NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 6

NCERT Solutions for Class 12 Maths Chapter 6 MCQ’s with Answers

NCERT Books are textbooks which are issued & distributed by the National Council of Educational Research and Training (NCERT). NCERT books are important for the schooling system. NCERT Books are available in E-Books. If you are searching for MCQs (Multiple Choice Questions) with Answers of for NCERT Class 12 Mathematics then you have came to right way. CBSE students can also solve NCERT Class 12 Maths 6 Application of Derivatives PDF Download w their preparation level. MCQs are Prepared Based on Latest Exam Patterns. MCQs Questions with Answers for Class 12 Maths Chapter 6 Application of Derivatives are prepared to help students to understand concepts very well. Objective wise Questions 12th class Maths Chapter 6 Application of Derivatives wise PDF over here are available in the following links. Score maximum marks in the exam.

NCERT Maths MCQs for Class 12 Question and Answers Chapter 6 Application of Derivatives PDF

Q1. 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) 10/3cm²/s

Option c – 10√3 cm²/s

Q2. 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

Option a – 126

Q3. 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)

Option b – (3, 9)

Q4. 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)

Option b – (1, 2)

Q5. 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

Option d – 6

Q6. The absolute maximum value of y = x3 – 3x + 2 in 0 ≤ x ≤ 2 is

(a) 4
(b) 6
(c) 2
(d) 0

Option a – 4

Q7. 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

Option c – x + y = 0

Q8. 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) 1/20radian/sec
(c) 20 radiah/sec
(d) 10 radiah/sec

Option b – 1/20radian/sec

Q9. 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

Option c – x + 3y ± 8 = 0

Q10. 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

Option d – 6

Q11. If y = x4 – 10 and if x changes from 2 to 1.99 what is the change in y

(a) 0.32
(b) 0.032
(c) 5.68
(d) 5.968

Option a – 0.32

Q12. 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

Option a – x + 5y = 2

Q13. The points at which the tangents to the curve y = x² – 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).

Option d – (2, 2),(-2, 34).

Q14. 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

Option d – is an increasing function

Q15. 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

Option a – 1 < x < 3

Q16. The function f(x) = tan x – x

(a) always increases
(b) always decreases
(c) sometimes increases and sometimes decreases
(d) never increases

Option a – always increases

Q17. If x is real, the minimum value of x² – 8x + 17 is

(a) -1
(b) 0
(c) 1
(d) 2

Option d – 2

Q18. The function f(x) = 2x³ – 3x² – 12x + 4 has

(a) two points of local maximum
(b) two points of local minimum
(c) one maxima and one minima
(d) no maxima or minima

Option c – one maxima and one minima

Q19. one maxima and one minima

(a) a constant
(b) proportional to the radius
(c) inversely proportional to the radius
(d) inversely proportional to the surface area

Option d – inversely proportional to the surface area

Q20. A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform

(a) rotation
(b) velocity
(c) acceleration
(d) retardation

Option c – acceleration

Q21. The value of b for which the function f (x) = sin x – bx + c is decreasing for x ∈ R is given by

(a) b < 1

(b) b ≥ 1

(c) b > 1
(d) b ≤ 1

Option c – b > 1

Q22. The function f (x) = 1 – x³ – x5 is decreasing for

(a) 1 < x < 5

(b) x < 1

(c) x > 1
(d) all values of x

Option d – all values of x

Q23. Find all the points of local maxima and local minima of the function f(x) = (x – 1)3 (x + 1)2.

(a) 25
(b) 43
(c) 62
(d) 49

Option d – 49

Q24. Find both the maximum and minimum values respectively of 3×4 – 8×3 + 12×2 – 48x + 1 on the interval [1, 4].

(a) -63, 257
(b) 257, -40
(c) 257, -63
(d) 63, -257

Option c – 257, -63

Q25. 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

Option c – isosceles

Q26. Find the area of the largest isosceles triangle having perimeter 18 metres.

(a) 9√3
(b) 8√3
(c) 4√3
(d) 7√3

Option a – 9√3

Q27. The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tant/2 )} at the point ‘t’ is

(a) tan t
(b) cot t
(c) tan t/2
(d) None of these

Option a – tan t

Q28. The two curves x3 – 3xy2 + 5 = 0 and 3x2y – y3 – 7 = 0

(a) cut at right angles
(b) touch each other
(c) cut at an angle 1/3
(d) cut at an angle 2/3

Option a – cut at right angles

Q29. The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point

(a) (0, 1)
(b) (-3, 0)
(c) (-4, 4)
(d) (1, 4)

Option a -(-3, 0)

Q30. 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%

Option a – 1%

We hope that the given NCERT MCQ Questions for Class 12 Mathematics Chapter 6 Application of Derivatives Free Pdf download will help you in gaining knowledge on the subject.

Leave a Reply

Your email address will not be published.