**Find here the NCERT chapter-wise Multiple Choice Questions from Class 12 Mathematics book Chapter 8 Application of Integrals with Answers Pdf free download. This may assist you to understand and check your knowledge about the chapters. Students also can take a free test of the Multiple Choice Questions of Application of Integrals. Each question has four options followed by the right answer. These MCQ Questions are selected supported by the newest exam pattern as announced by CBSE.**

## NCERT MCQ Chapters for Class 12 Mathematics

## Q1. Tangents to the curve x² + y²= 2 at the points (1, 1) and (-1, 1) are

(i) parallel

(ii) perpendicular

(iii) intersecting but not at right angles

(iv) none of these

(ii) perpendicular

## Q2. The equation of the normal to the curves y = sin x at (0, 0) is

(i) x = 0

(ii) x + y = 0

(iii) y = 0

(iv) x – y = 0

(ii) x + y = 0

## Q3. The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are

(i) (2, -4)

(ii) (18, -12)

(iii) (2, 4)

(iv) none of these

(i) (2, -4)

## Q4. The function f(x) = cot^{-1} x + x increases in the interval

(i) (1, ∞)

(ii) (-1, ∞)

(iii) (0, ∞)

(iv) (-∞, ∞)

(iv) (-∞, ∞)

## Q5. The distance ‘s’ metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after

(i) 1 s

(ii) 3/4 s

(iii) 4/3 s

(iv) 4 s

(iii) 43 s

## Q6. A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform

(i) rotation

(ii) velocity

(iii) acceleration

(iv) retardation

(iii) acceleration

## Q7. Find a point on the curve y = (x – 2)². at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

(i) (3, 1)

(ii) (4, 1)

(iii) (6,1)

(iv) (5, 1)

(i) (3, 1)

## Q8. The tangent to the curve y = 2x² -x + 1 is parallel to the line y = 3x + 9 at the point

(i) (2, 3)

(ii) (2, -1)

(iii) (2, 1)

(iv) (1, 2)

(iv) (1, 2)

## Q9. Find the area of the largest isosceles triangle having perimeter 18 metres.

(i) 9√3

(ii) 8√3

(iii) 4√3

(iv) 7√3

(i) 9√3

## Q10. If y = x³ + x² + x + 1, then y

(i) has a local minimum

(ii) has a local maximum

(iii) neither has a local minimum nor local maximum

(iv) None of these

(iii) neither has a local minimum nor local maximum

## Q11. The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is

(i) √3 cm2/s

(ii) 10 cm2/s

(iii) 10√3 cm2/s

(iv) 10/√3 cm2/s

(iii) 10√3 cm2/s

## Q12. Find the approximate value of f(3.02), where f(x) = 3x² + 5x + 3

(i) 45.46

(ii) 45.76

(iii) 44.76

(iv) 44.46

(i) 45.46

## Q13. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

(i) 25

(ii) 43

(iii) 62

(iv) 49

(iv) 49

## Q14. If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is

(i) 1%

(ii) 2%

(iii) 3%

(iv) 4%

(i) 1%

## Q15. Find all the points of local maxima and local minima of the function f(x) = (x – 1)³ (x + 1)²

(i) 1, -1, -1/5

(ii) 1, -1

(iii) 1, -1/5

(iv) -1, -1/5

(i) 1, -1, -1/5

### Q16. 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

(i) 80π cu m/s

(ii) 144π cu m/s

(iii) 80 cu m/s

(iv) 64 cu m/s

(i) 80π cu m/s

## Q17. Area of the region bounded by the curve y = cos x between x = 0 and x = π is

(i) 2 sq. units

(ii) 4 sq, units

(iii) 3 sq.units

(iv) 1 sq. units

(i) 2 sq. units

## Q18. If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.

(i) 2.46π cm³

(ii) 8.62π cm³

(iii) 9.72π cm³

(iv) 7.46π cm³

(iii) 9.72π cm³

## Q19. f(x) = 3x² + 6x + 8, x ∈ R

(i) 2

(ii) 5

(iii) -8

(iv) does not exist

(iv) does not exist

## Q20. The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is

(i) 1 sq. unit

(ii) 2 sq. unit

(iii) 2√2 sq. units

(iv) 4 sq. units

(ii) 2 sq. unit

I Think the given NCERT MCQ Questions for class 12 Maths book Chapter 8 Application of Integrals with Answers Pdf free download will assist you. If you’ve got any queries regarding CBSE Class 12 Maths Application of Integrals MCQs Multiple Choice Questions with Answers, drop a comment below and that we will come back to you soon.

## MCQ Questions for Class 12 Mathematics Chapter wise with Answers

**Lesson 1. Relations and Functions MCQs****Lesson 2. Inverse Trigonometric Functions MCQs****Lesson 3. Matrices MCQs****Lesson 4. Determinants MCQs****Lesson 5. Continuity and Differentiability MCQs****Lesson 6. Application of Derivatives MCQs****Lesson 7. Integrals MCQs****Lesson 8. Application of Integrals MCQs****Lesson 9. Differential Equations MCQs****Lesson 10. Vector Algebra MCQs****Lesson 11. Three Dimensional Geometry MCQs****Lesson 12. Linear Programming MCQs****Lesson 13. Probability MCQs**