CUET Mathematics MCQs Continuity and Differentiability

Question :  If the function f(x)=(2x- sin^-1x)/(2x+tan^-1x) is continuous at each point of its domain , then the value of f(0) is

a) 1/3

b) -1/3

c) 2/3

d) 2

Answer : 1/3

Question :

a) x=0,and x=1

b) x=0 ,but not at x=1

c) x=1 but not at x=0

d) none of these

Answer : x=0,and x=1

Question : If f(x)= x sin (1/x) ,x is not zero, then the value of the function at x=0,so that the function is continuous at x=0 ,is

a) 0

b) -1

c) 1

d) indeterminate

Answer : 0

Question : The function f(x)=1+|cosx| is

a) continuous everywhere

b) continuous no where

c) not differentiable at x=0

d) None of these

Answer : continuous everywhere

Question :

a) 1

b) 0

c) 1/2

d) None of these

Answer : 1

Question :

a)

b)

c)

d) m=1,n=0

Answer :

Question :  Let f(x)=|x| and g(x)=|x³| then

a) f(x) and g(x) both are continuous at x=0

b) f(x) and g(x) both are differentiable at x=0

c) f(x) is differentiable but g(x) is not differentiable at x=0

d) f(x) and g(x) both are not differentiable at x=0

Answer : f(x) and g(x) both are continuous at x=0

Question :  The derivative of cos^-1(2x²-1) with respect to cos-1x is

a) 2

b) 1/2(1-x2)^1/2

c) 2/x

d) 1-x²

Answer : 2

Question : The function f(x)=tanx is discontinuos on the set

a)

b)

c)

d)

Answer :

Question : If sin(x+y)=log(x+y) then dy/dx =

a) -1

b) 1

c) -2

d) 2

Answer : -1