The resistance of a bulb filament is $100\, \Omega$ at a temperature of $100\, ^oC$. If its temperature coefficient of resistance is $0.005\, (^oC)^{-1}$,at what temperature will its resistance become $200\, \Omega$?

A prism of angle $75^\circ$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index $1.5$ only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be . . . . . . .
$(\sin 15^\circ = 0.25$ and $\sin 25^\circ = 0.43)$

When acetylene is passed through a red-hot iron tube,compound $X$ is formed. Which one of the following reactions will yield $X$ as the major product?

In a quadrilateral $ABCD$,the point $P$ divides $DC$ in the ratio $1:2$ and $Q$ is the midpoint of $AC$. If $\overrightarrow{AB}+2\overrightarrow{AD}+\overrightarrow{BC}-2\overrightarrow{DC}=k\overrightarrow{PQ}$,then $k$ is equal to

The calculated magnetic moment (in Bohr magnetons) of $Cu^{2+}$ ion is

The area (in sq units) bounded by the curves $y^2=4x$ and $x^2=4y$ is