In the given circuit, the current through the battery is ........ $A$.

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

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

If $y = \sin(m \sin^{-1} x)$,then $(1 - x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

Which one of the following conditions correctly describes the manner of determining the sex?

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 ~Hz$ when like poles are tied together and it is $2 ~Hz$ when the unlike poles are tied together,then the ratio $M_1: M_2$ is