MCA Entrance Previous Year Question Bank

For real number a, b (a > b > 0), let: $\text{Area }\{(x,y):x^2+y^2\le a^2\text{ and }\frac{x^2}{a^2}+\frac{y^2}{b^2}\ge 1\}=30\pi$ $\text{Area }\{(x,y):x^2+y^2\ge b^2\text{ and }\frac{x^2}{a^2}+\frac{y^2}{b^2}\le 1\}=18\pi$ Then the value of $(a-b{)}^2$ is equal to ________.

The area enclosed by $y^2=8x$ and $y=\sqrt{2}x$ that lies outside the triangle formed by $y=\sqrt{2}x$, $x=1$, $y=2\sqrt{2}$, is equal to:

The area of the region given by $\{(x,y):xy\le 8,1\le y\le x^2\}$ is:

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12A$ is equal to:

Let A be the area of the region {(x,y):y≥x2,y≥(1−x)2,y≤2x(1−x)}. Then 540A is equal to ________.

Let $\alpha$ be the area of the larger region bounded by $y^2=8x$, $y=x$ and $x=2$ in the first quadrant. Then the value of $3\alpha$ is:

The area of the region $A=\{(x,y):|\cos x-\sin x|\le y\le \sin x,0\le x\le \frac{\pi }{2}\}$ is:

Let $A=\{(x,y)\in {\mathbb{R}}^2:y\ge 0,2x\le y\le \sqrt{4-(x-1{)}^2}\}$ and $B=\{(x,y)\in \mathbb{R}\times \mathbb{R}:0\le y\le \min \{2x,\sqrt{4-(x-1{)}^2}\}\}$. Then the ratio of the area of $A$ to the area of $B$ is

Let $\Delta$ be the area of the region $\{(x,y)\in {\mathbb{R}}^2:x^2+y^2\le 21,y^2\le 4x,x\ge 1\}$. Then $\frac{1}{2}\left(\Delta -21{\sin }^{-1}\frac{2}{\sqrt{7}}\right)$ is equal to:

The area enclosed by the curves $y^2+4x=4$ and $y-2x=2$ is: