Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 8 Application of Integrals. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Application of Integrals MCQs Pdf with Answers to know their preparation level.

## Application of Integrals Class 12 Maths MCQs Pdf

Question 1.

The area bounded by the curves \(y=-\sqrt{4-x^{2}}\), x^{2} = -√2y and x = y is

(a) \(\left(\pi+\frac{1}{3}\right)\) sq. units

(b) \(\left(\pi-\frac{1}{3}\right)\) sq. units

(c) \(\left(\pi+\frac{2}{3}\right)\) sq. units

(d) \(\left(\pi-\frac{2}{3}\right)\) sq. units

Answer:

(a) \(\left(\pi+\frac{1}{3}\right)\) sq. units

Question 2.

The area common to the ellipses \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) and \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\), 0 < b < a is

(a) \((a+b)^{2} \tan ^{-1} \frac{b}{a}\)

(b) \((a+b)^{2} \tan ^{-1} \frac{a}{b}\)

(c) \(4 a b \tan ^{-1} \frac{b}{a}\)

(d) \(4 a b \tan ^{-1} \frac{a}{b}\)

Answer:

(c) \(4 a b \tan ^{-1} \frac{b}{a}\)

Question 3.

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) \(\frac{4}{3}\) sq. units

(d) \(\frac{8}{3}\) sq. units

Answer:

(d) \(\frac{8}{3}\) sq. units

Question 4.

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

(a) \(\frac{15}{2}\) sq. units

(b) \(\frac{9}{2}\) sq. units

(c) \(\frac{13}{2}\) sq. units

(d) None of these

Answer:

(a) \(\frac{15}{2}\) sq. units

Question 5.

The area bounded by the curves x + 2y^{2} = 0 and x + 3y^{2} = 1 is

(a) 1 sq. units

(b) \(\frac{1}{3}\) sq. units

(c) \(\frac{2}{3}\) sq. units

(d) \(\frac{4}{3}\) sq. units

Answer:

(d) \(\frac{4}{3}\) sq. units

Question 6.

The area bounded by \(y=(2 x)^{1 / 2}\) and \(x=(2 y)^{1 / 2}\) is

(a) \(\frac{4}{3}\) sq. units

(b) \(\frac{13}{2}\) sq. units

(c) \(\frac{12}{5}\) sq. units

(d) \(\frac{4}{25}\) sq. units

Answer:

(a) \(\frac{4}{3}\) sq. units

Question 7.

The area of the region {(x, y) : y^{2} = x, x^{2} + y^{2} = 2} is

(a) \(\left(\frac{\pi}{4}-\frac{1}{3}\right)\) sq. units

(b) \(\left(\frac{\pi}{4}+\frac{1}{3}\right)\) sq. units

(c) \(\left(\frac{\pi}{4}-\frac{1}{6}\right)\) sq. units

(d) \(\left(\frac{\pi}{2}+\frac{1}{3}\right)\) sq. units

Answer:

(d) \(\left(\frac{\pi}{2}+\frac{1}{3}\right)\) sq. units

Question 8.

The area of the circle 4x^{2} + 4y^{2} = 9 which is interior to the parabola x^{2} = 4y is

(a) \(\frac{\sqrt{2}}{6}+\frac{9}{4} \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)\) sq. units

(b) \(\frac{\sqrt{2}}{6}-\frac{1}{4} \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)\) sq. units

(c) \(\frac{3}{2}\) sq. units

(d) \(\frac{7}{2}\) sq. units

Answer:

(a) \(\frac{\sqrt{2}}{6}+\frac{9}{4} \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)\) sq. units

Question 9.

The area bounded by the curve x^{2} = 4y = 4y + 4 and line 3x + 4y = 0 is

(a) \(\frac{25}{4}\) sq. units

(b) \(\frac{125}{8}\) sq. units

(c) \(\frac{125}{16}\) sq. units

(d) \(\frac{125}{24}\) sq. units

Answer:

(d) \(\frac{125}{24}\) sq. units

Question 10.

The area enclosed between the graph of y = x^{3} and the lines x = 0, y = 1, y = 8 is

(a) \(\frac{45}{4}\)

(b) 14

(c) 7

(d) none of these

Answer:

(a) \(\frac{45}{4}\)

Question 11.

The area enclosed by the curve y = √x and x = -√y , the circle x^{2} + y^{2} = 2 above the x-axis is

(a) \(\frac{\pi}{4}\) sq. units

(b) \(\frac{3 \pi}{2}\) sq. units

(c) π sq. units

(d) \(\frac{\pi}{2}\) sq. units

Answer:

(d) \(\frac{\pi}{2}\) sq. units

Question 12.

The ratio in which the x-axis 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

Answer:

(a) 4 : 23

Question 13.

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 14.

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 15.

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

(a) \(\frac{9}{2}\) sq. units

(b) \(\frac{43}{6}\) sq. units

(c) \(\frac{35}{6}\) sq. units

(d) None of these

Answer:

(d) None of these

Question 16.

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

Answer:

(d) none of these

Question 17.

The area lying above x-axis and included between the circle x^{2} + y^{2} = 8x and inside of parabola y^{2} = 4x is

(a) \(\frac{1}{3}\) (2 + 3π) sq. units

(b) \(\frac{2}{3}\) (4 + 3π) sq. units

(c) (6 + 3π) sq. units

(d) \(\frac{4}{3}\) (8 + 3π) sq. units

Answer:

(d) \(\frac{4}{3}\) (8 + 3π) sq. units

Question 18.

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

Answer:

(a) 27 sq. units

Question 19.

The area included between the curves x^{2} = 4by and y^{2} = 4ax

(a) 16ab sq. units

(b) \(\frac{16 a b}{3}\) sq. units

(c) 4ab sq. units

(d) 16πab sq. units

Answer:

(b) \(\frac{16 a b}{3}\) sq. units

Question 20.

Area of the region between the curves x^{2} + y^{2} = π^{2}, y = sin x and y-axis in first quadrant is

(a) \(\left(\frac{\pi^{3}-8}{4}\right)\) sq. units

(b) \(\left(\frac{\pi^{3}-4}{8}\right)\) sq. units

(c) \(\left(\frac{\pi^{2}-8}{4}\right)\) sq. units

(d) \(\left(\frac{\pi^{2}-4}{8}\right)\) sq. units

Answer:

(a) \(\left(\frac{\pi^{3}-8}{4}\right)\) sq. units

Question 21.

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

(a) \(\frac{9}{2}\) sq. units

(b) 8 sq. units

(c) 12 sq. units

(d) 4 sq. units

Answer:

(c) 12 sq. units

Question 22.

The area bounded by the curve y = x^{2} + 4x + 5, the axes of coordinates and minimum ordinate is

(a) \(3 \frac{2}{3}\) sq. units

(b) \(4 \frac{2}{3}\) sq. units

(c) \(5 \frac{2}{3}\) sq. units

(d) None of these

Answer:

(b) \(4 \frac{2}{3}\) sq. units

Question 23.

The area of the ellipse \(\frac{x^{2}}{4^{2}}+\frac{y^{2}}{9^{2}}=1\) is

(a) 6π sq. units

(b) \(\frac{\pi\left(a^{2}+b^{2}\right)}{4}\) sq. units

(c) p(a + b) sq. units

(d) none of these

Answer:

(d) none of these

Question 24.

The area bounded by the curve 2x^{2} + y^{2} = 2 is

(a) π sq. units

(b) √2π sq. units

(c) \(\frac{\pi}{2}\) sq. units

(d) 2π sq. units

Answer:

(b) √2π sq. units

Question 25.

Area of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is

(a) 4πab sq.units

(b) 2πab sq.units

(c) πab sq.units

(d) \(\frac{\pi a b}{2}\) sq.units

Answer:

(c) πab sq.units

Question 26.

Determine the area under the curve \(y=\sqrt{a^{2}-x^{2}}\) included between the lines x = 0 and x = a.

(a) \(\frac{\pi a^{a}}{4}\)

(b) \(\frac{\pi a^{3}}{4}\)

(c) \(\frac{\pi a^{2}}{8}\)

(d) None of these

Answer:

(a) \(\frac{\pi a^{a}}{4}\)

Question 27.

The area enclosed by curve \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) is

(a) 10π sq. units

(b) 20π sq. units

(c) 5π sq. units

(d) 4π sq. units

Answer:

(b) 20π sq. units

Question 28.

The area bounded by the curve y = x^{2} – 1 and the straight line x + y = 3 is

(a) \(\frac{9}{2}\) sq. units

(b) 4 sq. units

(c) \(\frac{7 \sqrt{17}}{2}\) sq. units

(d) \(\frac{17 \sqrt{17}}{6}\) sq. units

Answer:

(d) \(\frac{17 \sqrt{17}}{6}\) sq. units

Question 29.

The area of the region R = ((x, y) : |x| ≤ |y| and x^{2} + y^{2} ≤ 1) is

(a) \(\frac{3 \pi}{8}\) sq. units

(b) \(\frac{5 \pi}{8}\) sq. units

(c) \(\frac{\pi}{2}\) sq. units

(d) \(\frac{\pi}{8}\) sq. units

Answer:

(c) \(\frac{\pi}{2}\) sq. units

Question 30.

The area enclosed between the curve y^{2} = 4x and the line y = x is

(a) \(\frac{8}{3}\) sq. units

(b) \(\frac{4}{3}\) sq. units

(c) \(\frac{2}{3}\) sq. units

(d) \(\frac{1}{2}\) sq. units

Answer:

(a) \(\frac{8}{3}\) 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) \(\left(\frac{2 \sqrt{2}}{3}+\frac{9 \pi}{2}-9 \sin ^{-1} \frac{1}{3}\right)\) sq. units

(c) 16π sq. units

(d) None of these

Answer:

(b) \(\left(\frac{2 \sqrt{2}}{3}+\frac{9 \pi}{2}-9 \sin ^{-1} \frac{1}{3}\right)\) 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 x^{2} + y^{2} = 16a^{2} and the parabola y^{2} = 6ax is

(a) \(\frac{4 a^{2}}{3}(4 \pi-\sqrt{3})\) sq. units

(b) \(\frac{4 a^{2}}{3}(8 \pi-3) \text { sq. units }\) sq. units

(c) \(\frac{4 a^{2}}{3}(4 \pi+\sqrt{3})\) sq. units

(d) None of these

Answer:

(c) \(\frac{4 a^{2}}{3}(4 \pi+\sqrt{3})\) sq. units

Question 34.

The area included between curves y = x^{2} – 3x + 2 and y = -x^{2} + 3x – 2 is

(a) \(\frac{1}{6}\) sq. units

(b) \(\frac{1}{2}\) sq. units

(c) 1 sq. units

(d) \(\frac{1}{3}\) sq. units

Answer:

(d) \(\frac{1}{3}\) sq. units

Question 35.

The area bounded by x = – 4y^{2} and x – 1 = -5y^{2} is

(a) 1 sq. unit

(b) \(\frac{2}{3}\) sq. units

(c) \(\frac{2}{3}\) sq. units

(d) 2 sq. units

Answer:

(c) \(\frac{2}{3}\) sq. units

Question 36.

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 37.

Area of the region bounded by the curve y = x^{2} and the line y = 4 is

(a) \(\frac{11}{3}\) sq. units

(b) \(\frac{32}{3}\) sq. units

(c) \(\frac{43}{3}\) sq. units

(d) \(\frac{47}{3}\) sq. units

Answer:

(b) \(\frac{32}{3}\) sq. units

Question 38.

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

Answer:

(c) (9sec^{-1} 3 – √8) sq. units

Question 39.

The area bounded by the curve y^{2} = x, line y = 4 and y-axis is

(a) \(\frac{16}{3}\) sq. units

(b) \(\frac{64}{3}\) sq. units

(c) 7√2 sq. units

(d) none of these

Answer:

(b) \(\frac{64}{3}\) sq. units

Question 40.

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) \(\frac{8}{3}\) sq. units

(c) \(\frac{3}{8}\) sq. units

(d) 3 sq. units

Answer:

(a) 8 sq. units

Question 41.

Area bounded by the curve y^{2} = 16x and line y = mx is \(\frac{2}{3}\) then m is equal to

(a) 3

(b) 4

(c) 1

(d) 2

Answer:

(b) 4

Question 42.

Find the area enclosed by parabola y^{2} = x and the line y + x = 2 and the x-axis.

(a) \(\frac{5}{6}\) sq. units

(b) \(\frac{7}{6}\) sq. units

(c) \(\frac{6}{7}\) sq. units

(d) \(\frac{4}{7}\) sq. units

Answer:

(b) \(\frac{7}{6}\) sq. units

Question 43.

The area bounded by the curve x^{2} + y^{2} = 1 and 1st quadrant is

(a) \(\frac{\pi}{4}\) sq.units

(b) \(\frac{\pi}{2}\) sq. units

(c) \(\frac{\pi}{3}\) sq.units

(d) \(\frac{\pi}{6}\) sq.units

Answer:

(a) \(\frac{\pi}{4}\) sq.units

Question 44.

Area bounded by the curve y = cos x between x = 0 and x = \(\frac{3 \pi}{2}\) is

(a) 1 sq. units

(b) 2 sq. units

(c) 3 sq. units

(d) 4 sq. units

Answer:

(c) 3 sq. units

Question 45.

The area of the region bounded by the curve \(y=\sqrt{4-x^{2}}\) 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

We hope the given Maths MCQs for Class 12 with Answers Chapter 8 Application of Integrals will help you. If you have any query regarding CBSE Class 12 Maths Application of Integrals MCQs Pdf, drop a comment below and we will get back to you at the earliest.