MCA Entrance Previous Year Question Bank

Let $Q$ be the mirror image of the point $P(1,2,1)$ with respect to the plane $x+2y+2z=16$. Let $T$ be a plane passing through the point $Q$ and contains the line $\vec{r}=-\hat{k}+\lambda (\hat{i}+\hat{j}+2\hat{k}),\lambda \in R$. Then, which of the following points lies on $T$?

Let the line $\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}$ lie on the plane $px-qy+z=5$, for $p,q\in \mathbb{R}$. The shortest distance of the plane from the origin is:

Let $P_1:\vec{r}\cdot (2\hat{i}+\hat{j}-3\hat{k})=4$ be a plane. Let $P_2$ be another plane which passes through the points $(2,-3,2),(2,-2,-3)$ and $(1,-4,2)$. If the direction ratios of the line of intersection of $P_1$ and $P_2$ be $16,\alpha ,\beta$, then the value of $\alpha +\beta$ is equal to:

Let $d$ be the distance between the foot of perpendiculars of the points $P(1,2,-1)$ and $Q(2,-1,3)$ on the plane $-x+y+z=1$. Then $d^2$ is equal to:

If the mirror image of the point $(2,4,7)$ in the plane $3x-y+4z=2$ is $(a,b,c)$, then $2a+b+2c$ is equal to:

The point of intersection $C$ of the plane $8x+y+2z=0$ and the line joining $A(-3,-6,1)$ and $B(2,4,-3)$ divides $AB$ internally in ratio $k:1$. If $a,b,c$ are coprime direction ratios of the perpendicular from $C$ on the line $\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}$, then $|a+b+c|$ is equal to:

Let $\alpha x+\beta y+\gamma z=1$ be the equation of a plane through the point $(3,-2,5)$ and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$. Then the value of $\alpha \beta \gamma$ is equal to:

Let $P(x_0,y_0)$ be the point on the hyperbola $3x^2-4y^2=36$, which is nearest to the line $3x+2y=1$. Then $\sqrt{2}(y_0-x_0)$ is equal to:

Let the plane $P$ pass through the intersection of the planes $2x+3y-z=2$ and $x+2y+3z=6$ and be perpendicular to the plane $2x+y-z=0$. If $d$ is the distance of $P$ from the point $(-7,1,1)$, then $d^2$ is equal to:

Let the image of the point $P(2,-1,3)$ in the plane $x+2y-z=0$ be $Q$. Then the distance of the plane $3x+2y+z+29=0$ from the point $Q$ is