Two large parallel plates are connected to a $100\, V$ power supply. These plates have a fine hole at the centre. An electron having energy $200\, eV$ is directed such that it passes through the holes. When it emerges,its de-Broglie wavelength is ............. $\mathring{A}$.

If the pair of lines given by $(x^2+y^2) \cos^2 \theta = (x \cos \theta + y \sin \theta)^2$ are perpendicular to each other,then $\theta$ is equal to

The velocity at the mean position of a particle executing $S.H.M.$ is $v$. What is the velocity of the particle at a distance equal to half of the amplitude?

How many isomeric forms of $C_7H_9N$ contain a benzene ring?

An inductor $(L = 0.03 \ H)$ and a resistor $(R = 0.15 \ k\Omega)$ are connected in series to a battery of $15 \ V$ $EMF$ in a circuit as shown below. The key $K_1$ has been kept closed for a long time. Then at $t = 0$,$K_1$ is opened and key $K_2$ is closed simultaneously. At $t = 1 \ ms$,the current in the circuit will be ....... $mA$ $(e^5 \cong 150)$.

In a book of $500$ pages,it is found that there are $250$ typing errors. Assume that Poisson law holds for the number of errors per page. Then,the probability that a random sample of $2$ pages will contain no error,is :