Two spheres made of the same substance have diameters in the ratio $1: 2$. Their thermal capacities are in the ratio of .............

In an atom,the order of increasing energy of electrons with quantum numbers $(i)$ $n=4, l=1$,$(ii)$ $n=4, l=0$,$(iii)$ $n=3, l=2$,and $(iv)$ $n=3, l=1$ is:

The length of the subtangent at any point of the curve $x^m y^n = a^{m+n}$ is proportional to -

At $25^{\circ} C$, the concentration of $H ^{+}$ions in $1.00 \times 10^{-3} M$ aqueous solution of a weak monobasic acid having acid dissociation constant $\left(K_a\right)=4.00 \times 10^{-11}$ is $X \times 10^{-7} M$. The value of $X$ is $...$ .
Use: Ionic product of water $\left(K_w\right)=1.00 \times 10^{-14}$ at $25^{\circ} C$

$\frac{1}{e^{3x}}(e^x + e^{5x}) = a_0 + a_1x + a_2x^2 + \ldots$
$\Rightarrow 2a_1 + 2^3a_3 + 2^5a_5 + \ldots$ is equal to

How many different types of gametes will be produced by a plant with the genotype $AABbCC$?