$A$ body cools from $62^{\circ}C$ to $50^{\circ}C$ in $10$ minutes and to $42^{\circ}C$ in the next $10$ minutes. The temperature of the surrounding is ........... $^{\circ}C$.

For all values of $a$ and $b$,the line $(a+2b)x + (a-b)y + (a+5b) = 0$ passes through a fixed point. Find that point.

If the coefficient of $x$ in the expansion of $\left(x^2+\frac{k}{x}\right)^5$ is $270$,then $k$ is equal to

Five capacitors,each of capacitance $C$,are connected as shown in the figure. The ratio of the equivalent capacitance between $P$ and $R$ to the equivalent capacitance between $P$ and $Q$ is:

What is the primary purpose of data entry in the context of mathematical research?

$A$ complex compound of $Co^{3+}$ with molecular formula $CoCl_{x} \cdot yNH_3$ gives a total of $3$ ions when dissolved in water. How many $Cl^{-}$ ions satisfy both primary and secondary valencies in this complex?