$250 \, mL$,$6 \, M$ $HCl$ and $350 \, mL$,$8 \, M$ $HNO_3$ are mixed with water to make the strength of the resulting solution $3 \, N$. What is the volume of water added? $mL$

Select the correct option based on the given figure. Symbol $T$ indicates a true statement and $F$ indicates a false statement.
Solution $P = 8 \, N$ $H_2SO_{4(aq)}$ and Solution $Q = 8 \, N$ $HNO_{3(aq)}$.
$(1)$ The number of moles of solute in solution $P$ and solution $Q$ are equal.
$(2)$ The number of gram-equivalents of solute in solution $P$ and solution $Q$ are equal.
$(3)$ The mole fraction of solvent in solution $P$ and solution $Q$ are equal.
$(4)$ The concentration of $H^+_{(aq)}$ in solution $P$ and solution $Q$ are equal.

Dinitrogen and dioxygen react with each other to form different compounds. The experimental data is given below:

Mass of Dinitrogen	Mass of Dioxygen
$(i) \ 14 \ g$	$16 \ g$
$(ii) \ 14 \ g$	$32 \ g$
$(iii) \ 28 \ g$	$32 \ g$
$(iv) \ 28 \ g$	$80 \ g$

$(a)$ Which law of chemical combination is followed by the above experimental data? State the law.
$(b)$ Fill in the blanks in the following conversions:
$(i) \ 1 \ km = \dots \ mm = \dots \ pm$
$(ii) \ 1 \ mg = \dots \ kg = \dots \ ng$
$(iii) \ 1 \ mL = \dots \ L = \dots \ dm^3$

Hydrochloric acid solutions $A$ and $B$ have concentrations of $0.5 \ N$ and $0.1 \ N$ respectively. The volumes of solutions $A$ and $B$ required to make $2 \ L$ of $0.2 \ N$ $HCl$ are:

$(i)$ Calculate the total number of electrons present in one mole of methane.
$(ii)$ Find $(a)$ the total number and $(b)$ the total mass of neutrons in $7 \, mg$ of $^{14}C$. (Assume that mass of a neutron $= 1.675 \times 10^{-27} \, kg$).
$(iii)$ Find $(a)$ the total number and $(b)$ the total mass of protons in $34 \, mg$ of $NH_3$. Will the answer change if the temperature and pressure are changed?

$A$ photon having a wavelength of $310 \ nm$ is used to break the bond of an $A_2$ molecule with a bond energy of $288 \ kJ \ mol^{-1}$. Calculate the percentage of the photon's energy that is converted into kinetic energy $(K.E.)$. [Given: $hc = 12400 \ eV \mathring{A}$,$1 \ eV/atom = 96 \ kJ/mol$]