MCQ On Class 12 Maths Chapter 6 Application of Derivatives

(1) The function f(x) = tan x – x

[A] always increases

[B] always decreases

[C] sometimes increases and sometimes decreases

[D] never increases

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

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

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

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] (-∞, ∞)

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

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

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

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

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

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

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

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

Answer: π

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

[A] (0, ∞)

[B] (0, e)

[C] (e, ∞)

[D] None of these

Answer: (e, ∞)

(15) The function f(x) = log (1 + x) – is increasing on

[A] (-1, ∞)

[B] (-∞, 0)

[C] (-∞, ∞)

[D] None of these

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

Answer: acceleration

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

[A] 126

[B] 0

[C] 135

[D] 160

Answer: 0

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

[A] 0

[B] 12

[C] 16

[D] 32

Answer: 0

(19) Function, f (x) = is monotonic increasing, if

[A] λ > 1

[B] λ < 1

[C] λ < 4

[D] λ > 4

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

[D]

Answer:

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