MCQs Applications of Integrals ISC Class 12 Questions with Answer

MCQs Applications of Integrals ISC Class 12 Questions with Answer. These MCQs / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming Sem-2 exam of council. Visit official website CISCE for detail information about ISC Class-12 Maths.

ISC Class 12 Questions with Answer MCQs Applications of Integrals 

Board	ISC
Class	12th (XII)
Subject	Maths
Chapter	Applications of Integrals
Syllabus	on bifurcated syllabus (after reduction)
Session	2021-22
Bifurcated	Sem-2
Topic	MCQs / Objective Type Question

ISC MCQs Applications of Integrals for Class 12 Questions with Answer

Question 1: Find the value of ∫∫ xydxdy over the area bpunded by parabola y=x² and x = -y², is?

(a) ¹⁄₆₇
(b) ¹⁄₂₄
(c) –¹⁄₆
(d) –¹⁄₁₂

Answer: b) ¹⁄₂₄

Question 2: Find the area inside a ellipse of minor-radius ‘b’ and major-radius ‘a’.

(a) –⁴⁄₃ a²
(b) –⁴⁄₃ ab²
(c) ⁴⁄₃ ab
(d) –⁴⁄₃

Answer: (b) –⁴⁄₃ ab²

Question 3: 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 pf these

Answer: (d) None pf these

Question 4: Area lying between the curves y² = 4x and y = 2 is:

(a) 2/3
(b) 1/3
(c) 1/4
(d) 3/4

Answer: (b) 1/3

Question 5: The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

(a) 4/3 (4π – √3)
(b) 1/3 (4π + √3)
(c) 2/3 (8π – √3)
(d) 4/3 (8π + √3)

Answer: (c) 2/3 (8π – √3)

Question 6: The area bounded by the curves y² = 4x and y = x is equal to

(a) 1/3

(b) 8/3

(c) 35/6

(d) None of these

Answer: (b) 8/3

Question 7: The area enclosed between the graph of y = x³ and the lines x = 0, y = 1, y = 8 is

(a) 7

(b) 14

(c) 45/4

(d) None of these

Answer: (c) 45/4

Question 8: The area of the region bounded by the curve y² = x, the y-axis and between y = 2 and y = 4 is

(a) 52/3 sq. units

(b) 54/3 sq. units

(c) 56/3 sq. units

(d) None of these

Answer: (c) 56/3

Question 9: Area of the region bounded by the curve y = cos x between x = 0 and x = π is

(a) 1 sq. units

(b) 2 sq. units

(c) 3 sq. units

(d) 4 sq. units

Answer: (b) 2 sq. units

Question 10: The area bounded by the curve y = x³, the x-axis and two ordinates x = 1 and x = 2 is

(a) 15/2 sq. units

(b) 15/4 sq. units

(c) 17/2 sq. units

(d) 17/4 sq. units

Answer: (b) 15/4 sq. units

Question 11: The area under the curve y = x² and the lines x = -1, x = 2 and x-axis is:

(a) 3 sq. units.

(a) 5 sq. units.

(a) 7 sq. units.

(a) 9 sq. units.

Answer: (a) 3 sq. units.

Question 12: Area of the region bounded by the curve y = √49−𝑥² and the x-axis is

(a) 49/2π sq units
(b) 98π sq units
(c) 49π sq units
(d) 240π sq units

Answer: (a) 49/2π sq units

Question 13:  The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ (π/2) is

(a) √2 sq.units
(b) (√2 + 1) sq. units
(c) (√2 – 1) sq. units
(d) (2√2 – 1) sq.units

Answer: (c) (√2 – 1) sq. units

Question 14: The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is

(a) 3/8 sq.units
(b) 5/8 sq.units
(c) 7/8 sq.units
(d) 9/8 sq. units

Answer: (d) 9/8 sq. units

Question 15: 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: (b) 4π sq. units

Question 16: 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: (a) 2 sq. units

Question 17: The area of the region bounded by parabola y² = x and the straight line 2y = x is

(a) 4/3 sq. unit
(b) 1 sq. unit
(c) 2/3 sq. units
(d) 1/3 sq. units

Answer: (a) 4/3 sq. unit

Question 18:  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: (c) 4 sq. units

Question 19: If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is

(a) 2 sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. units

Answer: (c) 12 sq. units

Question 20: The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = π/2 and the x-axis is

(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq, unit

Answer: (d) 1 sq, unit

Question 21: Area of the region bounded by the curve x = 2y + 3, the y-axis and between y = -1 and y = 1 is

(a) 6 sq. units

(b) 4 sq. units

(c) 8 sq. units

(d) 3/2 sq. units

Answer: (a) 6 sq. units

Question 22:  The area of the figure bounded by the curve y = log_ex, the x-axis and the straight line x = e is

(a) 5-e

(b) 3+e

(c) 1

(d) None of these

Answer: (c) 1

Question 23: The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is

(a) ⅜ sq. units

(b) ⅝ sq. units

(c) ⅞ sq. units

(d) 9/8 sq. units

Answer: (d) 9/8 sq. units

Question 24: 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: (b) √2π sq. units

Question 25: The area bounded by the curve x² = 4y + 4 and line 3x + 4y = 0 is

(a) 25/4 sq. units
(b) 125/8 sq. units
(c) 125/16 sq. units
(d) 124/4 sq. units

Answer: (d) 124/4 sq. units

Question 26: 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: (b) 7π sq. units

Question 27: The area of the region bounded by the and the lines x = 2 and x = 3

(a) 7/2 sq. unit
(b) 9/2 sq. unit
(c) 11/2 sq. units
(d) 13/2 sq. units

Answer: (a) 7/2 sq. unit

Question 28: 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) 3/2 sq. units
(c) 6 sq. units
(d) 8 sq, units

Answer: (c) 6 sq. units

Question 29: 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: (b) 2 sq. unit

Question 30: 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: (d) 1 sq. unit

Question 31: The area of the region bounded by the circle x² + y² = 1 is

(a) 2π sq. units

(b) 3π sq. units

(c) 4π sq. units

(d) 1π sq. units

Answer: (d) 1π sq. units

Question 32:  Area bounded by the curve y = sin x and the x-axis between x = 0 and x = 2π is

(a) 2 sq. units

(b) 3 sq. units

(c) 4 sq. units

(d) None of these

Answer: (c) 4 sq. units

Question 33: 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: (c) 12 sq. units

Question 34:  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: (a) 4 sq. units

Question 35:  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: (d) None of these

Question 36: 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: (b) 2 sq. units

Question 37: Area bounded between the parabola y² = 4ax and its latus rectum is

(a) 1/3 a sq. units
(b) 1/3 a² sq. units
(c) 8/3 a sq. units
(d) 8/3 a² sq. units

Answer: (d) 8/3 a² sq. units

Question 38: The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ π/2 is

(a) √2 sq. units
(b) (√2 + 1) sq. units
(c) (√2 – 1) sq. units
(d) (2√2 – 1) sq. units.

Answer: (c) (√2 – 1) sq. units

Question 39: Find the distance travelled by a car moving with acceleration given by a(t)=Sin(t), if it moves from t = 0 sec to t = π/2 sec, if velocity of a car at t=0sec is 10 km/hr.

(a) 10.19 km
(b) 19.13 km
(c) 15.13 km
(d) 13.13 km

Answer: (d) 13.13 km

–: End of MCQs Applications of Integrals ISC Class 12   :–