MCA Entrance Previous Year Question Bank

The absolute difference between the squares of the radii of the two circles passing through the point (-9, 4) and touching the lines $x+y=3$ and $x-y=3$, is equal to ______.

Three distinct numbers are selected randomly from the set $\{1,2,3,....,40\}.$ If the probability that the selected numbers are in an increasing GP. is $\frac{m}{n}$, gcd$(m,n)=1$, then $m+n$ is equal to

If the area of the region $\{(x,y):4-x^2\le y\le x^2,y\le 4,x\ge 0\}$ is $\frac{80\sqrt{2}}{\alpha }\cdot \beta$, $\alpha ,\beta \in \mathbb{N}$, then $\alpha +\beta$ is equal to ______.

Let $f:R\to R$ be a thrice differentiable odd function satisfying $f^{\prime }(x)\ge 0,f^{\prime \prime }(x)=f(x),f(0)=0,f^{\prime }(0)=3$. Then $9f(\log 3)$ is equal to .

Let $[.]$ denote the greatest integer function. If ${\int }_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha -{\log }_{e}2$, then ${\alpha }^3$ is equal to.

Let the focal chord PQ of the parabola y² = 4x make an angle of 60° with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point (0, α), then 5α² is equal to:

Let $a\in \mathbb{R}$ and $A$ be a matrix of order $3\times 3$ such that $\text{det}(A)=-4$ and $A+I=\left[\begin{array}{ccc}1& a& 1\\ 2& 1& 0\\ a& 1& 2\end{array}\right]$, where $I$ is the identity matrix of order $3\times 3$. If $\text{det}((a+1)\text{adj}((a-1)A))$ is $2^m{3}^n,m,n\in \{0,1,2,\dots ,20\}$, then $m+n$ is equal to:

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 squareunits, respectively. Then the area (in square units) of the DBCD is equal to:

Let the vertices $Q$ and $R$ of the triangle $PQR$ lie on the line $$\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$$$QR=5$ and the coordinates of the point $P$ be $(0,2,3)$. If the area of the triangle $PQR$ is $\frac{m}{n}$ then:

$S$ and $S^{\prime }$ are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$, and P be a point on the ellipse, then $\min (S{P}^{\prime }{S}^{\prime })+\max (S{P}^{\prime }{S}^{\prime })$ is equal to: