NCERT Solutions for class 12 Maths | Chapter 8 - Application of Integrals

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Questions
1 The area of the region bounded by the curve y= and x-axis is
A 8π sq. units
B 2π sq. units
C 16π sq. units
D 6π sq. units

Answer:2π sq. units
2 Area bounded by the ellipse 1 is
A 6π sq. units
B 3π sq. units
C 12π sq. units
D None of these

Answer:6π sq. units
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3 Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,
A 9 sq. units
B 3/2 sq. units
C 3 sq. units
D None of these

Answer:None of these
4 The area bounded by the line y = 2x – 2, y = -x and x-axis is given by
A 9/2 sq. units
B 43/6 sq. units
C 35/6 sq. units
D None of these

Answer:None of these
5 Area bounded by the curve y = cos x between x = 0 and x = 3π/2 is
A 1 sq. units
B 2 sq. units
C 3 sq. units
D 4 sq. units

Answer:3 sq. units
6 Find the area enclosed by parabola y2 = x and the line y + x = 2 and the x-axis.
A 5/6 sq. units
B 7/6 sq. units
C 6/7 sq. units
D 4/7 sq. units

Answer:7/6 sq. units
7 Area bounded by the curve y2 = 16x and line y = mx is 2/3 then m is equal to
A 3
B 4
C 1
D 2

Answer:4
8 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 8/3 sq. units
C 3/8 sq. units
D 3 sq. units

Answer:8 sq. units
9 The area bounded by the curve y2 = x, line y = 4 and y-axis is
A 16/3 sq. units
B 64/3 sq. units
C 7√2 sq. units
D none of these

Answer:64/3 sq. units
10 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:(9sec-1 3 – √8) sq. units
11 Area of the region bounded by the curve y = x2 and the line y = 4 is
A 11/3 sq. units
B 32/3 sq. units
C 43/3 sq. units
D 47/3 sq. units

Answer:32/3 sq. units
12 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:2 sq. units
13 The area bounded by x = – 4y2 and x – 1 = -5y2 is
A 1 sq. unit
B 2/3 sq. units
C 2/3 sq. units
D 2 sq. units

Answer:2/3 sq. units
14 The area included between curves y = x2 – 3x + 2 and y = -x2 + 3x – 2 is
A 1/6 sq. units
B 1/2 sq. units
C 1 sq. units
D 1/3 sq. units

Answer:1/3 sq. units
15 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:(√2 – 1) sq. units
16 The area bounded by the curves x2 + y2 = 9 and y2 = 8x is
A 0 sq. units
B sq. units
C 16π sq. units
D None of these

Answer: sq. units
17 The area enclosed between the curve y2 = 4x and the line y = x is
A 8/3 sq. units
B 4/3 sq. units
C 2/3 sq. units
D 1/2 sq. units

Answer:8/3 sq. units
18 The area of the region R = ((x, y) : |x| ≤ |y| and x2 + y2 ≤ 1) is
A 3π/8 sq. units
B 5π/8 sq. units
C π/2 sq. units
D π/8 sq. units

Answer:π/2 sq. units
19 The area bounded by the curve y = x2 – 1 and the straight line x + y = 3 is
A 9/2 sq. units
B 4 sq. units
C 7√17/2 sq. units
D 17√17/6 sq. units

Answer:17√17/6 sq. units
20 The area enclosed by curve is
A 10π sq. units
B 20π sq. units
C 5π sq. units
D 4π sq. units

Answer:20π sq. units

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