Below you will find **MCQ Questions of Chapter 6 Application of Derivatives Class 12 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives with answers

1. If the tangent at P of the curve y^{2} = x^{3} intersects the curve again at Q and the straight lines OP, OQ make angles a, b with the x–axis, where `O' is the origin, then tan a/tan b has the value equal to

(a) –1

(b) –2

(c) 2

(d) √2

► (b) –2

2. The maximum value of (1/x)^{x} is

(a) (1/e)^{1/e}

(b) (e)^{2/e}

(c) (e)^{-1/e}

(d) (e)^{1/e}

► (d) (e)^{1/e}

3. The global maximum and global minimum of f (x) = 2x^{3} - 9x^{2} + 12x + 6 in [0, 2]

(a) (11, 6)

(b) ( 6,11)

(c) ( -6,11)

(d) ( -11, 6)

► (a) (11, 6)

4. The maximum and the minimum value of 3x^{4} – 8x^{3} + 12x^{2} – 48x + 1 on the interval [1,4]

(a) -40,257

(b) -48,258

(c) -49,258

(d) -58,257

► (a) -40,257

5. Find the maximum and minimum values of f (x) = 2x^{3} – 24x + 107 in the interval [1, 3].

(a) 89, 69

(b) 89, 75

(c) 59, 56

(d) 89, -9

► (b) 89, 75

6. Find the approximate value of f(10.01) where f(x) = 5x2 +6x + 3

(a) 564.06

(b) 564.01

(c) 563.00

(d) 563.01

► (a) 564.06

7. The radius of air bubble is increasing at the rate of 0. 25 cm/s. At what rate the volume of the bubble is increasing when the radius is 1 cm.

(a) 4π cm^{3}/s

(b) 22π cm^{3}/s

(c) 2π cm^{3}/s

(d) π cm^{3}/s

► (d) π cm^{3}/s

8. The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 5x^{2} + 22x + 35. Find the marginal revenue, when x = 7, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant

(a) Rs 7

(b) Rs 127

(c) Rs 92

(d) Rs 48

► (c) Rs 92

9. The critical points of

(a) (3, 4)

(b) (5, 6)

(c) (1, 2)

(d) (0, 5)

► (c) (1, 2)

10. The volume of cube is increasing at the constant rate of 3 cm^{3}/s. Find the rate of change of edge of the cube when its edge is 5 cm.

(a) 25 cm^{3}/sec

(b) 25 cm/s

(c) 1/25 cm/s

(d) 1/25 cm^{3}/s

► (c) 1/25 cm/s

11. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24 x – 18x^{2}

(a) 56

(b) 49

(c) 23

(d) 89

► (b) 49

12. If the area of the triangle included between the axes and any tangent to the curve x^{n} y = a^{n} is constant, then n is equal to

(a) 1

(b) 2

(c) 3/2

(d) 1/2

► (a) 1

13. The x–intercept of the tangent at any arbitrary point of the curve is proportional to

(a) Square of the abscissa of the point of tangency

(b) Square root of the abscissa of the point of tangency

(c) Cube of the abscissa of the point of tangency

(d) Cube root of the abscissa of the point of tangency.

► (c) Cube of the abscissa of the point of tangency

14. The least value of k for which the function f(x) = x^{2} + kx + 1 is a increasing function in the interval 1 < x < 2

(a) -1

(b) -2

(c) 1

(d) 3

► (b) -2

15. The value of ‘c’ in Lagrange’s mean value theorem for f (x) = x (x- 2)^{2} in [0, 1]

(a) 0

(b) 2

(c) 2/3

(d) 3/2

► (c) 2/3

16. If the function has maximum at x =-3, then the value of ‘a’ is

(a) 54

(b) -54

(c) 10

(d) -10

► (b) -54

17. The height of a cylinder is equal to its radius. If an error of 1 % is made in its height. Then the percentage error in its volume is

(a) 1

(b) 2

(c) 3

(d) 4

► (c) 3

18. The number of stationary points of f (x) = sin x in [0,2π] are

(a) 0

(b) 1

(c) 2

(d) 3

► (c) 2

19. The maximum value of f (x) = sin x in the interval [π,2π] is

(a) 6

(b) 0

(c) -2

(d) -4

► (b) 0

20. At (0, 0), the curve y^{2} = x^{3} + x^{2}

(a) Touches X-axis

(b) Bisects the angle between the axes

(c) Makes an angle of 60° with OX

(d) None of these

► (b) Bisects the angle between the axes

21. If the subnormal at any point on y = a1 – n x^{n} is of constant length, then the value of n is

(a) 1

(b) 1/2

(c) 2

(d) –2

► (b) 1/2

22. The points on the curve at which the tangent is perpendicular to x-axis are

(a) (1, 1) only

(b) (±1,1)

(c) (1, ±1)

(d) (-1,1) only

► (b) (±1,1)

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Application of Derivatives MCQ Questions** will help you in practising more and more questions in less time.