MCQs Questions for Class 12 Maths Chapter 6 Application of Derivatives

# MCQs Questions for Class 12 Maths Chapter 6 Application of Derivatives

## MCQs Questions for Class 12 Maths Chapter 6 Application of Derivatives

In this 21st century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQ questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

## MCQs Questions for Class 12 Maths Chapter 6 Application of Derivatives

1. If f(x) = (x – 1)(x + 1)2, then the points of local maxima and local minima of the function are
(a) 1, -1, -1/5
(b) 1, -1
(c) 1, -1/5
(d) -1, -1/5

2. The slope of the tangent to the curve y = 2x/(x2 + 1) at (0, 0) is
(a) 1
(b) 0
(c) 3
(d) 2

3. The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area 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

4. The maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x2 is
(a) 25
(b) 49
(c) 62
(d) 43

5. The value of f’(x) is -1 at the point P on a continuous curve y = f(x). Find the angle between the tangent and the curve at P with the positive direction of x-axis.
(a) π/2
(b) 3π/4
(c) π/4
(d) 3π/2

6. 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

7. If y = x3 + x2 + x + 1, then y
(a) has a local minimum
(b) has a local maximum
(c) neither has a local minimum nor local maximum
(d) None of these

8. The differential function of log (x2 + 4) is
(a) 2x/(x2 + 4) dx
(b) 2x/(x2 – 4) dx
(c) -2x/(x2 + 4) dx
(d) -2x/(x2 – 4) dx

9. 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

10. The maximum and minimum values of 3x4 – 8x3 + 12x2 – 48x + 1 on the interval [1, 4] are
(a) -63 and 257
(b) 257 and -40
(c) 257 and -63
(d) 63 and -257

11. The rate of change of the radius of a sphere is 1/2π. If its radius is 5 cm, what will be the rate of change of the surface area of sphere with time?
(a) 10 sq cm
(b) 20 sq cm
(c) 30 sq cm
(d) 40 sq cm

12. The equation of tangent to the curve y (1 + x²) = 2 – x, where it crosses x-axis, is
(a) x + 5y = 2
(b) x – 5y = 2
(c) 5x – y = 2
(d) 5x + y = 2

13. The equation of the normal to the curve y = sin x at (0, 0) is
(a) x = 0
(b) x + y = 0
(c) y = 0
(d) x – y = 0

14. The nature of the function f(x) = x3 – 3x2 + 4x on R is
(a) Increasing
(b) Decreasing
(c) Constant
(d) Increasing and Decreasing

15. 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]

16. The tangent to the curve y = 2x2 -x + 1 is parallel to the line y = 3x + 9 at the point
(a) (2, 3)
(b) (2, -1)
(c) (2, 1)
(d) (1, 2)

17. The interval in which the function f(x) = sin x + cos x is increasing, is
(a) (5π/4, 2π)
(b) [0, π/4) and (5π/4, 2π]
(c) (π/4, -5π/4)
(d) (-π/4, π/4)

18. Which of the following functions is decreasing on (0, π/2)?
(a) cos 2x
(b) tan x
(c) sin x
(d) cos 3x

19. If there is an error of 2% in measuring the length of a simple pendulum, then the percentage error in its period is
(a) 4%
(b) 3%
(c) 2%
(d) 1%