Orbital having 3 angular nodes and 3 total nodes is:

In hydrogen atom, what is the de Broglie wavelength of an electron in the second Bohr orbit is: [Given that Bohr radius, $a_0=52.9$ $pm$]

1. 211.6 pm

2. 211.6 $\mathrm{\pi }$pm

3. $52.9$ $\mathrm{\pi }$pm

4. 105.8 pm

The volume occupied by 1.8 g of water vapour at 374 ${}^{\mathrm{o}}\mathrm{C}$ and 1 bar pressure will be -

[Use R=0.083 bar ${\mathrm{LK}}^{-1}$ ${\mathrm{mol}}^{-1}$]

1. 96.66 L

2. 55.87 L

3. 3.10 L

4. 5.31 L

What is the amount of work done by an ideal gas, if the gas expands isothermally from \(10^{-3}~m^3\) to \(10^{-2}~m^3\) at \(300~K\)against a constant pressure of \(10^{5}~Nm^{-2}\)?

Reversible expansion of an ideal gas under isothermal and adiabatic conditions are shown in the figure:

AB$\to$Isothermal expansion

AC$\to$Adiabatic expansion

Which of the following options is not correct?

The distance covered by a particle undergoing SHM in one time period is: (amplitude \(= A\))
1. zero
2. \(A\)
3. \(2 A\)
4. \(4 A\)

A mass falls from a height \(h\) and its time of fall \(t\) is recorded in terms of time period \(T\) of a simple pendulum. On the surface of the earth, it is found that \(t=2T\). The entire setup is taken on the surface of another planet whose mass is half of that of the Earth and whose radius is the same. The same experiment is repeated and corresponding times are noted as \(t'\) and \(T'\). Then we can say:

An object flying in the air with velocity \((20 \hat{i}+25 \hat{j}-12 \hat{k})\) suddenly breaks into two pieces whose masses are in the ratio of \(1:5.\) The smaller mass flies off with a velocity \((100 \hat{i}+35 \hat{j}+8 \hat{k})\)$\mathrm{}$. The velocity of the larger piece will be:
1. \( 4 \hat{i}+23 \hat{j}-16 \hat{k}\)
2. \( -100 \hat{i}-35 \hat{j}-8 \hat{k} \)
3. \( 20 \hat{i}+15 \hat{j}-80 \hat{k} \)
4. \( -20 \hat{i}-15 \hat{j}-80 \hat{k}\)