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RD Sharma Solution CLass 12 Mathematics Chapter 10 Differentiability

Chapter 10 – Differentiability Exercise Ex. 10.1

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 6

Find whether the following functions is differentiable at

 x = 1 and x = 2 or not:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Chapter 10 – Differentiability Exercise Ex. 10.2

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 7

Examine the differentiability of the function f defined by

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Chapter 10 – Differentiability Exercise Ex. 10VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability
Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

  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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

  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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Solution 13

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability 

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

  1. None of these
Solution 16

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

  1. None of these
Solution 17

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

  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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

  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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

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

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentiability

 

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