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

Questions
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
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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) = Class 12 Maths Application of Derivatives 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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