The conversion of $O$-acylated phenol to $C$-acylated phenol in the presence of $AlCl_3$ is an example of which type of organic reaction?

The equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is

In a $\triangle ABC$,if $\angle C = 90^{\circ}$,then $\frac{a^2-b^2}{a^2+b^2}$ is equal to

Two oxides of nitrogen,$NO$ and $NO_2$,react together at $253 \ K$ to form a compound of nitrogen $X$. $X$ reacts with water to yield another compound of nitrogen $Y$. The shape of the anion of $Y$ molecule is:

The radius of which of the following orbits is the same as that of the $1^{st}$ orbit of $H$ atom?

If $(1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}$,then $\sum_{r=1}^{15} r \frac{a_r}{a_{r-1}}$ is equal to