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## Thursday, 28 January 2021

### CBSE Class 12 Maths - MCQ and Online Tests - Unit 8 - Application of Integrals

#### CBSE Class 12 Maths – MCQ and Online Tests – Unit 8 – Application of Integrals

Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.

#### CBSE Class 12 Maths – MCQ and Online Tests – Unit 8 – Application of Integrals

Question 1.
The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = $$\frac{π}{2}$$ 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 2.
The area of the region bounded by the ellipse $$\frac{x²}{25}$$ + $$\frac{y²}{16}$$ = 1 is
(a) 20π sq. units
(b) 20π² sq. units
(c) 16π² sq. units
(d) 25π sq. units

Answer: (a) 20π sq. units

Question 3.
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 4.
The area of the region bounded by the and the lines x = 2 and x = 3
(a) $$\frac{7}{2}$$ sq. unit
(b) $$\frac{9}{2}$$ sq. unit
(c) $$\frac{11}{2}$$ sq. units
(d) $$\frac{13}{2}$$ sq. units

Answer: (a) $$\frac{7}{2}$$ sq. unit

Question 5.
The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ $$\frac{π}{2}$$ 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 6.
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) $$\frac{3}{2}$$ sq. units
(c) 6 sq. units
(d) 8 sq, units

Answer: (c) 6 sq. units

Question 7.
If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is
(a) $$\frac{9}{2}$$ sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. unjts

Answer: (c) 12 sq. units

Question 8.
Tne area bounded by the curve y = x² – 1 and the straight line x + y = 3 is
(a) $$\frac{9}{2}$$ sq. units
(b) 4 sq. units
(c) $$\frac{7\sqrt{17}}{6}$$ sq. units
(d) $$\frac{17\sqrt{17}}{6}$$ sq. unjts

Answer: (d) $$\frac{17\sqrt{17}}{6}$$ sq. unjts

Question 9.
The area of the region bounded by parabola y² = x and the straight line 2y = x is
(a) $$\frac{4}{3}$$ sq. unit
(b) 1 sq. unit
(c) $$\frac{2}{3}$$ sq. units
(d) $$\frac{1}{3}$$ sq. units

Answer: (a) $$\frac{4}{3}$$ sq. unit

Question 10.
The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is
(a) $$\frac{3}{8}$$ sq.units
(b) $$\frac{5}{8}$$ sq.units
(c) $$\frac{7}{8}$$ sq.units
(d) $$\frac{9}{8}$$ sq. units

Answer: (d) $$\frac{9}{8}$$ sq. units

Question 11.
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 12.
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 13.
Area bounded between the parabola y² = 4ax and its latus rectum is
(a) $$\frac{1}{3}$$ a sq. units
(b) $$\frac{1}{3}$$ a² sq. units
(c) $$\frac{8}{3}$$ a sq. units
(d) $$\frac{8}{3}$$ a² sq. units

Answer: (d) $$\frac{8}{3}$$ a² sq. units

Question 14.
The area bounded by the line y = 2x – 2, y = -x and x-axis is given by
(a) $$\frac{9}{2}$$ sq. units
(b) $$\frac{43}{6}$$ sq. units
(c) $$\frac{35}{6}$$ sq. units
(d) None pf these

Answer: (d) None pf these

Question 15.
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 16.
The area of the region bounded by the curve y = $$\sqrt{16-x^2}$$ and x-axis is
(a) 8π sq.units
(b) 20π sq. units
(c) 16π sq. units
(d) 256π sq. units

Answer: (a) 8π sq.units

Question 17.
Area bounded by the ellipse $$\frac{x^2}{4}$$ + $$\frac{y^2}{9}$$ = 1 is
(a) 6π sq. units
(b) 3π sq. units
(c) 12π sq. units
(d) None of these

Answer: (a) 6π sq. units

Question 18.
Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,
(a) 9 sq. units
(b) $$\frac{3}{2}$$ sq. units
(c) 3 sq. units
(d) None of these

Answer: (d) None of these

Question 19.
The area of ellipse $$\frac{x^2}{4^2}$$ + $$\frac{y^2}{9^2}$$ = 1 is
(a) 6π sq. units
(b) $$\frac{π(a^2+b^2)}{4}$$ sq. units
(c) π(a + b) sq. units
(d) None of these

Answer: (d) None of these

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: (b) 2 sq. units

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

Answer: (b) √2π sq. units

Question 22.
The area bounded by the curve x² = 4y + 4 and line 3x + 4y = 0 is
(a) $$\frac{25}{4}$$ sq. units
(b) $$\frac{125}{8}$$ sq. units
(c) $$\frac{125}{16}$$ sq. units
(d) $$\frac{124}{4}$$ sq. units

Answer: (d) $$\frac{124}{4}$$ sq. units

Question 23.
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 24.
Area of the ellipse $$\frac{x^2}{a^2}$$ + $$\frac{y^2}{b^2}$$ = 1 is
(a) 4π ab sq. units
(b) 2π ab sq. units
(c) π ab sq. units.
(d) $$\frac{π ab}{2}$$ sq. units

Answer: (c) π ab sq. units.

Question 25.
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

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