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

If $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$ and $x \neq y \neq z$,then $1+x y z$ is equal to

Given that:
$2C_{(s)} + 2O_{2(g)} \to 2CO_{2(g)}; \Delta H = -787 \ kJ$
$H_{2(g)} + 1/2 O_{2(g)} \to H_2O_{(l)}; \Delta H = -286 \ kJ$
$C_2H_{2(g)} + 2.5 O_{2(g)} \to 2CO_{2(g)} + H_2O_{(l)}; \Delta H = -1301 \ kJ$
Calculate the heat of formation of acetylene $(C_2H_{2(g)})$ in $kJ$.

The gas that cannot be collected over water is

$A$ radioactive sample $S_1$ having an activity of $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ can be

Two point white dots are $1 \, mm$ apart on black paper. They are viewed by an eye with a pupil diameter of $3 \, mm$. Approximately,what is the maximum distance at which these dots can be resolved by the eye? (Take $\lambda = 500 \, nm$)