JEE Main 2026 (Online) 2nd April Morning Shift

A tub is filled with water and a wooden cube $10\ \text{cm} \times 10\ \text{cm} \times 10\ \text{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by $3.87$ cm. The mass of the metal coin is ________ gram.

(Take water density as $1\ \text{g/cm}^3$ and density of wood as $0.4\ \text{g/cm}^3$)

At the transition temperature $T$, $A \rightleftharpoons B$ and $\Delta G^0 = 105 - 35 \log T$ where A and B are two states of substance X. The transition temperature in $^{\circ}\mathrm{C}$ when pressure is 1 atm is ________. (Nearest integer)

Let a, b, c ∈ {1, 2, 3, 4}. If the probability, that $a x^2 + 2\sqrt{2} bx + c > 0$ for all $x \in \mathbb{R}$, is $\frac{m}{n}$, $\gcd(m, n) = 1$, then $m + n$ is equal to ________.

A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $\left( \frac{W}{A} + \frac{2}{\gamma} \frac{w}{A} \right)$, where $A$ is the cross sectional area of the wire. The value of $\gamma$ is ________.

For reaction A → P, rate constant $k = 1.5 \times 10^3 \ \mathrm{s}^{-1}$ at $27^{\circ}\mathrm{C}$

If activation energy for the above reaction is $60\ \mathrm{kJ}\ \mathrm{mol}^{-1}$, then the temperature (in $^{\circ}\mathrm{C}$) at which rate constant, $k = 4.5 \times 10^3\ \mathrm{s}^{-1}$ is ______. (Nearest integer)

Given : $\log 2 = 0.30$, $\log 3 = 0.48$, $R = 8.3\ \mathrm{J}\ \mathrm{K}^{-1}\ \mathrm{mol}^{-1}$, $\ln 10 = 2.3$

If $\sum\limits_{k=1}^{n} a_k = 6 n^3$, then $\sum\limits_{k=1}^{6} \left( \frac{a_{k+1} - a_k}{36} \right)^2$ is equal to ________.