MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers

  

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 ≤ π2 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

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Question 2.
The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is
(a) 38 sq.units
(b) 58 sq.units
(c) 78 sq.units
(d) 98 sq. units

Answer

Answer: (d) 98 sq. units

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Question 3.
The area of the region bounded by the curve y = 16−x2−−−−−−√ 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

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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

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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

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Question 6.
The area of the region bounded by parabola y² = x and the straight line 2y = x is
(a) 43 sq. unit
(b) 1 sq. unit
(c) 23 sq. units
(d) 13 sq. units

Answer

Answer: (a) 43 sq. unit

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Question 7.
The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = π2 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

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Question 8.
The area of the region bounded by the ellipse x²25 + y²16 = 1 is
(a) 20π sq. units
(b) 20π² sq. units
(c) 16π² sq. units
(d) 25π sq. units

Answer

Answer: (a) 20π sq. units

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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

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Question 10.
The area of the region bounded by the and the lines x = 2 and x = 3
(a) 72 sq. unit
(b) 92 sq. unit
(c) 112 sq. units
(d) 132 sq. units

Answer

Answer: (a) 72 sq. unit

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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) 32 sq. units
(c) 6 sq. units
(d) 8 sq, units

Answer

Answer: (c) 6 sq. units

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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) 92 sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. unjts

Answer

Answer: (c) 12 sq. units

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Question 13.
Tne area bounded by the curve y = x² – 1 and the straight line x + y = 3 is
(a) 92 sq. units
(b) 4 sq. units
(c) 717√6 sq. units
(d) 1717√6 sq. unjts

Answer

Answer: (d) 1717√6 sq. unjts

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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

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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

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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

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Question 17.
Area bounded by the ellipse x24 + y29 = 1 is
(a) 6π sq. units
(b) 3π sq. units
(c) 12π sq. units
(d) None of these

Answer

Answer: (a) 6π sq. units

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Question 18.
Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,
(a) 9 sq. units
(b) 32 sq. units
(c) 3 sq. units
(d) None of these

Answer

Answer: (d) None of these

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Question 19.
The area of ellipse x242 + y292 = 1 is
(a) 6π sq. units
(b) π(a2+b2)4 sq. units
(c) π(a + b) sq. units
(d) None of these

Answer

Answer: (d) None of these

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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

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Question 21.
The area bounded by the curve 2x² + y² = 2 is
(a) π sq. units
(b) √2π sq. units
(c) π2 sq. units
(d) 2π sq. units

Answer

Answer: (b) √2π sq. units

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Question 22.
The area bounded by the curve x² = 4y + 4 and line 3x + 4y = 0 is
(a) 254 sq. units
(b) 1258 sq. units
(c) 12516 sq. units
(d) 1244 sq. units

Answer

Answer: (d) 1244 sq. units

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Question 23.
Area of the ellipse x2a2 + y2b2 = 1 is
(a) 4π ab sq. units
(b) 2π ab sq. units
(c) π ab sq. units.
(d) πab2 sq. units

Answer

Answer: (c) π ab sq. units.

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Question 24.
Area bounded between the parabola y² = 4ax and its latus rectum is
(a) 13 a sq. units
(b) 13 a² sq. units
(c) 83 a sq. units
(d) 83 a² sq. units

Answer

Answer: (d) 83 a² sq. units

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Question 25.
The area bounded by the line y = 2x – 2, y = -x and x-axis is given by
(a) 92 sq. units
(b) 436 sq. units
(c) 356 sq. units
(d) None pf these

Answer

Answer: (d) None pf these

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