MCA Entrance Previous Year Question Bank

Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is: (1) 5

Let the plane $P:8x+a_{1}y+a_{2}z+12=0$ be parallel to the line $L:\frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the intercept of $P$ on the $y$-axis is $1$, then the distance between $P$ and $L$ is:

The foot of perpendicular from the origin $O$ to a plane $P$ which meets the co-ordinate axes at the points $A,B,C$ is $(2,a,4),a\in \mathbb{N}$. If the volume of the tetrahedron $OABC$ is $144{\text{ unit}}^3$, then which of the following points is NOT on $P$?

Let the line $L:\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2x+y+3z=16$ at the point $P$. Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$. If $\alpha$ is the area of triangle $PQR$, then ${\alpha }^2$ is equal to:

Let $\theta$ be the angle between the planes $P_1:\vec{r}\cdot (\hat{i}+\hat{j}+2\hat{k})=9$ and $P_2:\vec{r}\cdot (2\hat{i}-\hat{j}+\hat{k})=15$. Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_2$. If $\alpha$ is the angle between $L$ and $P_2$, then $({\tan }^2\theta )({\cot }^2\alpha )$ is equal to:

Let the plane $P$ contain the line $2x+y-z-3=0=5x-3y+4z+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then, the distance of the point $A(8,-1,-19)$ from the plane $P$ measured parallel to the line $\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}$ is equal to _____.

Let the foot of the perpendicular of the point $P(3,-2,-9)$ on the plane passing through the points $(-1,-2,-3),(9,3,4),(9,-2,1)$ be $Q(\alpha ,\beta ,\gamma )$. Then, the distance of $Q$ from the origin is:

Let $N$ be the foot of the perpendicular from the point $P(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$. Then, the distance of $N$ from the plane $2x-2y+z+5=0$ is:

The plane, passing through the points (0, –1, 2) and (–1, 2, 1) and parallel to the line passing through (5, 1, –7) and (1, –1, –1), also passes through the point: