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 Bihar Board 12th Maths Objective Answers Chapter 8 Application of Integrals

Bihar Board 12th Maths Objective Answers Chapter 8 Application of Integrals

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

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

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

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