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

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## 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.