$A$ tuning fork vibrating with a sonometer having $20 \, cm$ wire produces $5$ beats per sec. The beat frequency does not change if the length of the wire is changed to $21 \, cm$. The frequency of the tuning fork must be ..... $Hz$.

In the reaction $\underset{\text{(Vapour)}}{C_2H_5OH} \xrightarrow[300^{\circ} C]{Cu} X$. The molecular formula of $X$ is

If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $hA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$,then the values of $h, a, b$ are respectively

Seminal plasma in human males is rich in

$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 ~Hz$. Then,the value of the fundamental frequency of the closed pipe is: (in $~Hz$)

When a ceiling fan is switched off,its angular velocity falls to half while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)