MCQ On Class 12 Maths Chapter 6 Application of Derivatives

Questions

1 The function f(x) = tan x – x

A always increases

B always decreases

C sometimes increases and sometimes decreases

D never increases

View Answer

Answer:always increases

2 The function f(x) = 2x³ – 3x² – 12x + 4 has

A two points of local maximum

B two points of local minimum

C one maxima and one minima

D no maxima or minima

View Answer

Answer:one maxima and one minima

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3 f(x) = x^x has a stationary point at

A x = e

B x = 1/e

C x = 1

D x = √e

View Answer

Answer:x = 1/e

4 If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

A a constant

B proportional to the radius

C inversely proportional to the radius

D inversely proportional to the surface area

View Answer

Answer:inversely proportional to the surface area

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

A (1, ∞)

B (-1, ∞)

C (0, ∞)

D (-∞, ∞)

View Answer

Answer:(-∞, ∞)

6 If f (x) = x³ – 6x² + 9x + 3 be a decreasing function, then x lies in

A (-∞, -1) ∩ (3, ∞)

B (1, 3)

C (3, ∞)

D None of these

View Answer

Answer:(1, 3)

7 2x³ – 6x + 5 is an increasing function, if

A 0 < x < 1

B -1 < x < 1

C x < -1 or x > 1

D -1 < x < –1/2

View Answer

Answer:x < -1 or x > 1

8 The function f(x) = x + cos x is

A always increasing

B always decreasing

C increasing for certain range of x

D None of these

View Answer

Answer:always increasing

9 The value of b for which the function f (x) = sin x – bx + c is decreasing for x ∈ R is given by

A b < 1

B b ≥ 1

C b > 1

D b ≤ 1

View Answer

Answer:b > 1

10 The function f (x) = 1 – x³ – x5 is decreasing for

A 1 < x < 5

B x < 1

C x > 1

D all values of x

View Answer

Answer:all values of x

11 The function /’defined by f(x) = 4⁴ – 2x + 1 is increasing for

A x < 1

B x > 0

C x < 1/2

D x > 1/2

View Answer

Answer:x > 1/2

12 If f (x) =

A both f (x) and g (x) are increasing functions

B both f (x) and g (x) are decreasing functions

C f(x) is an increasing function

D g (x) is an increasing function

View Answer

Answer:f(x) is an increasing function

13 The length of the longest interval, in which the function 3 sin x – 4 sin³ x is increasing is

A π/3

B π/2

C 3π/2

D π

View Answer

Answer:π

14 The function f(x) = x/logx increases on the interval

A (0, ∞)

B (0, e)

C (e, ∞)

D None of these

View Answer

Answer:(e, ∞)

15 The function f(x) = log (1 + x) –

is increasing on

A (-1, ∞)

B (-∞, 0)

C (-∞, ∞)

D None of these

View Answer

Answer:(-1, ∞)

16 A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform

A rotation

B velocity

C acceleration

D retardation

View Answer

Answer:acceleration

17 The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is

A 126

B 0

C 135

D 160

View Answer

Answer:0

18 Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is

A 0

B 12

C 16

D 32

View Answer

Answer:0

19 Function, f (x) =

is monotonic increasing, if

A λ > 1

B λ < 1

C λ < 4

D λ > 4

View Answer

Answer:λ > 4

20 The position of a point in time Y is given by x = a + bt + ct², y = at + bt². Its acceleration at timet Y is

A b – c

B b + c

C 2b – 2c

View Answer

Answer:

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