JEE Main 2026 (Online) 4th April Morning Shift

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm , at a resolution of $5 \times 10^{-7}$ radian. The value of $R$ is

$\_\_\_\_$ cm .

$$\text { Consider the following sequence of reactions to give the major product }(\mathrm{X})$$

P g of the major product $(\mathrm{X})$ formed is reacted with $\mathrm{NaHCO}_3$ solution to liberate a gas which occupied $11.2 \mathrm{dm}^3$ at STP.

$$\mathrm{P}=\text {______________ g. }$$

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{O}: 16, \mathrm{Cl}: 35.5$ )

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is $p$, then $96 p$ is equal to $\_\_\_\_$ .

The surface tension of a soap solution is $3.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha \times 10^{-6} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

$$(\pi=22 / 7)$$

According to Lewis theory, the total number of $\sigma$ bond-pairs and lone pair of electrons around the central atom of $\mathrm{XeO}_6{ }^{4-}$ ion is $\_\_\_\_$ .

The number of points, at which the function $f(x)=\max \left\{6 x, 2+3 x^2\right\}+|x-1| \cos \left|x^2-\frac{1}{4}\right|, x \in(-\pi, \pi)$, is not differentiable, is

$\_\_\_\_$ .