$A$ variable circle passes through the fixed point $A(p, q)$ and touches the $x$-axis. The locus of the other end of the diameter through $A$ is

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to

Three moles of an ideal monoatomic gas undergo a cyclic process as shown in the figure. The temperatures of the gas in different states marked as $1, 2, 3$ and $4$ are $400 \ K, 700 \ K, 2500 \ K$ and $1100 \ K$ respectively. The work done by the gas during the process $1-2-3-4-1$ is (universal gas constant is $R$): (in $R$)

Which of the following complexes exhibits both geometrical and optical isomerism?

Vegetative propagation in mint occurs by

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is