# RD Sharma Solution CLass 12 Mathematics Chapter 10 Differentiability

## Chapter 10 – Differentiability Exercise Ex. 10.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4

Question 5

Solution 5

Question 6

Find whether the following functions is differentiable at

x = 1 and x = 2 or not:

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

## Chapter 10 – Differentiability Exercise Ex. 10.2

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7

Examine the differentiability of the function f defined by

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6
Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

## Chapter 10 – Differentiability Exercise MCQ

Question 1

Let f(x) = |x| and g(x) = |x3|, then

1. f(x) and g(x) both are continuous at x = 0
2. f(x) and g(x) both are differentiable at x = 0
3. f(x) is differentiable but g(x) is not differentiable at x = 0
4. f(x) and g(x) both are not differentiable at x = 0
Solution 1

Correct option: (a)

Absolute value function is continuous on R.

Question 2

The function f(x) = sin-1 (cos x) is

1. discontinuous at x = 0
2. continuous at x = 0
3. differentiable at x = 0
4. none of these
Solution 2

Correct option: (b)

Question 3

The set of points where the function f(x) = x|x| is differentiable is

1. (-∞, ∞)
2. (-∞, 0) ∪ (0, ∞)
3. (0, ∞)
4. [0, ∞]
Solution 3

Correct option: (a)

Question 4

1. continuous at x = -2
2. not continuous at x = -2
3. differentiable at x = -2
4. continuous but not derivable at x = -2
Solution 4

Correct option: (b)

Question 5

Let f(x) = (x + |x|) |x|. Then, for all x

1. f is continuous
2. f is differentiable for some x
3. f ‘ is continuous
4. f” is continuous
Solution 5

Correct option: (a), (c)

Question 6

The function f (x) = e-|x| is

1. continuous everywhere but not differentiable at x =0
2. continuous and differentiable everywhere
3. not continuous at x =0
4. none of these
Solution 6

Correct option: (a)

Question 7

The function f (x) =|cos x| is

1. everywhere continuous and differentiable
2. everywhere continuous but not differentiable at (2n+1)π /2, n ∊ Z
3. neither continuous nor differentiable at (2n +1) π/2,n∊ Z
4. none of these
Solution 7

Correct option : (b)

Question 8

1. continuous on [-1,1] and differentiable on (-1,1)
2. continuous on [-1,1] and differentiable (-1,0)∪ ϕ(0,1)
3. continuous and differentiable on [-1,1]
4. none of these
Solution 8

Correct option: (b)

Question 9

If f (x) = a |sin x| +b e|x|+c|x|3 and if f (x) is differentiable at x =0,then

1. a = b = c = 0
2. a = 0, b = 0; c ∊ R
3. b = c = 0; a ∊ R
4. c = 0 , a = 0 , b ∊ R
Solution 9

Correct option: (b)

Question 10

1. has no limit
2. is discontinuous
3. is continuous but not differentiable
4. is differentiable
Solution 10

Correct option: (b)

Question 11

If f (x)= |loge x|, then

1. f’ (1+) =1
2. f’ (1) =1
3. f’ (1) =1
4. f’ (1) = -1
Solution 11

Correct option: (a), (b)

Question 12

If f (x) = loge |x|, then

1. f(x) is continuous and differentiable for all x in its domain
2. f (x) is continuous for all for all x in its domain but not differentiable at x = ± 1
3. f (x) is neither continuous nor differentiable at x =  ± 1
4. none of these
Solution 12

Correct option: (b)

Question 13

Solution 13

Correct option: (b)

Question 14

The function f(x) =x -[x], where [.] denotes the greatest integer function is

1. continuous everywhere
2. continuous at integer point only
3. continuous at non-integer points only
4. differentiable everywhere
Solution 14

Correct option: (c)

Question 15

1. a = 2
2. a = 1
3. a =0
4. a =1/2
Solution 15

Correct option: (d)

Question 16

Let f (x) =|sin x|. Then,

1. f (x) is everywhere differentiable.
2. f (x) everywhere continuous but not differentiable at x = n π, n ∊ Z

1. None of these
Solution 16

Correct option: (b)

Question 17

Let f (x) =|cos x|. Then,

1. f (x) is everywhere differentiable
2. f (x) everywhere continuous but not differentiable at x = n π, n ∊ Z

1. None of these
Solution 17

Correct option: (c)

Question 18

The function f (x) =1+|cos x| is

1. Continuous no where
2. Continuous everywhere
3. Not differentiable at x =0
4. Not differentiable at x =n π, n ∊ Z
Solution 18

Correct option: (b)

Question 19

The function f (x) = |cos x| is

1. Differentiable at x = (2n+1) π/2, n∊ Z
2. Continuous but not differentiable at x =(2n+1) π/2, n ∊ Z
3. Neither differentiable nor continuous at x = n π, n ∊ Z
4. None of these
Solution 19

Correct option: (b)

Question 20

1. Continuous as well differentiable for all x ∊ R
2. Continuous for all x but not continuous at some x.
3. Differentiable for all but not continuous at same x’.
4. None of these
Solution 20

Correct option: (a)

Question 21

Let f (x) = ɑ + b |x|+c|x|4, where ɑ, b and c are real constants. Then f (x) is differentiable at x =0 , if

1. a =0
2. b =0
3. c =0
4. none of these
Solution 21

Correct option: (b)

Question 22

If f (x) = |3-x|+(3+x) , where (x) denotes the least integer greater than or equal to x, then f (x) is

1. continuous and differentiable at x =3
2. continuous but not differentiable at x = 3
3. differentiable but not continuous at x =3
4. neither differentiable nor continuous at x =3
Solution 22

Correct option: (d)

Question 23

1. continuous as well as differentiable at x =0
2. continuous but not differentiable at x = 0
3. differentiable but not continuous at x =0
4. none of these
Solution 23

Correct option: (d)

Question 24

1. continuous and differentiable
2. differentiable but not continuous
3. continuous but not differentiable
4. neither continuous nor differentiable
Solution 24

Correct option: (a)

Question 25

The set of point where the function f (x) = |x-3| cos x is differentiable

1. R
2. R – {3}
3. (0,∞ )
4. None of these
Solution 25

Correct option: (b)

Question 26

1. Continuous at x =1
2. Differentiable at x = -1
3. Everywhere continuous
4. Everywhere differentiable
Solution 26

Correct option: (b)

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