$A$ stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making $n$ revolutions per minute. The total tension in the string when the stone is at its lowest point is

If $PM$ is the perpendicular from $P(2, 3)$ onto the line $x+y=3$,then the coordinates of $M$ are

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass of the system is:

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?

$A$ small fish $0.4\, m$ below the surface of a lake is viewed through a simple converging lens of focal length $3\, m$. The lens is kept at $0.2\, m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at (given $\mu_{water} = 4/3$):

Double fertilization is a characteristic feature of which of the following?