In a galvanometer,$5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer is $G$,the shunt resistance $S$ connected to the galvanometer is

The gravitational force acting on a particle,due to a solid sphere of uniform density and radius $R$,at a distance of $3 R$ from the centre of the sphere is $F_1$. $A$ spherical hole of radius $(R / 2)$ is now made in the sphere as shown in the figure. The sphere with hole now exerts a force $F_2$ on the same particle. Ratio of $F_1$ and $F_2$ is

$A$ horizontal force of $10\, N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is ........ $N$.

If the pair of straight lines given by $Ax^2+2Hxy+By^2=0$ $(H^2 > AB)$ forms an equilateral triangle with the line $ax+by+c=0$,then $(A+3B)(3A+B)$ is equal to:

$A$ bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased,while keeping the voltage of the source constant,then

The equation of the tangent to the curve $y = b e^{-x/a}$ at the point where it crosses the $y$-axis is: