MCA Entrance Previous Year Question Bank

Let the area of the region $\{(x,y):0\le x\le 3,0\le y\le \min (x^2+2,2x+2)\}$ be A. Then $12A$ is equal to .........

$\text{If }{\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\sqrt{1-\sin 2x}dx=\alpha +\beta \sqrt{2}+\gamma \sqrt{3},\text{ where}$ α, β and γ are rational numbers, then 3α + 4β – γ is equal to ...............

Let the set $C=\{(x,y)|x^2-2^y=2023,x,y\in \mathbb{N}\}$. Then, ${\sum }_{(x,y)\in C}(x+y)$ is equal to.............

Let $f(x)=\sqrt{{\lim }_{r\to x}\left\{2r^2|f(r){|}^2-f(x)f(r)\right\}-r^3}$ be differentiable in $(-\infty ,0)\cup (0,\infty )$ and $f(1)=1$. Then the value of $e_a$, such that $f(a)=0$, is equal to ________.

Remainder when 64³² is divided by 9 is equal to ................ .

Let for any three distinct consecutive terms $a$, $b$, $c$ of an A.P. the lines $ax+by+c=0$ be concurrent at the point $P$ and $Q(\alpha ,\beta )$ be a point such that the system of equations $x+y+z=6,2x+5y+\alpha z=\beta$ and $x+2y+3z=4$, has infinitely many solutions. Then $(PQ{)}^2$ is equal to.

Let $O$ be the origin, and $M$ and $N$ be the points on the lines $$\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$$ and $$\frac{x+8}{12}=\frac{y+2}{5}=\frac{z+11}{9}$$ respectively such that $MN$ is the shortest distance between the given lines. Then $\overrightarrow{OM}\cdot \overrightarrow{ON}$ is equal to

Let $\mathbf{P}(\alpha ,\beta )$ be a point on the parabola $y^2=4x$. If $\mathbf{P}$ also lies on the chord of the parabola $x^2=8y$ whose mid-point is $\left(1\frac{5}{4}\right)$, then $(\alpha -28)(\beta -8)$ equals to ________.

Let the slope of the line $45x+5y+3=0$ be $27r_1+\frac{9r_2}{2}$ for some $r_1,r_2\in \mathbb{R}$. Then $$\underset{x\to 0}{\lim }\left(\frac{x}{3\frac{3r_{2}x}{2}-r_2{x}^2-r_1{x}^3-3x}\right)$$

The function $f(x)=\frac{x}{x^2-6x-16}$, $x\in \mathbb{R}\setminus \{-2,8\}$