# NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 8

## NCERT Solutions for Class 12 Maths Chapter 8 MCQ’s with Answers

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## NCERT Maths MCQs for Class 12 Question and Answers Chapter 8 Application of Integrals PDF

### Q1. Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is

(a) 16π sq.units
(b) 4π sq. units
(c) 32π sq. units
(d) 24π sq. unit

Option b – 4π sq. units

### Q2. Area of the region bounded by the curve y = cos x between x = 0 and x = π is

(a) 2 sq. units
(b) 4 sq, units
(c) 3 sq.units
(d) 1 sq. units

Option a – 2 sq. units

### Q3. The area of the region bounded by the circle x² + y² = 1 is

(a) 2π sq. units
(b) 7π sq. units
(c) 3π sq. units
(d) 4π sq. units

Option a – 7π sq. units

### Q4. The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is

(a) 4 sq. units
(b) sq. units
(c) 6 sq. units
(d) 8 sq, units

Option c – 6 sq. units

### Q5. If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is

(a) 9sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. unjts

Option c – 12 sq. units

### Q6. Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to

(a) 4 sq. units
(b) 6 sq. units
(c) 2 sq. units
(d) 8 sq. units

Option a – 4 sq. units

### Q7. The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is

(a) 1 sq. unit
(b) 2 sq. unit
(c) 2√2 sq. units
(d) 4 sq. units

Option a – 2 sq. units

### Q8. The area bounded by the curve 2x² + y² = 2 is

(a) π sq. units
(b) √2π sq. units
(c) 2sq. units
(d) 2π sq. units

Option a – √2π sq. units

### Q9. Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,

(a) 9 sq. units
(b) 2sq. units
(c) 3 sq. units
(d) None of these

Option d -None of these

### Q10. The area of the region bounded by the line y = | x – 2 |, x = 1, x = 3 and x-axis is

(a) 4 sq. units
(b) 2 sq, units
(c) 3 sq. units
(d) 1 sq. unit

Option d -1 sq. unit

### Q11. The area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5 is

(a) 15/2 sq. units
(b)9/2 sq. units
(c) 3/9sq. units
(d) None of these

Option a – 15/2 sq. units

### Q12. The area enclosed by the parabola y2 = 2x and tangents through the point (-2, 0) is

(a) 3 sq. units
(b) 4 sq. units
(c)4/3 sq. units
(d) 8/3 sq. units

Option a – 8/3 sq. units

### Q13. The area bounded by the curve x2 = 4y = 4y + 4 and line 3x + 4y = 0 is

(a) 25/4sq. units
(b) 125/8 sq. units
(c) 125/16 sq. units
(d) 125/24 sq. units

Option d – 125/24 sq. units

### Q14. The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is

(a) 45/4
(b) 14
(c) 7
(d) none of these

Option a – 45/4

### Q15. The ratio in which the x-axis divides the area of the region bounded by the curves y = x2 – 4x and y = 2x – x2

(a) 4 : 23
(b) 4 : 27
(c) 4 : 19
(d) none of these

Option a – 4:23

### Q16. The area of smaller portion bounded by |y| = -x + 1 and y2 = 4x is

(a) 1 sq. units
(b) 2 sq. units
(c) 3 sq. units
(d) none of these

Option d – none of these

### Q17. Find the area enclosed by the parabola 4y = 3×2 and the line 2y = 3x + 12.

(a) 27 sq. units
(b) 28 sq. units
(c) 54 sq. units
(d) 30 sq. units

Option a – 27 sq. units

### Q18. The area included between the curves x2 = 4by and y2 = 4ax

(a) 16ab sq. units
(b) 16ab/3 sq. units
(c) 4ab sq. units
(d) 16πab sq. units

Option a – 27 sq. units

### Q19. If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is

(a) 9/2sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. units

Option a – 12 sq. units

### Q20. The area bounded by the curve y = x2 + 4x + 5, the axes of coordinates and minimum ordinate is

(a) 3/2sq. units
(b) 4 2/3 sq. units
(c) 4/7sq. units
(d) None of these

Option b – 4 2/3 sq. units

### Q21. The area bounded by the curves y = sin x, y = cos x and x = 0 is

(a) (√2 – 1) sq. units
(b) 1 sq. units
(c) √2 sq. units
(d) (1 + √2) sq. units

Option a – (√2 – 1) sq. units

### Q22. The area included between curves y = x2 – 3x + 2 and y = -x2 + 3x – 2 is

(a) 2/3 sq. units
(b) 7/4 sq. units
(c) 1 sq. units
(d) 1/3 sq. units

Option d – 1/3 sq. units

### Q23. The area bounded by the lines y = |x – 2|, x = 1, x = 3 and the x-axis is

(a) 1 sq. units
(b) 2 sq. units
(c) 3 sq. units
(d) 4 sq. units

Option b – 2 sq. units

### Q24. Area of the smaller region bounded by x2 + y2 = 9 and the line x = 1

(a) (2 – 3 sec-1 3) sq. units
(b) (√8 – 3sec-1 3) sq.units
(c) (9sec-1 3 – √8) sq. units
(d) (sec-1 3 – 3√8) sq.units

Option c – (9sec-1 3 – √8) sq. units

### Q25. The area bounded by the curve x = 3y2 – 9 and the line x = 0, y = 0 and y = 1 is

(a) 8 sq. units
(b) 8/3 sq. units
(c) 3/8 sq. units
(d) 3 sq. units

Option a – 8 sq. units

We hope that the given NCERT MCQ Questions for Class 12 Mathematics Chapter 8 Application of Integrals Free Pdf download will help you in gaining knowledge on the subject.