$A$ man is watching two trains,one leaving and the other coming in with equal speeds of $4\, m/s$. If they sound their whistles,each of frequency $240\, Hz$,the number of beats heard by the man (velocity of sound in air $= 320\, m/s$) will be equal to

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is

In a hydrogen-like atom,an electron makes a transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$. If $n >> 1$,the frequency of the emitted radiation is proportional to:

Which of the following is a fossil plant?

Find the values of $x$,if: $(i)$ $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|$ (ii) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$