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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Answer: (a) 2 sq. units
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