MCA Entrance Previous Year Question Bank

The position vectors of $A,B,C$ and $D$ are $\hat{i}+\hat{j}+\hat{k}$, $2\hat{i}+5\hat{j}$, $3\hat{i}+2\hat{j}-3\hat{k}$ and $\hat{i}-6\hat{j}-\hat{k}$, then the angle between $\overrightarrow{AB}$ and $\overrightarrow{CD}$ is:

If $C$ is the middle point of $AB$ and $P$ is any point outside $AB$, then:

If three vectors $2\hat{i}-\hat{j}+\hat{k}$, $\hat{i}+2\hat{j}-3\hat{k}$ and $3\hat{i}+\lambda \hat{j}+5\hat{k}$ are co-planar, then $\lambda$ is:

The area of the parallelogram whose diagonals are $\vec{a}=3\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=\hat{i}-3\hat{j}+4\hat{k}$ is:

Forces $3\hat{i}+2\hat{j}+5\hat{k}$ and $2\hat{i}+\hat{j}-3\hat{k}$ are acting on a particle and displace it from the point $2\hat{i}-\hat{j}-3\hat{k}$ to the point $4\hat{i}-3\hat{j}+7\hat{k}$. The work done by the force is:

If the vectors $2\hat{i}-3\hat{j}$, $\hat{i}+\hat{j}-\hat{k}$ and $3\hat{i}-\hat{k}$ form the three co-terminous edges of a parallelepiped, then the volume of parallelepiped is:

Let $\vec{a}=\hat{j}-\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$. Then the vector $\vec{b}$ satisfying $(\vec{a}\times \vec{b})+\vec{c}=0$ and $\vec{a}\cdot \vec{b}=3$, is:

If $\vec{A}=4\hat{i}+3\hat{j}+\hat{k}$ and $\vec{B}=2\hat{i}-\hat{j}+2\hat{k}$, then the unit vector $\hat{N}$ perpendicular to the vectors $\vec{A}$ and $\vec{B}$, such that $\vec{A},\vec{B}$ and $\hat{N}$ form a right handed system, is:

Constant forces $\vec{P}=2\hat{i}-5\hat{j}+6\hat{k}$ and $\vec{Q}=-\hat{i}+2\hat{j}-\hat{k}$ act on a particle. The work done when the particle is displaced from $A$ whose position vector is $4\hat{i}-3\hat{j}-2\hat{k}$, to $B$ whose position vector is $6\hat{i}+\hat{j}-3\hat{k}$, is:

If $y=co{s}^2{x}^2$, find $dy/dx$