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NCERT Solutions for class 12 Maths | Chapter 6 - Application of Derivatives

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Free download in PDF Class 12 Maths Chapter 6 Application of Derivatives Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

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(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) = xx 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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