Two bodies of mass $4 ~kg$ and $5 ~kg$ are moving along east and north directions with velocities $5 ~m/s$ and $3 ~m/s$ respectively. The magnitude of the velocity of the centre of mass of the system is

Cuscuta is an example of

$A$ train whistling at a constant frequency is moving towards a station at a constant speed $V_s$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r$ $(r << R)$ at its bottom,the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of the water stream when it hits the ground is $x$,then:

$(\sim (p \vee q)) \vee (\sim p \wedge q)$ is logically equivalent to

$2 \pi - \left(\sin ^{-1} \frac{4}{5} + \sin ^{-1} \frac{5}{13} + \sin ^{-1} \frac{16}{65}\right)$ is equal to