Four light sources produce the following four waves:
$(i)$ $y_1 = a \sin(\omega t + \phi_1)$
(ii) $y_2 = a \sin(2\omega t)$
(iii) $y_3 = d' \sin(\omega t + \phi_2)$
(iv) $y_4 = d' \sin(3\omega t + \phi)$
Superposition of which two waves gives rise to interference?

In the arrangement shown in the figure,the masses of blocks $B$ and $A$ are $2m$ and $m$ respectively. The surface between $B$ and the floor is smooth. Block $B$ is connected to block $C$ by means of a string-pulley system. If the whole system is released,find the minimum value of the mass of block $C$ so that block $A$ remains stationary with respect to $B$. The coefficient of friction between $A$ and $B$ is $\mu$.

If the lengths of the tangents drawn from a point $P$ to the three circles $x^2+y^2-4=0$,$x^2+y^2-2x+3y=0$,and $x^2+y^2+7y-18=0$ are equal,then the coordinates of $P$ are

If $f(x) = \sin x + \cos x$,then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to

During the change of $O_2$ to $O_2^-$ ion,the electron adds to which one of the following orbitals?

For a binomial variate $X$,if $n=4$ and $P(X=4)=6 P(X=2)$,then the value of $p$ is