In the arrangement shown in the figure,the ends $P$ and $Q$ of an unstretchable string move downwards with a uniform speed $U$. Pulleys $A$ and $B$ are fixed. The mass $M$ moves upwards with a speed:

$A$ fire hydrant delivers water of density $\rho$ at a volume rate $L$. The water travels vertically upward through the hydrant and then makes a $90^o$ turn to emerge horizontally at speed $V$. The pipe and nozzle have a uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is

Match the following columns:

Column-$I$	Column-$II$
$A$. Halophiles	$i$. Gram-negative bacteria
$B$. Thermoacidophiles	$ii$. Inhabit extremely salty areas
$C$. Spirochetes	$iii$. Responsible for methane production
$D$. Firmicutes	$iv$. Survive in acidic and high-temperature conditions
	$v$. Gram-positive bacteria

If $x = \frac{1 - t^2}{1 + t^2}$ and $y = \frac{2at}{1 + t^2}$,then $\frac{dy}{dx} = $

In an elastic collision of two particles,which of the following is conserved?

Three charges $2q, -q$ and $-q$ are located at the vertices of an equilateral triangle. At the centre of the triangle,