MCA Entrance Previous Year Question Bank

Equation of the common tangent touching the circle $(x-3{)}^2+y^2=9$ and the parabola $y^2=4x$ above the x-axis is:

If $a,b,c$ are the roots of the equation $x^3-3p{x}^2+3qx-1=0$, then the centroid of the triangle with vertices $(a,\frac{1}{a}),(b,\frac{1}{b})$ and $(c,\frac{1}{c})$ is at the point:

A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line has intercepts $p$ and $q$. Which of the following statements is true?

If the distance of any point $(x,y)$ from the origin is defined as $d(x,y)=\max (|x|,|y|)$, then the locus of the point $(x,y)$, where $d(x,y)=1$, is:

If $(4,-3)$ and $(-9,7)$ are the two vertices of a triangle and $(1,4)$ is its centroid, then area of triangle is:

The equation of the plane passing through the point $(1,2,3)$ and having the vector $\vec{N}=3\hat{i}+\hat{j}+2\hat{k}$ as its normal, is:

The area enclosed within the lines $|x|+|y|=1$ is:

A polygon has 44 diagonals, the number of its sides is:

The eccentricity of ellipse $9x^2+5y^2-30y=0$ is:

The vertex of parabola $y^2-8y-x+19=0$ is: