RD SHARMA Solutions for Class 12-science Maths Chapter 17 - Increasing and Decreasing Functions

Page / Exercise

Chapter 17 - Increasing and Decreasing Functions Exercise Ex. 17.1

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Chapter 17 - Increasing and Decreasing Functions Exercise Ex. 17.2

Question 1(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(vi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(vi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(viii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(viii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(ix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(ix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(x)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(x)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xvi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xvi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xvii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xvii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xviii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xviii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xx)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xx)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xxi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xxi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xxii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xxii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xxiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xxiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xxiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xxiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xxv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 1(xxv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 1(xxvi)

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

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

Solution 1(xxvi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 1(xxvii)

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 1(xxvii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 1(xxviii)

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 1(xxviii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 39(i)

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 39(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 39(ii)

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 39(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 39(iii)

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 39(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

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

 

Solution 7

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

  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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing FunctionsRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

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

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Question 21

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

 

  1. a = b
  2. a = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
  3. a ≤ Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
  4. a > Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions
Solution 21

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

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

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

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

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

 

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions 

Chapter 17 - Increasing and Decreasing Functions Exercise Ex.17VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Increasing And Decreasing Functions