Check the below NCERT MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Application of Integrals Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Application of Integrals Class 12 MCQs Questions 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

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