$3$ moles of ethanol react with $1$ mole of phosphorus tribromide to form $3$ moles of bromoethane and $1$ mole of $X$. Which of the following is $X$?

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is

If in a $\triangle ABC$,$r_1=2$,$r_2=3$ and $r_3=6$,then $a$ equals to

$A$ body cools from $62^{\circ}C$ to $50^{\circ}C$ in $10 \text{ minutes}$ and to $42^{\circ}C$ in the next $10 \text{ minutes}$. The temperature of the surroundings is ........ $^{\circ}C$.

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has a moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{i}-\hat{j}$,$4 \hat{i}$,$3 \hat{i}+3 \hat{j}$ and $-3 \hat{i}+2 \hat{j}$ respectively. Then the quadrilateral $PQRS$ must be a