$A$ random variable $X$ takes the values $0, 1, 2, 3, \ldots$ with probability $P(X=x)=k(x+1)\left(\frac{1}{5}\right)^x$,where $k$ is a constant. Then $P(X=0)$ is

In a compound microscope,the focal lengths of the two lenses are $1.5 \, cm$ and $6.25 \, cm$. If an object is placed at $2 \, cm$ from the objective lens and the final image is formed at $25 \, cm$ from the eye lens,the distance between the two lenses is ...... $cm$.

The correct order of second $I.E.$ of $C, N, O$ and $F$ is:

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

$A$ metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $n$ rotations per second. It is suddenly stopped and $50 \%$ of its energy is used in increasing its temperature. Then,the rise in temperature of the sphere is

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$).