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

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

Choose the correct or the most suitable answer from the given four alternatives
Question 1.

(a) 1
(b) 0
(c) ∞
(d) -∞
Solution:
(b) 0

Question 2.

(a) 2
(b) 1
(c) -2
(d) 0
Solution:
(c) -2

Question 3.

(a) 0
(b) 1
(c) 2
(d) does not exist
Solution:
(d) does not exist

Question 4.

(a) 1
(b) -1
(c) 0
(d) 2
Solution:
(a) 1

Question 5.

(a) e⁴
(b) e²
(c) e³
(d) 1
Solution:
(a) e⁴

Question 6.

(a) 1
(b) 0
(c) -1
(d) \(\frac{1}{2}\)
Solution:
(d) \(\frac{1}{2}\)

Question 7.

(a) log ab
(b) log \(\left(\frac{a}{b}\right)\)
(c) log \(\left(\frac{b}{a}\right)\)
(d) \(\frac{a}{b}\)
Solution:
(b) log \(\left(\frac{a}{b}\right)\)

Question 8.

(a) 2 log 2
(b) 2 (log 2)²
(c) log 2
(d) 3 log 2
Solution:
(b) 2 (log 2))²

Question 9.
If f(x) = \(x(-1)^{ \left\lfloor \frac { 1 }{ x } \right\rfloor }\), x ≤ θ, then the value of is equal to …………….
(a) -1
(b) 0
(c) 2
(d) 4
Solution:
(b) 0

Question 10.

(a) 2
(b) 3
(c) does not exist
(d) 0
Solution:
(c) does not exist

Limit does not exist

Question 11.
Let the function f be defined f(x) = then ……………

Solution:

The limit does not exist

Question 12.
If f: R → R is defined by f(x) = \(\lfloor x-3\rfloor+|x-4|\) for x ∈ R, then is equal to …………..
(a) -2
(b) -1
(c) 0
(d) 1
Solution:
(c) 0

Question 13.

(a) 1
(b) 2
(c) 3
(d) 0
Solution:
(d) 0

Question 14.
If then the value of p is ………….
(a) 6
(b) 9
(c) 12
(d) 4
Solution:
(c) 12

Question 15.

(a) \(\sqrt{2}\)
(b) \(\frac{1}{\sqrt{2}}\)
(c) 1
(d) 2
Solution:
(a) \(\sqrt{2}\)

Question 16.

(a) \(\frac{1}{2}\)
(b) 0
(c) 1
(d) ∞
Solution:
(a) \(\frac{1}{2}\)

Question 17.

(a) 1
(b) e
(c) \(\frac{1}{e}\)
(d) 0
Solution:
(a) 1

Question 18.

(a) 1
(b) e
(c) \(\frac{1}{2}\)
(d) 0
Solution:
(a) 1

Question 19.
The value of is ……………
(a) 1
(b) -1
(c) 0
(d) ∞
Solution:
(d) ∞
Hint:

So limit does not exist

Question 20.
The value of where k is an integer is …………..
(a) -1
(b) 1
(c) 0
(d) 2
Solution:
(b) 1

Question 21.
At x = \(\frac{3}{2}\) the function f(x) = \(\frac{|2 x-3|}{2 x-3}\) is ………….
(a) Continuous
(b) discontinuous
(c) Differentiate
(d) non-zero
Solution:
(b) discontinuous

Question 22.
Let f: R → R be defined by f(x) = then f is ……………
(a) Discontinuous at x = \(\frac{1}{2}\)
(b) Continuous at x = \(\frac{1}{2}\)
(c) Continuous everywhere
(d) Discontinuous everywhere
Solution:
(b) Continuous at x = \(\frac{1}{2}\)

Question 23.
The function f(x) = is not defined for x = -1. The value of f(-1) so that the function extended by this value is continuous is …………..
(a) \(\frac{2}{3}\)
(b) \(-\frac{2}{3}\)
(c) 1
(d) 0
Solution:
(b) \(-\frac{2}{3}\)
Hint: For the function to be continuous at x = 1

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 ……………
(a) \(\frac{f(3)+f(4.5)}{7.5}\)
(b) 12
(c) 17.5
(d) \(\frac{f(4.5)-f(3)}{1.5}\)
Solution:
(b) 12

Question 25.
Let a function f be defined by f(x) = \(\frac{x-|x|}{x}\) for x ≠ 0 and f(0) = 2. Then f is …………..
(a) Continuous nowhere
(b) Continuous everywhere
(c) Continuous for all x except x = 1
(d) Continuous for all x except x = 0
Solution:
(d) Continuous for all x except x = 0
Hint:

∴ f(x) is not continuous at x = 0
⇒ f(x) is continuous for all except x = 0