If the pressure at half the depth of a lake is equal to $2/3$ of the pressure at the bottom of the lake,then what is the depth of the lake in $m$? (Assume atmospheric pressure $P_0 = 10^5 \ Pa$,density of water $\rho = 10^3 \ kg/m^3$,and $g = 10 \ m/s^2$)

Two resistances $X$ and $Y$ are connected in the two gaps of a meter bridge,and the null point is obtained at $20 \text{ cm}$ from the zero end. When a resistance of $20 \text{ } \Omega$ is connected in series with the smaller of the two resistances $X$ and $Y$,the null point shifts to $40 \text{ cm}$ from the left end. The value of the smaller resistance in ohms is:

Data Entry - Physics

In which plant group are the sporophylls arranged spirally along an axis to form distinct compact structures called strobili or cones?

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to

If a wire of length $L$ forms a loop of radius $R$ and has $n$ turns,find the magnetic field at the center of the loop. The current flowing in the loop is $I$.