Which of the following species has no $p\pi-p\pi$ bond but has a bond order equal to $O_2$?

If $0 < y < 2^{1/3}$ and $x(y^3 - 1) = 1$,then $\frac{2}{x} + \frac{2}{3x^3} + \frac{2}{5x^5} + \dots$ is equal to:

The refractive index of a material of a plano-concave lens is $5/3$,and the radius of curvature is $0.3 ~m$. The focal length of the lens in air is (in $~m$)

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ \AA}$. The maximum energy of a photon in the radiation in $eV$ is $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$. (in $27,500$)

$A$ photoelectric cell is connected to a source of variable potential difference. The resulting photoelectric current $(\mu A)$ is plotted against the applied potential difference $(V)$. The graph with the broken line represents the data for a given frequency and intensity of the incident radiation. If the frequency is increased and the intensity is reduced, which of the following graphs (represented by unbroken lines) corresponds to the new situation?

If $\frac{x+1}{(2x-1)(3x+1)}=\frac{A}{(2x-1)}+\frac{B}{(3x+1)}$, then $16A+9B$ is equal to