Class 12-commerce RD SHARMA Solutions Maths Chapter 9: Continuity
Continuity Exercise Ex. 9.1
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10(i)
Solution 10(ii)
Solution 10(iii)
Solution 10(iv)
Solution 10(v)
Solution 10(vi)
Solution 10(vii)
Solution 10(viii)
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36(i)
Solution 36(ii)
Solution 36(iii)
Solution 36(iv)
Solution 36(v)
Solution 36(vi)
Solution 36(vii)
Solution 36(viii)
Solution 36(ix)
Solution 37
Solution 38
Solution 39(i)
Solution 39(ii)
Solution 40
Solution 41
Solution 42
Given: 
At x = 0, we have
∴ LHL ≠ RHL
So, f(x) is discontinuous at x = 0.
Thus, there is no
value of 
for which
f(x) is continuous at x = 0.
At x = 1, we have
∴ LHL = RHL
So, f(x) is continuous at x = 1.
At x = -1, we have
∴ LHL = RHL
So, f(x) is continuous at x = -1.
Solution 43
Solution 44
Solution 45
Solution 46
Continuity Exercise Ex. 9.2
Solution 1
Solution 2
Solution 3(i)
Solution 3(ii)
Solution 3(iii)
Solution 3(iv)
Solution 3(v)
Solution 3(vi)
Solution 3(vii)
Solution 3(viii)
Solution 3(ix)
Solution 3(x)
Solution 3(xi)
Solution 3(xii)
Solution 3(xiii)
Solution 4(i)
Solution 4(ii)
Solution 4(iii)
Solution 4(iv)
Solution 4(v)
Solution 4(vi)
Solution 4(vii)
Solution 4(viii)
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Continuity Exercise MCQ
Solution 1
Correct option: (c)
Solution 2
Correct option: (a), (b)
Solution 3
Correct option: (a),(d)
Solution 4
Correct option: (c)
Solution 5
Correct option: (d)
Solution 6
Correct option: (c)
Solution 7
Correct option: (c)
Solution 8
Correct option: (b)
Solution 9
Correct option: (b)
Solution 10
Correct option: (d)
Solution 11
Correct option: (b)
Solution 12
Correct option: (a)
Solution 13
Correct option: (d)
Solution 14
Correct option: (c)
Solution 15
Correct option: (c)
Solution 16
Correct option: (c)
Solution 17
Correct option: (c)
Solution 18
Correct option: (c)
Solution 19
Correct option: (d)
Solution 20
Correct option: (b)
Solution 21
Correct option: (a)
Solution 22
Correct option: (a)
Solution 23
Correct option:(d)
Solution 24
Correct option: (c)
Solution 25
Correct option: (b)
Solution 26
Correct option: (b)
Solution 27
Correct option: (a)
Solution 28
Correct option: (a)
Solution 29
Correct option: (b)
Solution 30
Correct option: (a)
Solution 31
Correct option: (a)
Solution 32
Correct option: (d)
Solution 33
Correct option: (b)
Solution 34
Correct option: (b)
Solution 35
Correct option: (a)
Solution 36
Correct option: (d)
Solution 37
Correct option: (c)
Solution 38
Correct option: (b)
Solution 39
Correct option: (b)
Solution 40
Correct option: (b)
Solution 41
Correct option: (d)
Solution 42
Correct option: (a)
Solution 43
We know that, if f(x) and g(x) are continuous then
[f(x) + g(x)], [f(x) - g(x)], f(x)g(x) are continuous functions.
Now, 
For f(x) = 0
∴ 4x = 0
∴ x = 0
Thus, 
is
discontinuous at x =0.
Solution 44
The function f(x) = cot x is discontinuous if cot x → ∞
Solution 45
Given: 
As f(x) is continuous at x = 0, then
Hence, the value of f(x) is 0.
Solution 46
Given: 
As {x} = 0 for integral values of x.
Therefore, domain of f(x) is set of all non-integral values.
Thus, f(x) is discontinuous at all integers.
Solution 47
The function f(x) = [x] is continuous everywhere except for integral values.
Therefore, f(x) = [x] is continuous at x = 1.5.
Solution 48
Given: 
As f(x) is continuous at x = 0, we have
Continuity Exercise Ex. 9VSAQ
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Given: 
As f(x) is continuous at x = 0, we have
Solution 12
Given: 
As f(x) is continuous at x = 2, we have
