# Class 12 Mathematics Chapter 6 Application of Derivatives MCQ Questions with Answer

Application of Derivatives Class 12 MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Application of Derivatives Class 12, which will help them all through their board test.

## Application of Derivatives Class 12 MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to Chapter 6 Application of Derivatives. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Application of Derivatives Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Application of Derivatives MCQ with answers given below.

Question 1. The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is
(a) 1
(b) 1/3
(c) 2
(d) 1/2

A

Question 2. 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

A

Question 3. The curve y = x1/5 has at (0, 0)
(a) a vertical tangent (parallel to y-axis)
(b) a horizontal tangent (parallel to x-axis)
(c) an oblique tangent
(d) no tangent

A

Question 4. The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(a) 10p
(b) 12p
(c) 8p
(d) 11p

B

Question 5. A ladder, 5 meter long, standing on 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

B

Question 6. The total revenue in rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. The marginal revenue, when x = 15 is
(a) 116
(b) 96
(c) 90
(d) 126

D

Question 7. The maximum value of (1/x)x is
(a) e
(b) ee
(c) e1/e
(d) (1/e)1/e

C

Question 8. f(x) = xx has a stationary point at
(a) x = e
(b) x=1/ e
(c) x = 1
(d) x = e

B

Question 9. The tangent to the curve given by x = et.cos t, y = et. sint at t = π/4 makes with x-axis an angle
(a) 0
(b) π/4
(c) π/3
(d) π/2

D

Question 10. The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 [NCERT Exemplar]
(a) touch each other
(b) cut at right angle
(c) cut at an angle π/3
(d) cut at an angle π/4

B

Question 11. 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

C

Question 12. The point on the curve y2 = x, where the tangent makes an angle of π/4 with x-axis is
(a) (1/2 , 1/4)
(b) (1/2 , 1/4)
(c) (4, 2)
(d) (1, 1)

B

Question 13. The tangent to the curve y = e2x at the point (0, 1) meets x-axis at
(a) (0, 1)
(b) b(–1/2, 0l
(c) (2, 0)
(d) (0, 2)

B

Question 14. The point on the curve x= 2y which is nearest to the point (0, 5) is
(a) (2√2, 4)
(b) (2√2, 0)
(c) (0, 0)
(d) (2, 2)

A

Question 15. The interval in which the function f given by f(x) = x2 e–x is strictly increasing, is
(a) (– ∞, ∞)
(b) (– ∞, 0)
(c) (2, ∞)
(d) (0, 2)

D

Question 16. The slope of normal to the curve y = 2x2 + 3 sin x at x = 0 is
(a) 3
(b) 1/3
(c) –3
(d) 1/3

D

Question 17. The equation of the normal to the curve y = sinx at (0, 0) is
(a) x = 0
(b) y = 0
(c) x + y = 0
(d) x – y = 0

C

Question 18. The line y = x +1 is a tangent to the curve y= 4x at the point
(a) (1, 2)
(b) (2, 1)
(c) (1, – 2)
(d) (–1, 2)

A

Question 19. The points at which the tangents to the curve y = x3 – 12x + 18 are parallel to x-axis are
(a) (2, –2), (–2, –34)
(b) (2, 34), (–2, 0)
(c) (0, 34), (–2, 0)
(d) (2, 2), (–2, 34)

D

Question 20. If x is real, the minimum value of x2 – 8x + 17 is [NCERT Exemplar]
(a) – 1
(b) 0
(c) 1
(d) 2

C

Question 21. The maximum value of slope of the curve y = – x3 + 3x2 + 12x – 5 is [CBSE 2020 (65/3/1)]
(a) 15
(b) 12
(c) 9
(d) 0

A

Question 22. If the function f(x) = 2x– kx + 5 is increasing on [1, 2], then k lies in the interval
(a) (– ∞, 4)
(b) (4, ∞)
(c) (– ∞, 8)
(d) (8, ∞)

A

Question 23. 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

C

Question 24. The equation of the normal to the curve y = x (2 – x) at the point (2, 0) is
(a) x – 2y = 2
(b) x – 2y + 2 = 0
(c) 2x + y = 4
(d) 2x + y – 4 = 0

A

Question 25. The angle of intersection of the parabolas y2 = 4ax and x2 = 4ay at the origin, is
(a) π/6
(b) π/3
(c) π/2
(d) π/4

C

Question 26. 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

D

Question 27. The approximate value of (33)1/5is
(a) 2.0125
(b) 2.1
(c) 2.01
(d) none of these

A

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Application of Derivatives Class 12 MCQ are ready by the subject specialists themselves.

## Fill in the blanks

Question 1. The rate of change of the area of a circle with respect to its radius r, when r = 3 cm, is_____________ .

6πcm2/cm

Question 2. The slope of the tangent to the curve y = x3 – x at the point (2, 6) is _____________ .

11

Question 3. If f (x) = 1/4x2+ 2x+ 1 , then its maximum value is _____________ .

4/3

Question 4. The maximum value of f (x)=x+1/x , x< 0 is _____________ .

2

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