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Class 12-science RD SHARMA Solutions Maths Chapter 10 - Differentiability

Differentiability Exercise Ex. 10.1

Solution 1


Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7(i)

Solution 7(ii)

Solution 7(iii)

Solution 8

Solution 9

Solution 10

Solution 11

Given:

As f(x) is differentiable at x = 1, we have

  … (i)

Now, Rf'(1) exist when (b - 2 - a) = 0 … (ii)

  

From (i), we get, b = 5

Putting this in (ii), we get, a = 3.

Differentiability Exercise Ex. 10.2

Solution 1


Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9


Solution 10

Solution 11

Solution 12

Differentiability Exercise MCQ

Solution 1

Correct option: (a)

Absolute value function is continuous on R.

Solution 2

Correct option: (b)

  

Solution 3

Correct option: (a)

  

Solution 4

Correct option: (b)

  

Solution 5

Correct option: (a), (c)

  

 

Solution 6

Correct option: (a)

  

Solution 7

  

  

Therefore, f(x) is continuous at x = 1.

Now,

  

  

Therefore, Lf'(1) ≠ Rf'(1).

Hence, f(x) is not differentiable at x = 1.

Solution 8

Correct option: (b)

  

Solution 9

Correct option: (b)

  

Solution 10

Correct option: (b)

  

Solution 11

Correct option: (a), (b)

  

Solution 12

Correct option: (b)

  

Solution 13

Correct option: (b)

  

Solution 14

Correct option: (c)

  

Solution 15

Correct option: (d)

  

Solution 16

Correct option: (b)

  

Solution 17

Correct option: (c)

  

Solution 18

Correct option: (b)

  

Solution 19

Correct option: (b)

  

Solution 20

Correct option: (a)

  

Solution 21

Correct option: (b)

  

Solution 22

Correct option: (d)

  

Solution 23

Correct option: (d)

  

Solution 24

Correct option: (a)

  

Solution 25

Correct option: (b)

  

Solution 26

Correct option: (b)

  

Solution 27

Given:

Now, f(x) is continuous everywhere except at x = 0.

  

Therefore, f(x) is continuous everywhere.

Now,

  

  

Therefore, Lf'(1) ≠ Rf'(1).

Thus, f(x) is not differentiable at x = 0.

Hence, f(x) is continuous everywhere but not differentiable at x = 0.

Solution 28

Given:

Now,

  

  

Therefore, Lf'(1) ≠ Rf'(1).

Thus, f(x) is not differentiable at

Hence, the set of points where f(x) is differentiable is

Differentiability Exercise Ex. 10VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

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