If the population grows at the rate of $8 \%$ per year,then the time taken for the population to be doubled is (Given $\log 2=0.6912$ ) (in $text{ years}$)

An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is: (in $/T$)

Which chemical must be applied to the roots to keep the leaves of a plant green?

The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

Let $a, b$ and $c$ be distinct and none of them is equal to $1$. If the lines $x+ay+a=0$,$bx+y+b=0$ and $cx+cy+1=0$ are concurrent,then the value of $\frac{a}{a-1}+\frac{b}{b-1}+\frac{c}{c-1}$ is

If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2 + cx$ on the interval $x \in [-1, 1]$ at the point $x = \frac{1}{2}$,then $(2b + c)$ is equal to: