The particles emitted during the sequential radioactive decay of ${}^{238}U_{92}$ to ${}^{206}Pb_{82}$ are

$K_1, K_2$ and $K_3$ are the equilibrium constants of the following reactions $(I), (II)$ and $(III)$,respectively :
$(I) \ N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(II) \ 2NO_2 \rightleftharpoons N_2 + 2O_2$
$(III) \ NO_2 \rightleftharpoons \frac{1}{2}N_2 + O_2$
The correct relation from the following is

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

What is the $IUPAC$ name of the following compound?

$\lim _{x \rightarrow 0} \frac{4^x-9^x}{x(4^x+9^x)}$ is equal to

In the circuit shown below,the ammeter reading is zero. Then the value of the resistance $R$ is (in $\Omega$)