Continuity and Differentiability - 2 - JEE MCQ

ƒ(x) is continuous everywhere

ƒ(x) is not continuous at x = 2

ƒ(x) is not differentiable at exactly three points

None of these

0

1

2

3

continuous as well as diff. at x = 0

continuous at x = 0, but not diff. at = 0

neither continuous at x = 0 nor diff. at x = 0

none of these

a = –1, b = 3

a = 1, b = –3

a = 1, b = 3

a = –1, b = –3

Discontinuous at only one point

Discontinuous exactly at two points

Continuous everywhere

None of these

a – b

a + b

In a – In b

None of these

1/8

1/4

1/2

None

continuous no where

differentiable no where

continuous but not differentiable exactly at one point

differentiable and continuous only at one point and discontinuous elsewhere

f(α) = e^tanα

f(α) = ecotα

f(α) = e^2cotα

f(α) = e2tanα

(3, 0)

(2, 0)

(1, 0)

None of these

–1

0

1

2

g(x) is everywhere continuous except at two points

g(x) is everywhere differentiable except at two points

g(x) is everywhere differentiable except at x = 1

none of these

f is derivable at x = 0 but g is not.

g is derivable at x = 0 but f is not.

both f and g are derivable at x = 0.

nither f nor g is derivable at x = 0.

n = 1, m = 1

n = 1, m = –1

n = 2, m = 2

n > 2, m = n

0

1

2

more than 2

f(x)/x is differentiable in R

f(x) is continuous but not differentiable in R

f(x) is continuous in R (

f(x) is bounded in R

8

16

32

64

–1

0

2

1

0

1

2

more than 2

–1

0

1

2

f is differentiable at x = 0 and at x = 1.

f is differentiable at x = 0 but not at x = 1.

f is differentiable at x = 1 but not at x = 0.

f is neither differentiable at x = 0 nor at x = 1

a = – 1, b = 2

a = 1, b = – 2

a = – 3, b = 4

a = 3, b = – 4