JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT

In a system two particles of masses \(m_1=3 \mathrm{~kg}\) and \(m_2=2 \mathrm{~kg}\) are placed at certain distance from each other. The particle of mass \(m_1\) is moved towards the center of mass of the system through a distance \(2 \mathrm{~cm}\). In order to keep the center of mass of the system at the original position, the particle of mass \(m_2\) should move towards the center of mass by the distance _________ \(\mathrm{cm}\).

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is ________.

From \(6.55 \mathrm{~g}\) of aniline, the maximum amount of acetanilide that can be prepared will be ________ \(\times 10^{-1} \mathrm{~g}\).

The displacement of a particle executing SHM is given by \(x=10 \sin \left(w t+\frac{\pi}{3}\right) m\). The time period of motion is \(3.14 \mathrm{~s}\). The velocity of the particle at \(t=0\) is _______ \(\mathrm{m} / \mathrm{s}\).

In a tournament, a team plays 10 matches with probabilities of winning and losing each match as \(\frac{1}{3}\) and \(\frac{2}{3}\) respectively. Let \(x\) be the number of matches that the team wins, and $y$ be the number of matches that team loses. If the probability \(\mathrm{P}(|x-y| \leq 2)\) is \(p\), then \(3^9 p\) equals _________.

The maximum number of orbitals which can be identified with \(\mathrm{n}=4\) and \(m_l=0\) is _________.