If $a_k$ is the coefficient of $x^k$ in the expansion of $(1+x+x^2)^n$ for $k=0, 1, 2, \ldots, 2n$,then $a_1+2a_2+3a_3+\ldots+2na_{2n}$ is equal to

If $Alpha$,$Beta$,and $\Gamma$ rays carry the same momentum,which has the longest wavelength?

An electron microscope is operated at $40 \ kV$. The ratio of the resolving power of this microscope to another one which uses yellow light of wavelength $6 \times 10^{-7} \ m$ is:

The solution of $\frac{dy}{dx} + \frac{1}{3}y = 1$ is

Regarding the molecular orbital $(MO)$ energy levels for homonuclear diatomic molecules, the $\text{INCORRECT}$ statement$(s)$ is$($are$)$
$(A)$ Bond order of $Ne _2$ is zero.
$(B)$ The highest occupied molecular orbital $\text{(HOMO)}$ of $F_2$ is $\sigma$-type.
$(C)$ Bond energy of $O _2^{+}$is smaller than the bond energy of $O _2$.
$(D)$ Bond length of $Li _2$ is larger than the bond length of $B _2$

Which of the following sets of quantum numbers belongs to the highest energy orbital?