0 = y

0 = y

= e^{0} × 1 = 1 × 1 = 1

Question 19.

The value of is

(1) 1

(2) -1

(3) 0

(4) ∞

Answer:

(1) 1

Explaination:

Question 20.

The value of , where k is an integer is

(1) -1

(2) 1

(3) 0

(4) 2

Answer:

(2) 1

Explaination:

Question 21.

At x = \(\frac{3}{2}\) the function f(x) = \(\frac{|2 x-3|}{2 x-3}\) is

(1) continuous

(2) discontinuous

(3) differentiable

(4) non zero

Answer:

(2) discontinuous

Explaination:

f(x) = \(\frac{|2 x-3|}{2 x-3}\)

f(x) is not defined at x = \(\frac{3}{2}\)

∴ f(x) is discontinuous at x = \(\frac{3}{2}\)

Question 22.

Let f : R → R be defined by

(1) discontinuous x = \(\frac{1}{2}\)

(2) continuous x = \(\frac{1}{2}\)

(3) continuous everywhere

(4) discontinuous everywhere

Answer:

(2) continuous x = \(\frac{1}{2}\)

Explaination:

Question 23.

(1) \(\frac{2}{3}\)

(2) –\(\frac{2}{3}\)

(3) 1

(4) 0

Answer:

(2) –\(\frac{2}{3}\)

Explaination:

At = -1, f(x) has a removable discontinuity Redefining f(x) as

Question 24.

Let f be a continuous function on [2, 5]. If f takes only rational values for all x and f(3) = 12, then f (4.5) is equal to

(1)

(2) 12

(3) 17.5

(4)

Answer:

(2) 12

Explaination:

Given f(3) = 12

f takes only rational values

f(x) = 12

f(3) = 12

f(4.5) = 12

Question 25.

Let a function f be defined by f(x) = \(\) for x ≠ 0 and f(0) = 2. Then f is

(1) continuous nowhere

(2) continuous everywhere

(3) continuous for all x except x = 1

(4) continuous for all x except x = 0

Answer:

(4) continuous for all x except x = 0

Explaination: