JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT

A solid circular disc of mass \(50 \mathrm{~kg}\) rolls along a horizontal floor so that its center of mass has a speed of \(0.4 \mathrm{~m} / \mathrm{s}\). The absolute value of work done on the disc to stop it is ________ J.

Consider the following reaction at \(298 \mathrm{~K} \cdot \frac{3}{2} \mathrm{O}_{2(g)} \rightleftharpoons \mathrm{O}_{3(g)} \cdot \mathrm{K}_{\mathrm{P}}=2.47 \times 10^{-29}\). \(\Delta_r G^{\ominus}\) for the reaction is _________ \(\mathrm{kJ}\). (Given \(\mathrm{R}=8.314 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}\))

Let \(A=\{1,2,3,4\}\) and \(R=\{(1,2),(2,3),(1,4)\}\) be a relation on \(\mathrm{A}\). Let \(\mathrm{S}\) be the equivalence relation on \(\mathrm{A}\) such that \(R \subset S\) and the number of elements in \(\mathrm{S}\) is \(\mathrm{n}\). Then, the minimum value of \(n\) is __________.

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is _______ \(m\).

(Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{~Nm}^{-2}\), and \(g=10 \mathrm{~ms}^{-2}\))

Number of moles of methane required to produce \(22 \mathrm{~g} \mathrm{~CO}_{2(\mathrm{~g})}\) after combustion is \(\mathrm{x} \times 10^{-2}\) moles. The value of \(\mathrm{x}\) is _________.

In the expansion of \((1+x)\left(1-x^2\right)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5, x \neq 0\), the sum of the coefficients of $x^3$ and \(x^{-13}\) is equal to __________.