The $9^{th}$ pair of cranial nerves in a frog is:

The $pH$ of a buffer solution made by mixing $25 \ mL$ of $0.02 \ M \ NH_4OH$ and $25 \ mL$ of $0.2 \ M \ NH_4Cl$ at $25^{\circ}C$ is ($pK_b$ of $NH_4OH = 4.8$).

Condenser $A$ has a capacity of $15 \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1 \mu F$ with air between the plates. Both are charged separately by a battery of $100 V$. After charging,both are connected in parallel without the battery and the dielectric material being removed from condenser $A$. The common potential now is.......$V$

The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

The phase difference between two waves,represented by $y_1 = 10^{-6} \sin \{100t + (x/50) + 0.5\} \ m$ and $y_2 = 10^{-6} \cos \{100t + (x/50)\} \ m$,where $x$ is in meters and $t$ is in seconds,is approximately .... $radians$.

If $\tanh ^{-1} x = a \log \left(\frac{1+x}{1-x}\right)$,$|x| < 1$,then $a$ is equal to