JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT

For a certain thermochemical reaction \(\mathrm{M} \rightarrow \mathrm{N}\) at \(\mathrm{T}=400 \mathrm{~K}, \Delta \mathrm{H}^{\ominus}=77.2 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{S}=122 \mathrm{~JK}^{-1}, \log\) equilibrium constant \((\log K)\) is __________ \(\times 10^{-1}\).

The electric potential at the surface of an atomic nucleus \((z=50)\) of radius \(9 \times 10^{-13} \mathrm{~cm}\) is __________ \(\times 10^6 \mathrm{~V}\).

Let \(A\) be a \(2 \times 2\) real matrix and \(I\) be the identity matrix of order 2. If the roots of the equation \(|\mathrm{A}-x \mathrm{I}|=0\) be \(-1\) and 3, then the sum of the diagonal elements of the matrix \(\mathrm{A}^2\) is

The Spin only magnetic moment value of square planar complex \(\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}\left(\mathrm{NH}_2 \mathrm{CH}_3\right)\right] \mathrm{Cl}\) is _________ B.M. (Nearest integer)

(Given atomic number for \(\mathrm{Pt}=78\))

A body falling under gravity covers two points \(A\) and \(B\) separated by \(80 \mathrm{~m}\) in \(2 \mathrm{~s}\). The distance of upper point A from the starting point is _________ \(\mathrm{m}\) (use \(\mathrm{g}=10 \mathrm{~ms}^{-2}\)).

Let the complex numbers \(\alpha\) and \(\frac{1}{\bar{\alpha}}\) lie on the circles \(\left|z-z_0\right|^2=4\) and \(\left|z-z_0\right|^2=16\) respectively, where \(z_0=1+i\). Then, the value of \(100|\alpha|^2\) is __________.