Check the below NCERT MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Application of Derivatives Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is

(a) scalene

(b) equilateral

(c) isosceles

(d) None of these

## Q.2 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

## Q.3 Find the area of the largest isosceles triangle having perimeter 18 metres.

(a) 9√3

(b) 8√3

(c) 4√3

(d) 7√3

## Q.4 The equation of the normal to the curves y = sin x at (0, 0) is

(a) x = 0

(b) x + y = 0

(c) y = 0

(d) x – y = 0

## Q.5 Let the f: R → R be defined by f (x) = 2x + cos x, then f

(a) has a minimum at x = 3t

(b) has a maximum, at x = 0

(c) is a decreasing function

(d) is an increasing function

## Q.6 The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is

(a) 80π cu m/s

(b) 144π cu m/s

(c) 80 cu m/s

(d) 64 cu m/s

## Q.7 The rate of change of the area of a circle with respect to its radius r at r = 6 cm is:

(a) 10π

(b) 12π

(c) 8π

(d) 11π

## Q.8 A cylindrical tank of radius 10 mis being filled with wheat at the rate of 314 cubic m per minute. Then the depth of the wheat is increasing at the rate of:

(a) 1 m/minute

(b) 0 × 1 m/minute

(c) 1 × 1 m/minute

(d) 0 × 5 m/minute

## Q.9 The function f(x) = tan x – x

(a) always increases

(b) always decreases

(c) sometimes increases and sometimes decreases

(d) never increases

## Q.10 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

## Q.11 The point(s) on the curve y = x², at which y-coordinate is changing six times as fast as x-coordinate is/are

(a) (2, 4)

(b) (3, 9)

(c) (3, 9), (9, 3)

(d) (6, 2)

## Q.12 The equation of the normal to the curve y = sin x at (0, 0) is

(a) x = 0

(b) y = 0

(c) x + y = 0

(d) x – y = 0

## Q.13 The side of an equilateral triangle is increasing at the rate of 2 cm/s. The rate at which area increases when the side is 10 is

(a) 10 cm²/s

(b) √3 cm²/s

(c) 10√3 cm²/s

(d) 103cm²/s

## Q.14 The real number k for which the equation 2x³ + 3x + k = 0 has two distinct real roots in [0,1]:

(a) lies between 2 and 3

(b) lies between -1 and 0

(c) does not exist

(d) lies between 1 and 2

## Q.15 If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is

(a) 1%

(b) 2%

(c) 3%

(d) 4%

## Q.16 The total revenue in ₹ received from the sale of x units of an article is given by R(x) = 3x² + 36x + 5. The marginal revenue when x = 15 is (in ₹ )

(a) 126

(b) 116

(c) 96

(d) 90

## Q.17 If f and g are differentiable functions on [0, 1] satisfying f(0) = 2 = g(l), g(0) = 0 and f(1) = 6, then for some c ∈ ] 0, 1 [:

(a) 2f'(c) = 3g'(c)

(b) f'(c) = g'(c)

(c) f'(c) = 2g'(c)

(d) 2f'(c) = g'(c)

## Q.18 The equation of the normal to the curve y = sin x at (0, 0) is

(a) x = 0

(b) y = 0

(c) x + y = 0

(d) x – y = 0

## Q.19 The line y = x + 1 is a tangent to the curve y² = 4x at the point

(a) (-1, 2)

(b) (1, 2)

(c) (1, -2)

(d) (2, 1)

## Q.20 If the curves 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

## Q.21 Twenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is:

(a) 25

(b) 30

(c) 12.5

(d) 10