CBSE Class 12 Mathematics Application of Integrals MCQs Set 02

Question. The area of the region bounded by the ellipse x^2/16 + y²/9 = 1 is
(a) 12 π
(b) 3 π
(c) 24 π
(d) π

Answer : A

Question. The 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 : B

Question. Area bounded by the circle x² + y² = 1 and the curve | x | + | y | = 1 is
(a) 2π
(b) π– 2
(c) π
(d) π+ 3

Answer : B

Question. The area of the region bounded by the curve x = 2y + 3 and lines y = 1 and y = –1 is
(a) 4 sq. units
(b) 3/2 sq. units
(c) 6 sq. units
(d) 8 sq. units

Answer : C

Question. The area bounded by the parabola y² = 36x, the line x = 1 and x-axis is ______ sq. units.
(a) 2
(b) 4
(c) 6
(d) 8

Answer : B

Question. Area between the curves y = x and y = x³ is
(a) √3/2
(b) 1/2
(c) 2 √2
(d) 1/4

Answer : B

Question. 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 : D

Question. Area of the region between the curves x² + y² = π², y = sin x and y-axis in first quadrant is
(a) π³ – 8/4 sq. units
(b) π³ – 4/8 sq. units
(c) π² – 8/4 sq. units
(d) π² – 4/8 sq. units

Answer : A

Question. Area between the parabolas y² = 4ax and x² = 4ay is
(a) 2/3 a² – 5
(b) 15/4 a² + 5
(c) 16/3 a² + 2
(d) 16/3 a²

Answer : D

Question. The area of the smaller region bounded by the ellipse x²/9 + y²/4 = 1 and the line x/3 + y/2 = 1 is
(a) 3 (π – 2)
(b) 3/2 π
(c) 3/2(π – 2)
(d) 2/3 (π – 2)

Answer
C

Question. Area between the parabola x² = 4y and line x = 4y –2 is
(a) 8/9
(b) 9/7
(c) 7/9
(d) 9/8

Answer : D

Question. The area of the ellipse x²/9 + y²/4 = 1 in first quadrant is 6π sq. units.
The ellipse is rotated about its centre in anti-clockwise direction till its major axis coincides with y-axis. Now the area of the ellipse in first quadrant is π sq. units.
(a) 2
(b) 4
(c) 6
(d) 8

Answer : B

Question. Area bounded by the curve y = log x and the coordinate axes is
(a) 2
(b) 1
(c) 5
(d) 2 √2

Answer : B

Question. The line y = mx bisects the area enclosed by lines x =0, y = 0 and x = 3/2 and the curve y = 1 + 4x – x². Then the value of m is
(a) 13/6
(b) 13/2
(c) 13/5
(d) 13/7

Answer : A

Question. What is the area of the triangle bounded by the lines y = 0, x + y = 0 and x = 4 ?
(a) 4 units
(b) 8 units
(c) 12 units
(d) 16 units

Answer : B

Question. The area common to the ellipse x²/a² + y²/b² = 1 and x²/b² + y²/a² = 1 , 0 < b < a is
(a) (a + b)² tan^-1 b/a
(b) (a + b)² tan^-1 a/b
(c) 4ab tan^-1 b/a
(d) 4ab tan-1 a/b

Answer : C

Question. The area of the triangle formed by the tangent and normal at the point (1, √3) on the circle x² + y² = 4 and the x-axis is
(a) 3 sq. units
(b) 2 √3 sq. units
(c) 3 √2 sq. units
(d) 4 sq. units

Answer : B

Question. Area bounded by the curve y = cos x between x = 0 and x = 3π/2 is
(a) 1 sq. unit
(b) 2 sq. units
(c) 3 sq. units
(d) 4 sq. units

Answer : C

Question. The area of the region enclosed by the parabola x² = y, the line y = x + 2 and the x-axis, is
(a) 2/9
(b) 9/2
(c) 9
(d) 2

Answer : B

Question. The area (in sq. units) bounded by the curves y = √x , 2y – x + 3 = 0 and x-axis lying in the first quadrant is
(a) 9
(b) 36
(c) 18
(d) 27/4

Answer : A

Question. The area (sq. units) bounded by the parabola y² = 4ax and the line x = a and x = 4a is :
(a) 35 a²/3
(b) 4a²/3
(c) 7a²/3
(d) 56 a²/3

Answer : D

Question. The area bounded by the curve y = 3/2 √x , the line x = 1 and x-axis is ______ sq. units.
(a) 2
(b) 4
(c) 6
(d) 8

Answer : B

Question. Area bounded by the parabola y = x² – 2x + 3 and tangents drawn to it from the point P(1, 0) is equal to
(a) 4√2 sq. units
(b) 4√2/3 sq. units
(c) 8√2/3 sq. units
(d) 16/3 √2 sq. units

Answer : C

Question. The area of the region bounded by y = | x – 1 | and y = 1 is
(a) 2
(b) 1
(c) 1/2
(d) 1/4

Answer : B

Question. For the area bounded by the curve y = ax, the line x = 2 and x-axis to be 2 sq. units, the value of a must be equal to
(a) 2
(b) 4
(c) 6
(d) 8

Answer : B

Question. The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to
(a) 5/3
(b) 1/3
(c) 2/3
(d) 4/3

Answer : D

Question. The area of the region enclosed by the lines y = x, x = e and curve y = 1/x and the positive x-axis is
(a) 1 sq. unit
(b) 3/2 sq. units
(c) 5/2 sq. units
(d) 1/2 sq. units

Answer : B

Question. The area of the region bounded by the parabola y = x² and y = |x| is
(a) 3
(b) 1/2
(c) 1/3
(d) 2

Answer : C

Question. The area bounded by y –1 = |x|, y = 0 and |x| = 1/2 will be :
(a) 3/4
(b) 3/2
(c) 5/4
(d) None of these

Answer : C

Question. Area of the region bounded by y = |x – 1| and y = 1 is
(a) 2 sq. units
(b) 1 sq. unit
(c) 1/2 sq. units
(d) None of these

Answer : B

Question. Area of the region bounded by the curve y = |x + 1| + 1, x = –3, x = 3 and y = 0 is
(a) 8 sq units
(b) 16 sq units
(c) 32 sq units
(d) None of these

Answer : B

Question. The area bounded by the curves y = sin x, y = cos x and x = 0 is
(a) ( √2 -1) sq. units
(b) 1 sq. unit
(c) √2 sq. units
(d) (1+ √2 ) sq. units

Answer : A

Question. 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 : A

Question. The area bounded by curves (x – 1)² + y² = 1 and x² + y² = 1 is
(a) (2π/3 – √3/2)
(b) 2π/3
(c) √3/2
(d) 2π/3 + √3/2

Answer : A

Question. Consider the following statements
Statement I : The area bounded by the curve y =sin x between x = 0 and x = 2p is 2 sq. units.
Statement II : The area bounded by the curve y = 2 cos x and the x-axis from x = 0 to x = 2p is 8 sq. units.
(a) Statement I is true
(b) Statement II is true
(c) Both statements are true
(d) Both statements are false

Answer : B

Question. The area of the region bounded by the curves y =| x – 2 |, x = 1, x = 3 and the x-axis is
(a) 4
(b) 2
(c) 3
(d) 1

Answer : D

Question. The area bounded by f (x) = x², 0 • x • 1, g(x)= – x + 2,1≤ x≤ 2 and x – axis is
(a) 3/2
(b) 4/3
(c) 8/3
(d) None of these

Answer : D

Question. The area bounded by the curves x + 2y² = 0 and x + 3y² = 1 is
(a) 1 sq. unit
(b) 1/3 sq. units
(c) 2/3 sq. units
(d) 4/3 sq. units

Answer : D

Question. The area of the region {(x, y) : y² ≤ 4x, 4ײ + 4y² ≤ 9} is
(a) √2/6 + 9π/8 – 9/4 sin-1(1/5)
(b) √2/6 – 9π/8
(c) 9π/8 – 9/4 sin-1(1/3)
(d) None of these

Answer : A

Question. Area between the curve y = cos² x, x-axis and ordinates x = 0 and x = p in the interval (0, p) is
(a) 2π/3
(b) 2π
(c) π
(d) π/2

Answer : D