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 .... $cm$.

In which of the genetic disorders does an individual exhibit overall masculine development,gynaecomastia,and sterility?

The coefficient of $x^4$ in the expansion of $\frac{(1-3x)^2}{(1-2x)}$ is equal to

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to

$A$ particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

Two particles having position vectors $r_1 = (3 \hat{i} + 5 \hat{j}) \ m$ and $r_2 = (-5 \hat{i} - 3 \hat{j}) \ m$ are moving with velocities $v_1 = (4 \hat{i} + 3 \hat{j}) \ m/s$ and $v_2 = (a \hat{i} + 7 \hat{j}) \ m/s$. If they collide after $2 \ s$,then the value of $a$ is: