# RD Sharma Solution CLass 12 Mathematics Chapter 9 Continuity

## Chapter 9 – Continuity Exercise Ex. 9.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17

Discuss the continuity of the
following functions at the indicated points:

Solution 17

Question 18
Solution 18
Question 19
Solution 19
Question 20

Solution 20

Question 21

Solution 21

Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32

Solution 32

Question 33
Solution 33

Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44

Solution 44

Question 45
Solution 45
Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48
Question 49
Solution 49
Question 50
Solution 50
Question 51

In each of the following, find the value of the constant k so that
the given function is continuous at the indicated point:

Solution 51

Question 52
Solution 52
Question 53
Solution 53
Question 54
Solution 54
Question 55
Solution 55
Question 56

Solution 56

Question 57
Solution 57
Question 58
Solution 58
Question 59
Solution 59
Question 60
Solution 60

Question 61
Solution 61
Question 62
Solution 62

## Chapter 9 – Continuity Exercise Ex. 9.2

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4

Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11

Question 12
Solution 12

Question 13
Solution 13

Question 14
Solution 14

Question 15
Solution 15

Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22

Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25

Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29

Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32

Question 33
Solution 33

Question 34
Solution 34

Question 35
Solution 35

Question 36
Solution 36

Question 37

Given the
function

Find the
points of discontinuity of the functions f(f(x)).

Solution 37

Question 38

Find all
point of discontinuity of the function

Solution 38

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

## Chapter 9 – Continuity Exercise MCQ

Question 1

a. Discontinuous at only one point

b. Discontinuous exactly at two points

c. Discontinuous exactly at three points

d. None of these

Solution 1

Correct option: (c)

Question 2

If f(x) =|x – a| ϕ (x), where ϕ (x) continuous function, then

a. f'(a+) = ϕ(a)

b. f’ (a) = – ϕ(a)

c. f'(a+) = f'(a)

d. none of these

Solution 2

Correct option: (a), (b)

Question 3

If f(x) = |log10 x|, then at x = 1

a. f(x) is continuous and f'(1+) = log10e

b. f(x) is continuous and f'(1+) = log10e

c. f(x) is continuous and f’ (1) = log10e

d. f(x) is continuous and f'(1)= -log10e

Solution 3

Correct option: (a),(d)

Question 4

Solution 4

Correct option: (c)

Question 5

a. x

b. x except at x = 0

c. x except at x = 1

d. x except at x = 0 and x = 1.

Solution 5

Correct option: (d)

Question 6

Solution 6

Correct option: (c)

Question 7

If f(x) = (x + 1)cot x be continuous at x = 0, then f(0) is equal to

a. 0

b. 1/e

c. e

d. none of these

Solution 7

Correct option: (c)

Question 8

and f(x) is continuous at x = 0, then the value of k is

a. a – b

b. a + b

c. log a + log b

d. none of these

Solution 8

Correct option: (b)

Question 9

a. is continuous at x = 0

b. is not continuous at x = 0

c. is not continuous at x = 0, but can be made continuous at x = 0

d. none of these

Solution 9

Correct option: (b)

Question 10

Then, f(x) is continuous at x = 4 when

a. a = 0, b = 0

b. a = 1, b = 1

c. a = -1, b = 1

d. a = 1, b = -1

Solution 10

Correct option: (d)

Question 11

is continuous at x = 0, then the value of k is

a. 0

b. 1

c. -1

d. e

Solution 11

Correct option: (b)

Question 12

Let f(x) = |x| + |x – 1|, then

a. f(x) is continuous at x = 0, as well as at x = 1

b. f(x) is continuous at x = 0, but not at x = 1

c. f(x) is continuous at x = 1, but not at x = 0

d. none of these

Solution 12

Correct option: (a)

Question 13

Then, f(x) is continuous on the set

a. R

b. R – {1}

c. R – {2}

d. R – {1, 2}

Solution 13

Correct option: (d)

Question 14

Then, f(x) is continuous on the set

Solution 14

Correct option: (c)

Question 15

Solution 15

Correct option: (c)

Question 16

a. a3/2

b. a1/2

c. -a1/2

d. -a3/2

Solution 16

Correct option: (c)

Question 17

a. is discontinuous at finitely many points

b. is continuous everywhere

c.

d. none of these

Solution 17

Correct option: (c)

Question 18

Solution 18

Correct option: (c)

Question 19

a. -1

b. 1

c. 26

d. none of these

Solution 19

Correct option: (d)

Question 20

a. -1

b. -1/2

c. 1/2

d. 1

Solution 20

Correct option: (b)

Question 21

Solution 21

Correct option: (a)

Question 22

a. 1/8

b. 1/4

c. 1/2

d. none of these

Solution 22

Correct option: (a)

Question 23

a. 1

b. 2

c. 3

d. none of these

Solution 23

Correct option:(d)

Question 24

The function f(x) = tan x is discontinuous on the set

Solution 24

Correct option: (c)

Question 25

a. 3

b. 6

c. 9

d. 12

Solution 25

Correct option: (b)

Question 26

Solution 26

Correct option: (b)

Question 27

a. -1

b. 0

c. 13/3

d. 1

Solution 27

Correct option: (a)

Question 28

a. {1}

b. {0, 1}

c. {-1, 1}

d. none of these

Solution 28

Correct option: (a)

Question 29

a. 1

b. 1/2

c. 2

d. none of these

Solution 29

Correct option: (b)

Question 30

a. 0

b. 1

c. 2

d. 3

Solution 30

Correct option: (a)

Question 31

Solution 31

Correct option: (a)

Question 32

a. (2, 2)

b. (3, 1)

c. (4, 0)

d. (5, 2)

Solution 32

Correct option: (d)

Question 33

a. 1

b. 5

c. -1

d. none of these

Solution 33

Correct option: (b)

Question 34

a. 25

b. 50

c. -25

d. none of these

Solution 34

Correct option: (b)

Question 35

a. 0

b. -1

c. 1

d. indeterminate

Solution 35

Correct option: (a)

Question 36

a. 8

b. 1

c. -1

d. none of these

Solution 36

Correct option: (d)

Question 37

Solution 37

Correct option: (c)

Question 38

Solution 38

Correct option: (b)

Question 39

Solution 39

Correct option: (b)

Question 40

a.  x = 1

b.  x = 3

c.  x = 1, 3

d.  none of these

Solution 40

Correct option: (b)

Question 41

a. 13/3

b. 1

c. 0

d. -1

Solution 41

Correct option: (d)

Question 42

Solution 42

Correct option: (a)

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