# MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers

Question 1.

The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ \(\frac{π}{2}\) is

(a) √2 sq.units

(b) (√2 + 1) sq. units

(c) (√2 – 1) sq. units

(d) (2√2 – 1) sq.units

## Answer

Answer: (c) (√2 – 1) sq. units

Question 2.

The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is

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

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

(c) \(\frac{7}{8}\) sq.units

(d) \(\frac{9}{8}\) sq. units

## Answer

Answer: (d) \(\frac{9}{8}\) sq. units

Question 3.

The area of the region bounded by the curve y = \(\sqrt{16-x^2}\) and x-axis is

(a) 8π sq.units

(b) 20π sq. units

(c) 16π sq. units

(d) 256π sq. units

## Answer

Answer: (a) 8π sq.units

Question 4.

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. units

## Answer

Answer: (b) 4π sq. units

Question 5.

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

## Answer

Answer: (a) 2 sq. units

Question 6.

The area of the region bounded by parabola y² = x and the straight line 2y = x is

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

(b) 1 sq. unit

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

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

## Answer

Answer: (a) \(\frac{4}{3}\) sq. unit

Question 7.

The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = \(\frac{π}{2}\) and the x-axis is

(a) 2 sq. units

(b) 4 sq. units

(c) 3 sq. units

(d) 1 sq, unit

## Answer

Answer: (d) 1 sq, unit

Question 8.

The area of the region bounded by the ellipse \(\frac{x²}{25}\) + \(\frac{y²}{16}\) = 1 is

(a) 20π sq. units

(b) 20π² sq. units

(c) 16π² sq. units

(d) 25π sq. units

## Answer

Answer: (a) 20π sq. units

Question 9.

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

## Answer

Answer: (b) 7π sq. units

Question 10.

The area of the region bounded by the and the lines x = 2 and x = 3

(a) \(\frac{7}{2}\) sq. unit

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

(c) \(\frac{11}{2}\) sq. units

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

## Answer

Answer: (a) \(\frac{7}{2}\) sq. unit

Question 11.

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

(c) 6 sq. units

(d) 8 sq, units

## Answer

Answer: (c) 6 sq. units

Question 12.

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. unjts

## Answer

Answer: (c) 12 sq. units

Question 13.

Tne area bounded by the curve y = x² – 1 and the straight line x + y = 3 is

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

(b) 4 sq. units

(c) \(\frac{7\sqrt{17}}{6}\) sq. units

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

## Answer

Answer: (d) \(\frac{17\sqrt{17}}{6}\) sq. unjts

Question 14.

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

## Answer

Answer: (a) 4 sq. units

Question 15.

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

## Answer

Answer: (b) 2 sq. unit

Question 16.

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

## Answer

Answer: (d) 1 sq. unit

Question 17.

Area bounded by the ellipse \(\frac{x^2}{4}\) + \(\frac{y^2}{9}\) = 1 is

(a) 6π sq. units

(b) 3π sq. units

(c) 12π sq. units

(d) None of these

## Answer

Answer: (a) 6π sq. units

Question 18.

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

(a) 9 sq. units

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

(c) 3 sq. units

(d) None of these

## Answer

Answer: (d) None of these

Question 19.

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

(a) 6π sq. units

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

(c) π(a + b) sq. units

(d) None of these

## Answer

Answer: (d) None of these

Question 20.

The area bounded by the lines |x| + |y| = 1 is

(a) 1 sq. unit

(b) 2 sq. units

(c) 2√2 sq. units

(d) 4 sq. units

## Answer

Answer: (b) 2 sq. units

Question 21.

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

(a) π sq. units

(b) √2π sq. units

(c) \(\frac{π}{2}\) sq. units

(d) 2π sq. units

## Answer

Answer: (b) √2π sq. units

Question 22.

The area bounded by the curve x² = 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) \(\frac{124}{4}\) sq. units

## Answer

Answer: (d) \(\frac{124}{4}\) sq. units

Question 23.

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

(a) 4π ab sq. units

(b) 2π ab sq. units

(c) π ab sq. units.

(d) \(\frac{π ab}{2}\) sq. units

## Answer

Answer: (c) π ab sq. units.

Question 24.

Area bounded between the parabola y² = 4ax and its latus rectum is

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

(b) \(\frac{1}{3}\) a² sq. units

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

(d) \(\frac{8}{3}\) a² sq. units

## Answer

Answer: (d) \(\frac{8}{3}\) a² sq. units

Question 25.

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 pf these

## Answer

Answer: (d) None pf these

## 0 Comments