12th Math chapter 8: full solution, notes, MCQ, & free PDF | Bihar board

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12th Math chapter 8 Bihar board with NCERT-Details & Highlights

name of content	12th Math chapter 8 full solution
content	Math objective type MCQ question with answer
name of subjects	class 12 Math
important for exam	Bihar board & other state board
pattern & Level	NCERT & State level question

12th Math chapter 8 all objective solutions – download PDF

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

• • (a) 92 sq. units
    (b) 8 sq. units
    (c) 12 sq. units
    (d) 4 sq. units

Answer: (c) 12 sq. units

Question 2. The area bounded by the curve y = x² + 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

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

Answer: (d) none of these

Question 4. The area bounded by the curve 2x² + y² = 2 is

• • (a) π sq. units
    (b) √2π sq. units
    (c) π2 sq. units
    (d) 2π 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

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

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

Answer: (b) 20π sq. units

Question 8. The area bounded by the curve y = x² – 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

Answer: (d) 1717√6 sq. units

Question 9. The area of the region R = ((x, y) : |x| ≤ |y| and x² + y² ≤ 1) is

• • (a) 3π8 sq. units
    (b) 5π8 sq. units
    (c) π2 sq. units
    (d) π8 sq. units

Answer: (c) π2 sq. units

Question 10. The area enclosed between the curve y² = 4x and the line y = x is

• • (a) 83 sq. units
    (b) 43 sq. units
    (c) 23 sq. units
    (d) 12 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 x-axis is

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

Answer: (b) 2 sq. units

Question 12. Area of the region bounded by the curve y = x² and the line y = 4 is

• • (a) 113 sq. units
    (b) 323 sq. units
    (c) 433 sq. units
    (d) 473 sq. units

Answer: (b) 323 sq. units

Question 13. Area of the smaller region bounded by x² + y² = 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

Answer: (c) (9sec^-1 3 – √8) sq. units

Question 14. The area bounded by the curve y² = x, line y = 4 and y-axis is

• • (a) 163 sq. units
    (b) 643 sq. units
    (c) 7√2 sq. units
    (d) none of these

Answer: (b) 643 sq. units

Question 15. 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) 83 sq. units
    (c) 38 sq. units
    (d) 3 sq. units

Answer: (a) 8 sq. units

Question 16. Area bounded by the curve y² = 16x and line y = mx is 23 then m is equal to

• • (a) 3
    (b) 4
    (c) 1
    (d) 2

Answer: (b) 4

Question 17. Find the area enclosed by parabola y² = x and the line y + x = 2 and the x-axis.

• • (a) 56 sq. units
    (b) 76 sq. units
    (c) 67 sq. units
    (d) 47 sq. units

Answer: (b) 76 sq. units

Question 18. The area bounded by the curve x² + y² = 1 and 1st quadrant is

• • (a) π4 sq.units
    (b) π2 sq. units
    (c) π3 sq.units
    (d) π6 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

Answer: (c) 3 sq. units

Question 20. The area of the region bounded by the curve y=4−x2−−−−−√ and x-axis is

• • (a) 8π sq. units
    (b) 2π sq. units
    (c) 16π sq. units
    (d) 6π sq. units

Answer: (b) 2π sq. units

Question 21. The area enclosed by the curve y = √x and x = -√y , the circle x² + y² = 2 above the x-axis is

• • (a) π4 sq. units
    (b) 3π2 sq. units
    (c) π sq. units
    (d) π2 sq. units

Answer: (d) π2 sq. units

Bihar Board most mcq solution 12th math chapter 8

Question 22. 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

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

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

Answer: (c) 4 sq. units

Question 25. The area bounded by the line y = 2x – 2, y = -x and x-axis is given by

• • (a) 92 sq. units
    (b) 436 sq. units
    (c) 356 sq. units
    (d) None of these

Answer: (d) None of these

Question 26. 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

Answer: (d) none of these

Question 27. The area lying above x-axis and included between the circle x² + y² = 8x and inside of parabola y² = 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

Answer: (d) 43 (8 + 3π) sq. units

Question 28. Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12.

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

Answer: (a) 27 sq. units

Question 29. The area included between the curves x² = 4by and y² = 4ax

• • (a) 16ab sq. units
    (b) 16ab3 sq. units
    (c) 4ab sq. units
    (d) 16πab sq. units

Answer: (b) 16ab3 sq. units

Question 30. Area of the region between the curves x² + y² = π², y = sin x and y-axis in first quadrant is

• • (a) (π3−84) sq. units
    (b) (π3−48) sq. units
    (c) (π2−84) sq. units
    (d) (π2−48) sq. units

Answer: (a) (π3−84) sq. units

Question 31. The area bounded by the curves x² + y² = 9 and y² = 8x is

• • (a) 0 sq. units
    (b) (22√3+9π2−9sin−113) sq. units
    (c) 16π sq. units
    (d) None of these

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

Answer: (a) (√2 – 1) sq. units

BSEB 12th math chapter 8 most mcq solution

Question 33. The area common to the circle x² + y² = 16a² and the parabola y² = 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

Answer: (c) 4a23(4π+3–√) sq. units

Question 34. The area included between curves y = x² – 3x + 2 and y = -x² + 3x – 2 is

• • (a) 16 sq. units
    (b) 12 sq. units
    (c) 1 sq. units
    (d) 13 sq. units

Answer: (d) 13 sq. units

Question 35. The area bounded by x = – 4y² and x – 1 = -5y² is

• • (a) 1 sq. unit
    (b) 23 sq. units
    (c) 23 sq. units
    (d) 2 sq. units

Answer: (c) 23 sq. units

Question 36. The area bounded by the curves y=−4−x2−−−−−√, x² = -√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

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

Answer: (c) 4abtan−1ba

Question 38. 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) 43 sq. units
    (d) 83 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

Answer: (a) 152 sq. units

Question 40. The area bounded by the curves x + 2y² = 0 and x + 3y² = 1 is

• • (a) 1 sq. units
    (b) 13 sq. units
    (c) 23 sq. units
    (d) 43 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

Answer: (a) 43 sq. units

Question 42. The area of the region {(x, y) : y² = x, x² + y² = 2} is

• • (a) (π4−13) sq. units
    (b) (π4+13) sq. units
    (c) (π4−16) sq. units
    (d) (π2+13) sq. units

Answer:  (d) (π2+13) sq. units

Question 43. The area of the circle 4x² + 4y² = 9 which is interior to the parabola x² = 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

Answer: (a) 2√6+94sin−1(22√3) sq. units

Question 44. The area bounded by the curve x² = 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

Answer: (d) 12524 sq. units

Question 45. The area enclosed between the graph of y = x³ and the lines x = 0, y = 1, y = 8 is

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

Answer: (a) 454

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