Three concentric metallic spherical shells of radii $R, 2R, 3R$ are given charges $Q_1, Q_2, Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then,the ratio of the charges given to the shells,$Q_1 : Q_2 : Q_3$ is

When a certain circuit consisting of a constant $e.m.f.$ $E$, an inductance $L$, and a resistance $R$ is closed, the current in it increases with time according to curve $1$. After one parameter $(E, L, \text{or } R)$ is changed, the increase in current follows curve $2$ when the circuit is closed a second time. Which parameter was changed and in what direction?

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

Consider the following statements $A$ and $B$ and identify the correct answer given below.
$A$. Peltier coefficient is numerically equal to the potential difference across the junctions of the thermocouple through which current is flowing.
$B$. According to Thomson,energy is neither absorbed nor evolved at the junction of a thermocouple but is absorbed or evolved only along the lengths of both the conductors.

An ice ball melts at a rate proportional to the amount of ice present at that instant. Half the quantity of ice melts in $20 \text{ minutes}$. Let $x_0$ be the initial quantity of ice. If after $40 \text{ minutes}$ the amount of ice left is $k x_0$,then the value of $k$ is:

How many stereoisomers are possible for the following molecule?