M.C.Q (1 Marks)

MCQ 11 Mark

The area of the region bounded by the circle $x^2+y^2$ $=9$ in the first quadrant is :

A
$9 \pi$
B
$\frac{3 \pi}{4}$
✓
$\frac{9 \pi}{4}$
D
$3 \pi$

Answer

Correct option: C.

$\frac{9 \pi}{4}$

(C) Area bounded by circle in first quadrant
$
=\frac{1}{4} \pi a^2=\frac{1}{4} \pi \times(3)^2=\frac{9 \pi}{4}
$
Correct option is (C) $\frac{9 \pi}{4}$.

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MCQ 21 Mark

Area bounded by curve $y^2=4 x, y$-axis and line $y=3$ is:

A
2
✓
$\frac{9}{4}$
C
$\frac{9}{3}$
D
$\frac{9}{2}$.

Answer

Correct option: B.

$\frac{9}{4}$

(B) $\frac{9}{4}$

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MCQ 31 Mark

Area of circle $x^2+y^2=4$ :

A
$2 \pi$
B
$16 \pi$
✓
$4 \pi$
D
$\frac{\pi}{4}$

Answer

Correct option: C.

$4 \pi$

(C) $4 \pi$
Circle $x^2+y^2=4$
$
\begin{aligned}
\therefore \quad(x)^2+(y)^2 & =(2)^2 \\
\text { Area of circle } & =\pi(\text { radius })^2=\pi(2)^2 \\
& =4 \pi
\end{aligned}
$

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MCQ 41 Mark

The area of the region bounded by the curve $y=x^2$ and line $y=4$ is:

A
$\frac{33}{2}$
B
$\frac{8}{3}$
C
$\frac{32}{3}$
D
$\frac{4}{3}$

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MCQ 51 Mark

The whole area of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is :

A
$\pi$ square units
B
$5 \pi$ square units
C
$40 \pi$ square units
✓
$20 \pi$ square units.

Answer

Correct option: D.

$20 \pi$ square units.

(D)
$
\begin{aligned}
\text { Ellipse } \frac{x^2}{25}+\frac{y^2}{16} & =1 \\
\Rightarrow \quad \frac{x^2}{(5)^2}+\frac{y^2}{(4)^2} & =1
\end{aligned}
$

$\begin{array}{l}\Rightarrow \quad \frac{y^2}{(4)^2}=1-\frac{x^2}{(5)^2}=\frac{(5)^2-x^2}{(5)^2} \\ \Rightarrow \quad y^2=\frac{(4)^2}{(5)^2}\left((5)^2-x^2\right) \\ \Rightarrow \quad y=\frac{4}{5} \sqrt{(5)^2-x^2} \\ \begin{array}{l}\text { Required area }= ABCDA \\ =4 \times \text { OABO } \quad(\because \text { The ellipse is symmetrical } \\ \text { about both the axes })\end{array} \\ =4 \int_0^5 y d x \\ =4 \int_0^5 \frac{4}{5} \sqrt{(5)^2-x^2} d x \\ =\frac{16}{5}\left(\frac{1}{2} x \sqrt{(5)^2-x^2}+\frac{(5)^2}{2} \sin ^{-1}\left(\frac{x}{5}\right)\right)_0^5 \\ =\frac{16}{5}\left(0+\frac{(5)^2}{2} \times \frac{\pi}{2}-0-0\right) \\ =4 \times 5 \pi \\ =20 \pi \text { square units. } \\ \text { Hence the correct option is (D). }\end{array}$

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MCQ 61 Mark

The area of the region bounded by the curve $y=\sin x$ and $x$-axis when $0 \leq x \leq \pi$ will be :