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Class 12 Maths
Application Of Integrals
Quiz 1
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The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ \(\frac{π}{2}\) is
0%
√2 sq.units
0%
(√2 + 1) sq. units
0%
(√2 – 1) sq. units
0%
(2√2 – 1) sq.units
Explanation
(√2 – 1) sq. units
The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is
0%
\(\frac{3}{8}\) sq.units
0%
\(\frac{5}{8}\) sq.units
0%
\(\frac{7}{8}\) sq.units
0%
\(\frac{9}{8}\) sq. units
Explanation
\(\frac{9}{8}\) sq. units
The area of the region bounded by the curve y = \(\sqrt{16-x^2}\) and x-axis is
0%
8π sq.units
0%
20π sq. units
0%
16π sq. units
0%
256π sq. units
Explanation
8π sq.units
Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is
0%
16π sq.units
0%
4π sq. units
0%
32π sq. units
0%
24π sq. units
Explanation
4π sq. units
Area of the region bounded by the curve y = cos x between x = 0 and x = π is
0%
2 sq. units
0%
4 sq, units
0%
3 sq.units
0%
1 sq. units
Explanation
2 sq. units
The area of the region bounded by parabola y² = x and the straight line 2y = x is
0%
\(\frac{4}{3}\) sq. unit
0%
1 sq. unit
0%
\(\frac{2}{3}\) sq. units
0%
\(\frac{1}{3}\) sq. units
Explanation
\(\frac{4}{3}\) sq. unit
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
0%
2 sq. units
0%
4 sq. units
0%
3 sq. units
0%
1 sq, unit
Explanation
1 sq, unit
The area of the region bounded by the ellipse \(\frac{x²}{25}\) + \(\frac{y²}{16}\) = 1 is
0%
20π sq. units
0%
20π² sq. units
0%
16π² sq. units
0%
25π sq. units
Explanation
20π sq. units
The area of the region bounded by the circle x² + y² = 1 is
0%
2π sq. units
0%
7π sq. units
0%
3π sq. units
0%
4π sq. units
Explanation
7π sq. units
The area of the region bounded by the and the lines x = 2 and x = 3
0%
\(\frac{7}{2}\) sq. unit
0%
\(\frac{9}{2}\) sq. unit
0%
\(\frac{11}{2}\) sq. units
0%
\(\frac{13}{2}\) sq. units
Explanation
\(\frac{7}{2}\) sq. unit
The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is
0%
4 sq. units
0%
\(\frac{3}{2}\) sq. units
0%
6 sq. units
0%
8 sq, units
Explanation
6 sq. units
If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is
0%
\(\frac{9}{2}\) sq. units
0%
8 sq. units
0%
12 sq. units
0%
4 sq. unjts
Explanation
12 sq. units
Tne area bounded by the curve y = x² – 1 and the straight line x + y = 3 is
0%
\(\frac{9}{2}\) sq. units
0%
4 sq. units
0%
\(\frac{7\sqrt{17}}{6}\) sq. units
0%
\(\frac{17\sqrt{17}}{6}\) sq. unjts
Explanation
\(\frac{17\sqrt{17}}{6}\) sq. unjts
Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to
0%
4 sq. units
0%
6 sq. units
0%
2 sq. units
0%
8 sq. units
Explanation
4 sq. units
The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is
0%
1 sq. unit
0%
2 sq. unit
0%
2√2 sq. units
0%
4 sq. units
Explanation
2 sq. unit
The area of the region bounded by the line y = | x – 2 |, x = 1, x = 3 and x-axis is
0%
4 sq. units
0%
2 sq, units
0%
3 sq. units
0%
1 sq. unit
Explanation
1 sq. unit
Area bounded by the ellipse \(\frac{x^2}{4}\) + \(\frac{y^2}{9}\) = 1 is
0%
6π sq. units
0%
3π sq. units
0%
12π sq. units
0%
None of these
Explanation
6π sq. units
Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,
0%
9 sq. units
0%
\(\frac{3}{2}\) sq. units
0%
3 sq. units
0%
None of these
Explanation
None of these
The area of ellipse \(\frac{x^2}{4^2}\) + \(\frac{y^2}{9^2}\) = 1 is
0%
6π sq. units
0%
\(\frac{π(a^2+b^2)}{4}\) sq. units
0%
π(a + b) sq. units
0%
None of these
Explanation
None of these
The area bounded by the lines |x| + |y| = 1 is
0%
1 sq. unit
0%
2 sq. units
0%
2√2 sq. units
0%
4 sq. units
Explanation
2 sq. units
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