If $a \neq p, b \neq q, c \neq r$ and $\left|\begin{array}{ccc}p & b & c \\ p+a & q+b & 2c \\ a & b & r\end{array}\right|=0$,then $\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$ is equal to :

One mole of an ideal gas having initial volume $V$,pressure $2P$ and temperature $T$ undergoes a cyclic process $ABCDA$ as shown in the figure. The net work done in the complete cycle is:

Observe the following reactions at $T(K)$:
$I. A \rightarrow \text{products}$
$II. 5Br^{-}_{(aq)} + Br{O_{3}}^{-}_{(aq)} + 6H^{+}_{(aq)} \rightarrow 3Br_{2(aq)} + 3H_{2}O_{(l)}$
Both the reactions are started at $10.00 \text{ am}$. The rates of these reactions at $10.10 \text{ am}$ are same. The value of $-\frac{\Delta[Br^{-}]}{\Delta t}$ at $10.10 \text{ am}$ is $2 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1}$. The concentration of $A$ at $10.10 \text{ am}$ is $10^{-1} \text{ mol L}^{-1}$. What is the first order rate constant (in $\text{min}^{-1}$) of reaction $I$?

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

Which characteristic of living organisms ensures that the population size of each species remains limited?

Match the items in Column-$I$ with those in Column-$II$:

Column-$I$	Column-$II$
$A$. Tapetum	$i$. Degenerate during development
$B$. Intine	$ii$. Resistant organic materials
$C$. Vegetative cell	$iii$. Pollen tube
$D$. Sporopollenin	$iv$. Provide nourishment to pollen grains