Question 1. If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and xaxis is

 (a) 92 sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. units
 (a) 92 sq. units
Answer: (c) 12 sq. units
Question 2. The area bounded by the curve y = x^{2} + 4x + 5, the axes of coordinates and minimum ordinate is

 (a) 323 sq. units
(b) 423 sq. units
(c) 523 sq. units
(d) None of these
 (a) 323 sq. units
Answer: (b) 423 sq. units
Question 3. The area of the ellipse x242+y292=1 is

 (a) 6π sq. units
(b) π(a2+b2)4 sq. units
(c) p(a + b) sq. units
(d) none of these
 (a) 6π sq. units
Answer: (d) none of these
Question 4. The area bounded by the curve 2x^{2} + y^{2} = 2 is

 (a) π sq. units
(b) √2π sq. units
(c) π2 sq. units
(d) 2π sq. units
 (a) π sq. units
Answer: (b) √2π sq. units
Question 5. Area of the ellipse x2a2+y2b2=1 is

 (a) 4πab sq.units
(b) 2πab sq.units
(c) πab sq.units
(d) πab2 sq.units
 (a) 4πab sq.units
Answer: (c) πab sq.units
Question 6. Determine the area under the curve y=a2−x2−−−−−−√ included between the lines x = 0 and x = a.

 (a) πaa4
(b) πa34
(c) πa28
(d) None of these
 (a) πaa4
Answer: (a) πaa4
Question 7. The area enclosed by curve x225+y216=1 is

 (a) 10π sq. units
(b) 20π sq. units
(c) 5π sq. units
(d) 4π sq. units
 (a) 10π sq. units
Answer: (b) 20π sq. units
Question 8. The area bounded by the curve y = x^{2} – 1 and the straight line x + y = 3 is

 (a) 92 sq. units
(b) 4 sq. units
(c) 717√2 sq. units
(d) 1717√6 sq. units
 (a) 92 sq. units
Answer: (d) 1717√6 sq. units
Question 9. The area of the region R = ((x, y) : x ≤ y and x^{2} + y^{2} ≤ 1) is

 (a) 3π8 sq. units
(b) 5π8 sq. units
(c) π2 sq. units
(d) π8 sq. units
 (a) 3π8 sq. units
Answer: (c) π2 sq. units
Question 10. The area enclosed between the curve y^{2} = 4x and the line y = x is

 (a) 83 sq. units
(b) 43 sq. units
(c) 23 sq. units
(d) 12 sq. units
 (a) 83 sq. units
Answer: (a) 83 sq. units
Important mcq notes 12th math chapter 8
Question 11. The area bounded by the lines y = x – 2, x = 1, x = 3 and the xaxis is

 (a) 1 sq. units
(b) 2 sq. units
(c) 3 sq. units
(d) 4 sq. units
 (a) 1 sq. units
Answer: (b) 2 sq. units
Question 12. Area of the region bounded by the curve y = x^{2} and the line y = 4 is

 (a) 113 sq. units
(b) 323 sq. units
(c) 433 sq. units
(d) 473 sq. units
 (a) 113 sq. units
Answer: (b) 323 sq. units
Question 13. Area of the smaller region bounded by x^{2} + y^{2} = 9 and the line x = 1 is

 (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
 (a) (2 – 3 sec^{1} 3) sq. units
Answer: (c) (9sec^{1} 3 – √8) sq. units
Question 14. The area bounded by the curve y^{2} = x, line y = 4 and yaxis is

 (a) 163 sq. units
(b) 643 sq. units
(c) 7√2 sq. units
(d) none of these
 (a) 163 sq. units
Answer: (b) 643 sq. units
Question 15. The area bounded by the curve x = 3y^{2} – 9 and the line x = 0, y = 0 and y = 1 is

 (a) 8 sq. units
(b) 83 sq. units
(c) 38 sq. units
(d) 3 sq. units
 (a) 8 sq. units
Answer: (a) 8 sq. units
Question 16. Area bounded by the curve y^{2} = 16x and line y = mx is 23 then m is equal to

 (a) 3
(b) 4
(c) 1
(d) 2
 (a) 3
Answer: (b) 4
Question 17. Find the area enclosed by parabola y^{2} = x and the line y + x = 2 and the xaxis.

 (a) 56 sq. units
(b) 76 sq. units
(c) 67 sq. units
(d) 47 sq. units
 (a) 56 sq. units
Answer: (b) 76 sq. units
Question 18. The area bounded by the curve x^{2} + y^{2} = 1 and 1st quadrant is

 (a) π4 sq.units
(b) π2 sq. units
(c) π3 sq.units
(d) π6 sq.units
 (a) π4 sq.units
Answer: (a) π4 sq.units
Question 19. Area bounded by the curve y = cos x between x = 0 and x = 3π2 is

 (a) 1 sq. units
(b) 2 sq. units
(c) 3 sq. units
(d) 4 sq. units
 (a) 1 sq. units
Answer: (c) 3 sq. units
Question 20. The area of the region bounded by the curve y=4−x2−−−−−√ and xaxis is

 (a) 8π sq. units
(b) 2π sq. units
(c) 16π sq. units
(d) 6π sq. units
 (a) 8π sq. units
Answer: (b) 2π sq. units
Question 21. The area enclosed by the curve y = √x and x = √y , the circle x^{2} + y^{2} = 2 above the xaxis is

 (a) π4 sq. units
(b) 3π2 sq. units
(c) π sq. units
(d) π2 sq. units
 (a) π4 sq. units
Answer: (d) π2 sq. units
Bihar Board most mcq solution 12th math chapter 8
Question 22. The ratio in which the xaxis divides the area of the region bounded by the curves y = x^{2} – 4x and y = 2x – x^{2}

 (a) 4 : 23
(b) 4 : 27
(c) 4 : 19
(d) none of these
 (a) 4 : 23
Answer: (a) 4 : 23
Question 23. Area bounded by the lines y = x and y = 1 – x – 1 is equal to

 (a) 4 sq. units
(b) 6 sq. units
(c) 2 sq. units
(d) 8 sq. units
 (a) 4 sq. units
Answer: (a) 4 sq. units
Question 24. The area bounded by the lines y = x – 1 and y = 3 – x is

 (a) 2 sq. units
(b) 3 sq. units
(c) 4 sq. units
(d) 6 sq. units
 (a) 2 sq. units
Answer: (c) 4 sq. units
Question 25. The area bounded by the line y = 2x – 2, y = x and xaxis is given by

 (a) 92 sq. units
(b) 436 sq. units
(c) 356 sq. units
(d) None of these
 (a) 92 sq. units
Answer: (d) None of these
Question 26. The area of smaller portion bounded by y = x + 1 and y^{2} = 4x is

 (a) 1 sq. units
(b) 2 sq. units
(c) 3 sq. units
(d) none of these
 (a) 1 sq. units
Answer: (d) none of these
Question 27. The area lying above xaxis and included between the circle x^{2} + y^{2} = 8x and inside of parabola y^{2} = 4x is

 (a) 13 (2 + 3π) sq. units
(b) 23 (4 + 3π) sq. units
(c) (6 + 3π) sq. units
(d) 43 (8 + 3π) sq. units
 (a) 13 (2 + 3π) sq. units
Answer: (d) 43 (8 + 3π) sq. units
Question 28. Find the area enclosed by the parabola 4y = 3x^{2} and the line 2y = 3x + 12.

 (a) 27 sq. units
(b) 28 sq. units
(c) 54 sq. units
(d) 30 sq. units
 (a) 27 sq. units
Answer: (a) 27 sq. units
Question 29. The area included between the curves x^{2} = 4by and y^{2} = 4ax

 (a) 16ab sq. units
(b) 16ab3 sq. units
(c) 4ab sq. units
(d) 16πab sq. units
 (a) 16ab sq. units
Answer: (b) 16ab3 sq. units
Question 30. Area of the region between the curves x^{2} + y^{2} = π^{2}, y = sin x and yaxis in first quadrant is

 (a) (π3−84) sq. units
(b) (π3−48) sq. units
(c) (π2−84) sq. units
(d) (π2−48) sq. units
 (a) (π3−84) sq. units
Answer: (a) (π3−84) sq. units
Question 31. The area bounded by the curves x^{2} + y^{2} = 9 and y^{2} = 8x is

 (a) 0 sq. units
(b) (22√3+9π2−9sin−113) sq. units
(c) 16π sq. units
(d) None of these
 (a) 0 sq. units
Answer: (b) (22√3+9π2−9sin−113) sq. units
Question 32. 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
 (a) (√2 – 1) sq. units
Answer: (a) (√2 – 1) sq. units
BSEB 12th math chapter 8 most mcq solution
Question 33. The area common to the circle x^{2} + y^{2} = 16a^{2} and the parabola y^{2} = 6ax is

 (a) 4a23(4π−3–√) sq. units
(b) 4a23(8π−3) sq. units sq. units
(c) 4a23(4π+3–√) sq. units
(d) None of these
 (a) 4a23(4π−3–√) sq. units
Answer: (c) 4a23(4π+3–√) sq. units
Question 34. The area included between curves y = x^{2} – 3x + 2 and y = x^{2} + 3x – 2 is

 (a) 16 sq. units
(b) 12 sq. units
(c) 1 sq. units
(d) 13 sq. units
 (a) 16 sq. units
Answer: (d) 13 sq. units
Question 35. The area bounded by x = – 4y^{2} and x – 1 = 5y^{2} is

 (a) 1 sq. unit
(b) 23 sq. units
(c) 23 sq. units
(d) 2 sq. units
 (a) 1 sq. unit
Answer: (c) 23 sq. units
Question 36. The area bounded by the curves y=−4−x2−−−−−√, x^{2} = √2y and x = y is

 (a) (π+13) sq. units
(b) (π−13) sq. units
(c) (π+23) sq. units
(d) (π−23) sq. units
 (a) (π+13) sq. units
Answer: (a) (π+13) sq. units
Question 37. The area common to the ellipses x2a2+y2b2=1 and x2b2+y2a2=1, 0 < b < a is

 (a) (a+b)2tan−1ba
(b) (a+b)2tan−1ab
(c) 4abtan−1ba
(d) 4abtan−1ab
 (a) (a+b)2tan−1ba
Answer: (c) 4abtan−1ba
Question 38. The area enclosed by the parabola y^{2} = 2x and tangents through the point (2, 0) is

 (a) 3 sq. units
(b) 4 sq. units
(c) 43 sq. units
(d) 83 sq. units
 (a) 3 sq. units
Answer: (d) 83 sq. units
Question 39. The area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5 is

 (a) 152 sq. units
(b) 92 sq. units
(c) 132 sq. units
(d) None of these
 (a) 152 sq. units
Answer: (a) 152 sq. units
Question 40. The area bounded by the curves x + 2y^{2} = 0 and x + 3y^{2} = 1 is

 (a) 1 sq. units
(b) 13 sq. units
(c) 23 sq. units
(d) 43 sq. units
 (a) 1 sq. units
Answer: (d) 43 sq. units
Question 41. The area bounded by y=(2x)1/2 and x=(2y)1/2 is

 (a) 43 sq. units
(b) 132 sq. units
(c) 125 sq. units
(d) 425 sq. units
 (a) 43 sq. units
Answer: (a) 43 sq. units
Question 42. The area of the region {(x, y) : y^{2} = x, x^{2} + y^{2} = 2} is

 (a) (π4−13) sq. units
(b) (π4+13) sq. units
(c) (π4−16) sq. units
(d) (π2+13) sq. units
 (a) (π4−13) sq. units
Answer: (d) (π2+13) sq. units
Question 43. The area of the circle 4x^{2} + 4y^{2} = 9 which is interior to the parabola x^{2} = 4y is

 (a) 2√6+94sin−1(22√3) sq. units
(b) 2√6−14sin−1(22√3) sq. units
(c) 32 sq. units
(d) 72 sq. units
 (a) 2√6+94sin−1(22√3) sq. units
Answer: (a) 2√6+94sin−1(22√3) sq. units
Question 44. The area bounded by the curve x^{2} = 4y = 4y + 4 and line 3x + 4y = 0 is


 (a) 254 sq. units
(b) 1258 sq. units
(c) 12516 sq. units
(d) 12524 sq. units
 (a) 254 sq. units

Answer: (d) 12524 sq. units
Question 45. The area enclosed between the graph of y = x^{3} and the lines x = 0, y = 1, y = 8 is

 (a) 454
(b) 14
(c) 7
(d) none of these
 (a) 454
Answer: (a) 454
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