JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT

When \(\Delta \mathrm{H}_{\mathrm{vap}}=30 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta \mathrm{S}_{\mathrm{vap}}=75 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\), then the temperature of vapour, at one atmosphere is _________ K.

An electric field \(\vec{E}=(2 x \hat{i}) N C^{-1}\) exists in space. A cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is ______ \(\mathrm{Nm}^2 / \mathrm{C}\).

The integral \(\int_\limits{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-x}{1+x}}\right) d x\) is equal to

Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter \(10^{-15} \mathrm{~m}\) is ________ \(\times 10^9 \mathrm{~ms}^{-1}\) (nearest integer)

[Given : mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\), Plank's constant \((h)=6.626 \times 10^{-34} \mathrm{Js}\)] (Value of \(\pi=3.14\))

In the truth table of the above circuit the value of X and Y are :

\(\lim _\limits{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}\) is equal to