MCA Entrance Previous Year Question Bank

Let a triangle $ABC$ be inscribed in the circle $x^2-\sqrt{2}(x+y)+y^2=0$ such that $\angle BAC=\frac{\pi }{2}$. If the length of side $AB$ is $\sqrt{2}$, then the area of the $△ABC$ is equal to:

Let the tangent to the circle $C_1:x^2+y^2=2$ at the point $M(-1,1)$ intersect the circle $C_2:(x-3{)}^2+(y-2{)}^2=5$, at two distinct points $A$ and $B$. If the tangents to $C_2$ at the points $A$ and $B$ intersect at $N$, then the area of the triangle $ANB$ is equal to:

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P\left(\frac{1+a}{2},\frac{1-a}{2}\right)$ on the circle $2x^2+2y^2-(1+a)x-(1-a)y=0$, is equal to:

Let a circle $C_1$ be obtained on rolling the circle $x^2+y^2-4x-6y+11=0$ upwards $4$ units on the tangent $T$ to it at the point $(3,2)$. Let $C_2$ be the image of $C_1$ in $T$. Let $A$ and $B$ be the centers of circles $C_1$ and $C_2$ respectively, and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium $AMNB$ is :

Let $P(a_1,b_1)$ and $Q(a_2,b_2)$ be two distinct points on a circle with center $C(\sqrt{2},\sqrt{3})$. Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$. If the area of the triangle $OCP$ is $\frac{\sqrt{35}}{2}$, then the value of $a_1^2+a_2^2+b_1^2+b_2^2$ is:

Let $y=x+2,4y=3x+6$ and $3y=4x+1$ be three tangent lines to the circle $(x-h{)}^2+(y-k{)}^2=r^2$. Then $h+k$ is equal to:

A circle with centre $(2,3)$ and radius 4 intersects the line $x+y=3$ at the points $P$ and $Q$. If the tangents at $P$ and $Q$ intersect at the point $S(\alpha ,\beta )$, then $4\alpha -7\beta$ is equal to

Let the tangents at the points $A(4,-11)$ and $B(8,-5)$ on the circle $x^2+y^2-3x+10y-15=0$, intersect at the point $C$. Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to

Points $P(-3,2)$, $Q(9,10)$ and $R(a,4)$ lie on a circle $C$ with $PR$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the line $2x-ky=1$, then $k$ is equal to:

The points of intersection of the line $ax+by=0,(a\ne b)$ and the circle $x^2+y^2-2x=0$ are $A(\alpha ,0)$ and $B(1,\beta )$. The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is: