JEE Advanced Level Test: Continuity and Differentiability- 2 - JEE MCQ

x < 0

x > 1

0 < x < 1

x > 0

8

1/8

-8

0

x = 1, 2

x = ±1, ± 2

R

R - {1, 2}

a = 0, b= log 3

a = 1, b= log 2

a = 2, b= log 3

a = 0, b= log 2

0

a = 1 / 2

b =5

a =1

b =-4

a = 0, b= 1

x² +3x -2 = 0

x² -3x +2 = 0

x² +3x +2 = 0

x² -5x +6 = 0

continuous and differentiable at x = 3

continuous at x = 1, 2, 3

continuous but not differentiable at x = 3

discontinuous at x = 1, 2, 3

( 2, ∞)

(-∞,3)

(-∞, - 1) ∪ (3, ∞)

R

k ∈ [-2, 0)

k ∈ (0,∞)

k ∈ (-∞, 0)

k ∈ R

continuous for all x, but is not differentiable

neither differentiable nor continuous

discontinuous everywhere

continuous as well as differentiable for all x

continuous at x = π

Discontinuous at x = π

Discontinuous at x = -π

differentiable at x = 1

differentiable at x = 2

differentiable at x = 1 and x = 2

not differentiable at x = 0

f si continuous in [0, 2]

f' is continuous in [0, 2]

f (x) is discontinuous at x = 1

f(x) is differentiable at x = ± 1

f(x) is not differentiable at x = ± 1

f(x) is neither continuous nor differentiable at x = ± 1

f(x) is not continuous at x = 0 

f(x) is continuous at x = 1 and x = 4

f(x) is differentiable at x = 4

f(x) is continuous and differentiable at x = 1

f(x) is only continuous at x = 1

(0, ∞)

(-∞, ∞)

(-∞, ∞) - {0}

(-∞, ∞) - {0, 1, 2}

0

1

1/2

does not exist

f ' (1) = f ' (0)+ 1

f ' (1) = f ' (0)- 1

f ' (0) = f ' (1)+ 2

f ' (0) = f ' (1)- 2

2f (x)

2xf (x)

x =-1

x = 0

x =1

x = 2

(-∞,∞)

is equal to 1

is equal to 0

is equal to -1

does not exist

h is continuous for all x

h is differentiable for all x

h' (x) = 1 for all x >1

h is not differentiable at 2 values of x

6

12

4

3

1/2

1

-1

1/4

1/6

1/12

1/8

f (x) is differentiable everywhere

f (x) is not differentiable at x = 0

f (x) > 1 for all x ∈ R

f (x) is not differentiable at x = 1