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

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Questions
1 Area of the ellipse is
A 4πab sq.units
B 2πab sq.units
C πab sq.units
D πab/2 sq.units

Answer:πab sq.units
2 The area bounded by the curve 2x2 + y2 = 2 is
A π sq. units
B √2π sq. units
C π/2 sq. units
D 2π sq. units

Answer:√2π sq. units
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3 The area of the ellipse Class 12 Maths Chapter 8 Application of Integrals is
A 6π sq. units
B π(a2+b2)/4 sq. units
C p(a + b) sq. units
D none of these

Answer:none of these
4 If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is
A 9/2 sq. units
B 8 sq. units
C 12 sq. units
D 4 sq. units

Answer:12 sq. units
5 Area of the region between the curves x2 + y2 = π2, y = sin x and y-axis in first quadrant is
A sq. units
B sq. units
C sq. units
D sq. units

Answer:sq. units
6 The area included between the curves x2 = 4by and y2 = 4ax
A 16ab sq. units
B 16ab/3 sq. units
C 4ab sq. units
D 16πab sq. units

Answer:16ab/3 sq. units
7 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:27 sq. units
8 The area lying above x-axis and included between the circle x2 + y2 = 8x and inside of parabola y2 = 4x is
A 1/3 (2 + 3π) sq. units
B 2/3 (4 + 3π) sq. units
C (6 + 3π) sq. units
D 4/3 (8 + 3π) sq. units

Answer:4/3 (8 + 3π) sq. units
9 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:none of these
10 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
11 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:4 sq. units
12 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:4 sq. units
13 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:4 : 23
14 The area enclosed by the curve y = √x and x = -√y , the circle x2 + y2 = 2 above the x-axis is
A π/4 sq. units
B 3π/2 sq. units
C π sq. units
D π/2 sq. units

Answer:π/2 sq. units
15 The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is
A 45/4
B 14
C 7
D none of these

Answer:45/4
16 The area bounded by the curve x2 = 4y = 4y + 4 and line 3x + 4y = 0 is
A 0 sq. units
B 125/8 sq. units
C 125/16 sq. units
D 125/24 sq. units

Answer:125/24 sq. units
17 The area bounded by y= is
A 4/3 sq. units
B 13/2 sq. units
C 12/5 sq. units
D 42/5 sq. units

Answer:4/3 sq. units
18 The area bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is
A 1 sq. units
B 1/3 sq. units
C 2/3 sq. units
D 4/3 sq. units

Answer:4/3 sq. units
19 The area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5 is
A 15/2 sq. units
B 92 sq. units
C 13/2 sq. units
D None of these

Answer:15/2 sq. units
20 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 4/3 sq. units
D 8/3 sq. units

Answer:8/3 sq. units

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