$A$ ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, $25\%$ of incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio of $I_{max}$ and $I_{min}$ is (in $: 1$)

$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ} = $

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 $25^{\circ} C$

The order of catenation property for $C$,$Si$,and $Ge$ is $Ge < Si < C$. Which of the following represents the bond energy $\left( kJ \ mol^{-1} \right)$ for $C-C$,$Si-Si$,and $Ge-Ge$ bonds respectively?

The concentration of an organic compound in chloroform is $6.15 \ g$ per $100 \ mL$ of solution. $A$ portion of this solution in a $5 \ cm$ polarimeter tube causes an observed rotation of $-1.2^{\circ}$. What is the specific rotation of the compound?

Which of the following is an extinct human species?