Given that $a, b \in \{0, 1, 2, \ldots, 9\}$ with $a+b \neq 0$ and that $\left(a+\frac{b}{10}\right)^x = \left(\frac{a}{10}+\frac{b}{100}\right)^y = 1000$. Then,$\frac{1}{x}-\frac{1}{y}$ is equal to

If $f(x) = \frac{1}{x^2} \int_3^x (2t - 3f'(t)) dt$,then $f'(3)$ is equal to

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction,when the angle of inclination of the plane is $60^{\circ}$,is

Given below are $2$ statements:
Statement $I$: The number of species among $BF_4^-$, $SiF_4$, $XeF_4$ and $SF_4$, that have unequal $E-F$ bond lengths is $2$. Here, $E$ is the central atom.
Statement $II$: Among $O_2^-$, $O_2^{2-}$, $F_2$ and $O_2^+$, $O_2^-$ has the highest bond order.
In the light of the above statements, choose the correct answer from the options given below

The major product in the following reaction is:

Which of the following pairs is incorrectly matched?