Objective Type Question and Answers On Class 12 Maths Chapter 6

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

View Answer

Answer:cos x

2 If x is real, the minimum value of x² – 8x + 17 is

A -1

B 0

C 1

D 2

View Answer

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

View Answer

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]

View Answer

Answer:[-2, -1]

5 The maximum value of sin x . cos x is

A 1/4

B 1/2

C √2

D 2√2

View Answer

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]

View Answer

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

View Answer

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

View Answer

Answer:x + 5y = 2

9 The curve y – x^1/5 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

View Answer

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

View Answer

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

View Answer

Answer:1/20 radian/sec

12 The tangent to the curve y = e^2x at the point (0, 1) meets x-axis at

A (0, 1)

B (-1/2, 0)

C (2, 0)

D (0, 2

View Answer

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

View Answer

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

View Answer

Answer:4/3 s

15 f(x) =

A an increasing function

B a decreasing function

C an even function

D None of these

View Answer

Answer:an increasing function

16 The maximum value of (1/x)^x is

A e

B e²

C e^1/x

D (1/e)^1/e

View Answer

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|

View Answer

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

View Answer

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

View Answer

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

View Answer

Answer:x + 3y ± 8 = 0

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