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

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) Which of the following functions is decreasing on(0, π/2)?
[A] sin 2x
[B] tan x
[C] cos x
[D] cos 3x
Answer: cos x
(2) If x is real, the minimum value of x² – 8x + 17 is
[A] -1
[B] 0
[C] 1
[D] 2
Answer: 2
(3) y = x (x – 3)² decreases for the values of x given by
[A] 1 < x < 3
[B] x < 0
[C] x > 0
[D] 0 < x < 3/2
Answer: 1 < x < 3
(4) The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is
[A] [-1, ∞]
[B] [-2, -1]
[C] [-∞, -2]
[D] [-1, 1]
Answer: [-2, -1]
(5) The maximum value of sin x . cos x is
[A] 1/4
[B] 1/2
[C] √2
[D] 2√2
Answer: 1/2
(6) The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly
[A] increasing in (π, 3π/2)
[B] decreasing in (π/2, π)
[C] decreasing in [−π/2,π/2]
[D] decreasing in [0, π/2]
Answer: decreasing in [−π/2,π/2]
(7) The slope of tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, -1) is
[A] 22/7
[B] 6/7
[C] −6/7
[D] -6
Answer: −6/7
(8) The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:
[A] x + 5y = 2
[B] x – 5y = 2
[C] 5x – y = 2
[D] 5x + y = 2
Answer: x + 5y = 2
(9) The curve y – x1/5 at (0, 0) has
[A] a vertical tangent (parallel to y-axis)
[B] a horizontal tangent (parallel to x-axis)
[C] an oblique tangent
[D] no tangent
Answer: a horizontal tangent (parallel to x-axis)
(10) If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is
[A] 1
[B] 0
[C] -6
[D] 6
Answer: 6
(11) A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is
[A] 1/10 radian/sec
[B] 1/20 radian/sec
[C] 20 radiah/sec
[D] 10 radiah/sec
Answer: 1/20 radian/sec
(12) The tangent to the curve y = e2x at the point (0, 1) meets x-axis at
[A] (0, 1)
[B] (-1/2, 0)
[C] (2, 0)
[D] (0, 2
Answer: (-1/2, 0)
(13) At x = 5π/6, f (x) = 2 sin 3x + 3 cos 3x is
[A] maximum
[B] minimum
[C] zero
[D] neither maximum nor minimum
Answer: neither maximum nor minimum
(14) The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after
[A] 1 s
[B] 3/4 s
[C] 4/3 s
[D] 4 s
Answer: 4/3 s
(15) f(x) = is
[A] an increasing function
[B] a decreasing function
[C] an even function
[D] None of these
Answer: an increasing function
(16) The maximum value of (1/x)x is
[A] e
[B] e²
[C] e1/x
[D] (1/e)1/e
Answer: (1/e)1/e
(17) The function which is neither decreasing nor increasing in (π/2, 3π/2) is
[A] cosec x
[B] tan x
[C] x²
[D] |x – 1|
Answer: tan x
(18) The interval in which the function y = x³ + 5x² – 1 is decreasing, is
[A] (0, 1/3)
[B] (0, 10)
[C] (−10/3, 0)
[D] None of these
Answer: (−10/3, 0)
(19) The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is
[A] 10 cm²/s
[B] √3 cm²/s
[C] 10√3 cm²/s
[D] 10/3 cm²/s
Answer: 10√3 cm²/s
(20) The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is
[A] 3x – y = 8
[B] 3x + y + 8 = 0
[C] x + 3y ± 8 = 0
[D] x + 3y = 0
Answer: x + 3y ± 8 = 0

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