Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

$A$ circular coil of area $200 ~cm^2$ and $50$ turns is rotating about its vertical diameter with an angular speed of $40 ~rad/s$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} ~T$. The maximum emf induced in the coil is (in $~V$)

The angular resolution of a $10\,cm$ diameter telescope at a wavelength of $5000\,\mathring{A}$ is of the order of:

$A$ molecule $(X)$ has $(i)$ four sigma bonds formed by the overlap of $sp^2$ and $s$ orbitals,$(ii)$ one sigma bond formed by $sp^2$ and $sp^2$ orbitals,and $(iii)$ one $\pi$ bond formed by $p_z$ and $p_z$ orbitals. Which of the following is $X$?

Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

$A$ straight wire of length $20 \ cm$ carrying a current of $\frac{3}{\pi^2} \ A$ is bent in the form of a circle. The magnetic field at the centre of the circle is