Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

$A$ thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction,as shown in the figure. When the system is placed in a uniform magnetic field of strength $B$ directed into the plane of the paper,the wire takes the shape of a circle. The tension in the wire is

The maximum tension a rope can withstand is $60 ~kg-wt$. The ratio of maximum acceleration with which two boys of masses $20 ~kg$ and $30 ~kg$ can climb up the rope at the same time is

The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is:

Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

The binding energy per nucleon of $^{16}O$ is $7.97 \, MeV$ and that of $^{17}O$ is $7.75 \, MeV$. The energy (in $MeV$) required to remove a neutron from $^{17}O$ is: