Exercise 9.6: Choose the correct answer

Differential Calculus - Limits and Continuity (Mathematics)

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

(1) 

 (1) 1 

(2) 0 

(3) ∞ 

(4) −∞

Ans: (2)

Solution

(2) 

 (1) 2 

(2) 1 

(3) −2 

(4) 0 

Ans: (3)

Solution

(3) 

(1) 0 

(2) 1 

(3) √2 

(4) does not exist

Ans: (4)

(4) 

(1) 1 

(2) - 1 

(3) 0 

(4) 2

Ans: (1)

Solution

 (5)  is

(1) e⁴ 

(2) e² 

(3) e³ 

(4) 1

Ans: (1)

(6) 

(1) 1 

(2) 0 

(3) - 1 

(4) 1/2

Ans: (4)

Solution

(7) 

(1) log ab 

(2) log (a/b)

(3) log (a/b)

(4) a/b

Ans: (2)

(8) 

(1) 2 log 2 

(2) 2(log 2)² 

(3) log 2 

(4) 3 log 2

Ans: (2)

(9) If , then the value of lim_x→0 f (x) is equal to 

(1)  -1 

(2) 0 

(3) 2 

(4) 4 

Ans: (2)

(10) 

(1) 2 

(2) 3 

(3) does not exist 

(4) 0

Ans: (3)

Solution

(11) Let the function f be defined by f (x)= , then

Ans: (4)

Solution

 (12) If f : R→ R  is defined by  for x ∊ R, then lim_x→3 f (x) is equal to

 (1) - 2 

(2) - 1 

(3) 0 

 (4) 1

Ans: (3)

(13)  is 

(1) 1 

(2) 2 

(3) 3 

(4) 0

Ans: (4)

Solution

(14)  If , then the value of p is 

 (1) 6 

(2) 9 

(3) 12 

(4) 4

Ans: (3)

(15)  is 

(1) √2

(2) 1/√2

(3) 1 

(4) 2

Ans: (1)

(16)  is

(1) 1/2 

(2) 0 

(3) 1 

(4) ∞

Ans: (1)

Solution

(17) 

(1) 1 

(2) e 

(3) 1/ e

(4) 0

Ans: (1)

(18) 

(1) 1 

(2) e 

(3) 1/ 2 

(4)  0

Ans: (1)

(19) The value of  is 

(1) 1 

(2) - 1 

(3) 0 

(4) ∞

Ans: (4)

(20) The value of , where k is an integer is

(1) - 1 

(2) 1 

(3) 0 

(4) 2 

Ans: (2)

Solution

(21) At x = 3/2 the function f ( x) = | 2x -3 | / 2x -3 is 

(1) continuous 

(2) discontinuous 

(3) differentiable

(4) non-zero

Ans: (2)

Solution

(22) Let f : R→R be defined by  then f is

 (1) discontinuous at x = 1/2 

(2) continuous at x = 1/2 

(3) continuous everywhere 

(4) discontinuous everywhere

Ans: (2)

(23) The function  is not defined for x = −1 . The value of f (−1) so that the function extended by this value is continuous is 

(1) 2/3 

(2) −2/3 

(3) 1 

(4) 0

Ans: (2)

Solution

(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) [f (3) + f (4.5)] / 7.5 

(2) 12 

(3) 17.5 

(4) [f (4.5) − f (3)] / 1.5

Ans: (2)

Solution

 f is a constant function

(25)  Let a function f be defined by f (x) = x−|x|  / x for x ≠ 0 and f (0) = 2 . Then f is x

(1) continuous nowhere 

(2) continuous everywhere

(3) continuous for all x except x = 1 

(4) continuous for all x except x = 0

Ans: (4)

Solution