Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (\(g\)) is:

A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ\text{C}.\) Its density is:
(\(R=8.3~\text{J mol}^{-1} \text {K}^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)

A long solenoid of \(50~\text{cm}\) length having \(100\) turns carries a current of \(2.5~\text{A}\). The magnetic field at the centre of the solenoid is: 
\(\big(\mu_0 = 4\pi\times 10^{-7}~\text{TmA}^{-1} \big)\)
1. \(3.4\times 10^{-4}~\text{T}\)
2. \(6.28\times 10^{-5}~\text{T}\)
3. \(3.14\times 10^{-5}~\text{T}\)
4. \(6.28\times 10^{-4}~\text{T}\)

A resistance wire connected in the left gap of a meter bridge balances a \(10~\Omega\) $$resistance in the right gap at a point which divides the bridge wire in the ratio \(3:2\). lf the length of the resistance wire is \(1.5~\text{m}\), then the length of \(1~\Omega\) of the resistance wire will be:

The energy required to break one bond in DNA is \(10^{-20}~\text{J}\). This value in eV is nearly: 
1. \(0.6\)
2. \(0.06\)
3. \(0.006\)
4. \(6\)

Two cylinders \(A\) and \(B\) of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. \(B\) is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is:

Light with an average flux of \(20~\text{W/cm}^2\) falls on a non-reflecting surface at normal incidence having a surface area \(20~\text{cm}^2\). The energy received by the surface during time span of \(1\) minute is:
1. \(12\times 10^{3}~\text{J}\)
2. \(24\times 10^{3}~\text{J}\)
3. \(48\times 10^{3}~\text{J}\)
4. \(10\times 10^{3}~\text{J}\)