RD Sharma Solution CLass 12 Mathematics Chapter 17 Increasing and Decreasing Functions

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

Chapter 17 – Increasing and Decreasing Functions Exercise Ex. 17.2

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

Find the interval in
which the following function is increasing or decreasing.

f(x) = 3x4 4x3 12x2 + 5

Solution 26

Question 27

Find the interval in
which the following function is increasing or decreasing.

Solution 27

Question 28

Find the interval in
which the following function is increasing or decreasing.

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

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

Question 63

Solution 63

Question 64

Solution 64

Question 65

Solution 65

Question 66

Find the interval in
which f(x) is increasing or
decreasing:

Solution 66

Question 67

Find the interval in
which f(x) is increasing or
decreasing:

Solution 67

Question 68

Find the interval in
which f(x) is increasing or
decreasing:

Solution 68

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

Chapter 17 – Increasing and Decreasing Functions Exercise MCQ

Question 1

The interval of increase of the function f(x)=x – ex + tan (2π/7) is

1. (0, ∞)
2. (-∞, 0)
3. (1, ∞)
4. (-∞, 1)
Solution 1

Correct option: (b)

Question 2

The function f(x) = cot-1x + x increases in the interval

1. (1, ∞)
2. (-1, ∞)
3. (-∞, ∞)
4. (0, ∞)
Solution 2

Correct option: (c)

Question 3

The function f(x)=xx decreases on the interval

1. (0, e)
2. (0, 1)
3. (0, 1/e)
4. (1/e, e)
Solution 3

Correct option: (c)

Question 4

The function f(x)=2 log (x – 2) – x2+4x+1 increases on the interval

1. (1, 2)
2. (2, 3)
3. (1, 3)
4. (2, 4)
Solution 4

Correct option:(b)

Question 5

If the function f(x) = 2x2 – kx + 5 is increasing on [1, 2], then k lies in the interval

1. (-∞, 4)
2. (4, ∞)
3. (-∞, 8)
4. (8, ∞)
Solution 5

Correct option: (a)

Question 6

Let f(x)= x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then a and b satisfy

1. a2 – 3b – 15 > 0
2. a2 – 3b + 15 > 0
3. a2 – 3b + 15 < 0
4. a > 0 and b > 0

Solution 6

Correct option: (c)

Question 7

1. even and increasing
2. odd and increasing
3. even and decreasing
4. odd and decreasing

Solution 7

Correct option: (b)

Question 8

If the function f(x)= 2 tan x + (2a + 1) loge|sec x|+ (a-2) x is increasing on R, then

1. a ∈ (1/2, ∞)
2. a ∈ (-1/2, 1/2)
3. a = 1/2
4. a ∈ R

Solution 8

Correct option: (c)

Question 9

1. increasing on (0, π/2)
2. decreasing on (0, π/2)
3. increasing on (0, π/4) and decreasing on (π/4, π/2)
4. None of these

Solution 9

Correct option: (a)

Question 10

Let f(x) = x3 – 6x2 + 15x + 3. Then,

1. f(x) > 0 for all x ∈ R
2. f(x) > f(x + 1) for all x ∈ R
3. f(x) is invertible
4. f(x) < 0 for all x ∈ R
Solution 10

Correct option: (c)

Question 11

The function f(x) = x2e-x is monotonic increasing when

1. x ∈ R – [0, 2]
2. 0 < x < 2
3. 2 < x < ∞
4. x < 0
Solution 11

Correct option: (b)

Question 12

The function f(x) = cos x – 2 λ x is monotonic decreasing when

1. λ > 1/2
2. λ < 1/2
3. λ < 2
4. λ > 2
Solution 12

Correct option: (a)

Question 13

In the interval (1, 2), function f(x)= 2| x – 1|+ 3|x – 2| is

1. monotonically increasing
2. monotonically decreasing
3. not monotonic
4. constant

Solution 13

Correct option: (b)

Question 14

Function f(x) = x3 – 27x + 5 is monotonically increasing when

1. x < -3
2. |x| > 3
3. x ≤ -3
4. |x| ≥ 3
Solution 14

Correct option: (d)

Question 15

Function f(x) = 2x3 – 9x2 + 12x + 29 is monotonically decreasing when

1. x < 2
2. x > 2
3. x > 3
4. 1 < x < 2
Solution 15

Correct option: (d)

Question 16

If the function f(x) = kx3 – 9x2 + 9x + 3 is monotonically increasing in every interval, then

1. k < 3
2. k ≤ 3
3. k > 3
4. k > 3
Solution 16

Correct option: (c)

Question 17

1. x > 0
2. x < 0
3. x ∈ R
4. x ∈ R – {0}
Solution 17

Correct option: (c)

Question 18

Function f(x) = |x|-|x – 1| is monotonically increasing when

1. x < 0
2. x > 1
3. x < 1
4. 0 < x < 1
Solution 18

Correct option: (d)

Question 19

Every invertible function is

1. monotonic function
2. constant function
3. identity function
4. not necessarily monotonic function
Solution 19

Correct option: (a)

Every invertible function is always monotonic function.

Question 20

In the interval (1, 2), function f(x) = 2|x – 1| + 3|x – 2| is

1. increasing
2. decreasing
3. constant
4. none of these
Solution 20

Correct option: (b)

Question 21

If the function f(x) = cos|x| – 2ax + b increases along the entire number scale, then

1. a = b
2. a =
3. a ≤
4. a >
Solution 21

Correct option: (c)

Question 22

1. strictly increasing
2. strictly decreasing
3. neither increasing nor decreasing
4. none of these
Solution 22

Correct option: (a)

Question 23

1. λ < 1
2. λ > 1
3. λ < 2
4. λ > 2
Solution 23

Correct option: (d)

Question 24

Function f(x) = ax is increasing on R, if

1. a > 0
2. a < 0
3. 0 < a < 1
4. a > 1
Solution 24

Correct option: (d)

Question 25

Function f(x) = loga x is increasing on R, if

1. 0 < a < 1
2. a > 1
3. a < 1
4. a > 0
Solution 25

Correct option: (b)

Question 26

Let ϕ(x) = f(x) + f(2a – x) and f”(x) > 0 for all x [0, a]. Then, ϕ(x)

1. increases on [0, a]
2. decreases on [0, a]
3. increases on [-a, 0]
4. decreases on [a, 2a]
Solution 26

Correct option: (b)

Question 27

If the function f(x) = x2 – kx + 5 is increasing on [2, 4], them

1. k ∈ (2, ∞)
2. k ∈ (-∞, 2)
3. k ∈ (4, ∞)
4. k ∈ (-∞, 4)
Solution 27

Correct option: (d)

Question 28

The function f(x) = -x/2 + sin x defined on [-π/3, π/3] is

1. increasing
2. decreasing
3. constant
4. none of these
Solution 28

Correct option: (a)

Question 29

If the function f(x) = x3 – 9k x2 + 27x + 30 is increasing on R, then

1. -1 ≤ k < 1
2. K < -1 or k > 1
3. 0 < k < 1
4. -1 < k < 0
Solution 29

Correct option: (a)

NOTE: Option (a) should be -1 < k < 1.

Question 30

The function f(x) = x9 + 3x7 + 64 is increasing on

(a) R

(b) (-∞, 0)

(c) (0, )

(d) R0

Solution 30

Correct option: (a)

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