$A$ metal is burnt in air and the ash on moistening smells of $NH_3$. The metal is

$C_6H_6 + 3O_3$ $\longrightarrow X \stackrel{Zn / H_2O}{}$ ${\longrightarrow} Y$; $X$ and $Y$ are respectively

Which of the following statements is correct?

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \ pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has a dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$,while the other has a dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. The new capacitance of the capacitor is ........ $pF$.

The points with position vectors $60i + 3j$,$40i - 8j$,and $ai - 52j$ are collinear if $a = \dots$

If $\tan \theta + \tan \left(\theta + \frac{\pi}{3}\right) + \tan \left(\theta + \frac{2\pi}{3}\right) = 3$,then which of the following is equal to $1$?