$A$ parallel plate capacitor with air as medium between the plates has a capacitance of $10\,\mu F$. The area of the capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constants $k_1 = 2$ and $k_2 = 4$. The capacitance of the system will now be.......$\mu F$.

An electron (mass = $9.1 \times 10^{-31} \ kg$; charge = $1.6 \times 10^{-19} \ C$) experiences no deflection if subjected to an electric field of $3.2 \times 10^5 \ V/m$ and a magnetic field of $2.0 \times 10^{-3} \ Wb/m^2$. Both the fields are normal to the path of the electron and to each other. If the electric field is removed,then the electron will revolve in an orbit of radius.......$m$

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 :

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting $5$ on the top of the die and tail on the coin is

If $y = \log_{\cos x} \sin x$,then $\frac{dy}{dx}$ is equal to

The number of $p\pi-d\pi$ 'pi' bonds present in $XeO_3$ and $XeO_4$ molecules,respectively,are: