The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40 \pi t$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is .... $cm$.

Carbon,silicon,and germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(Eg)_C$,$(Eg)_{Si}$,and $(Eg)_{Ge}$ respectively. Which one of the following relationships is true in their case?

$A$ river is flowing from east to west at a speed of $5\ m/min$. $A$ man on the south bank of the river,capable of swimming $10\ m/min$ in still water,wants to swim across the river in the shortest time. He should swim:

In a college of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is:

Which gas is evolved when $SiO_2$ reacts with sodium carbonate?

The minimum value of $27 \tan ^2 \theta + 3 \cot ^2 \theta$ is