MCA Entrance Previous Year Question Bank

If the orthocentre of the triangle, whose vertices are $(1,2)$, $(2,3)$, and $(3,1)$ is $(\alpha ,\beta )$, then the quadratic equation whose roots are $\alpha +4\beta$ and $4\alpha +\beta$, is

The combined equation of the two lines $ax+by+c=0$ and $a^{\prime }x+b^{\prime }y+c^{\prime }=0$ can be written as $(ax+by+c)(a^{\prime }x+b^{\prime }y+c^{\prime })=0$. The equation of the angle bisectors of the lines represented by the equation $2x^2+xy-3y^2=0$ is

Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16x$. If one of these tangents touches the two curves at $Q$ and $R$, then $(QR{)}^2$ is equal to:

The number of points on the curve $y=54x^5-135x^4-70x^3+180x^2+210x$ at which the normal lines are parallel to $x+90y+2=0$ is :

Let $R$ be a rectangle given by the lines $x=0,x=2,y=0$ and $y=5$. Let $A(\alpha ,0)$ and $B(0,\beta )$, where $\alpha \in [0,2]$ and $\beta \in [0,5]$, be such that the line segment $AB$ divides the area of the rectangle $R$ in the ratio $4:1$. Then, the midpoint of $AB$ lies on a: