$A$ light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 \, cm$,the frequency of the tuning fork is .... $Hz$

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

The position of a projectile launched from the origin at $t=0$ is given by $\vec{r}=(40 \hat{i}+50 \hat{j}) \text{ m}$ at $t=2 \text{ s}$. If the projectile was launched at an angle $\theta$ from the horizontal,then $\theta$ is (take $g = 10 \text{ m/s}^2$)

The number of solutions for $z^3+\bar{z}=0$ is

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$

$A$ galvanometer $G$ deflects full scale when a potential difference of $0.50 \ V$ is applied. The internal resistance of the galvanometer $r_g$ is $25 \ \Omega$. An ammeter is constructed by incorporating the galvanometer and an additional shunt resistance $R_S$. The ammeter deflects full scale when a measurement of $2.0 \ A$ is made. The resistance $R_S$ is closest to ............. $\Omega$.