JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT

A car of \(800 \mathrm{~kg}\) is taking turn on a banked road of radius \(300 \mathrm{~m}\) and angle of banking \(30^{\circ}\). If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: \((\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73)\)

Match List I with List II.

Choose the correct answer from the options given below :

If the function \(f(x)=\left(\frac{1}{x}\right)^{2 x} ; x>0\) attains the maximum value at \(x=\frac{1}{\mathrm{e}}\) then :

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

For the reaction at \(298 \mathrm{~K}, 2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C}, \Delta \mathrm{H}=400 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(\Delta S=0.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). The reaction will become spontaneous above __________ \(\mathrm{K}\).

If the shortest distance between the lines \(\frac{x-\lambda}{3}=\frac{y-2}{-1}=\frac{z-1}{1}\) and \(\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-4}{4}\) is \(\frac{44}{\sqrt{30}}\), then the largest possible value of \(|\lambda|\) is equal to _________.