Which of the following has the highest octane number?

The area (in square units) of the triangle formed by the points with polar coordinates $(1, 0)$,$(2, \frac{\pi}{3})$,and $(3, \frac{2\pi}{3})$ is

Assertion $A$: Barium is not required in the normal biological processes of the human body.
Reason $R$: Barium does not exhibit more than one oxidation state.

$A$ bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$,the initial velocity of the block immediately after the collision will be

An aluminium (resistivity $\rho = 2.2 \times 10^{-8} \Omega \cdot m$) wire of a diameter $1.4 \text{ mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is: (in $\text{ m}$)

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