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
