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

## Differentiability Exercise Ex. 10.1

### 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 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