A \(72 \; \Omega\) galvanometer is shunted by a resistance of \(8 \; \Omega\). The percentage of the total current which passes through the galvanometer is \(.....\)

There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment \(1\) is filled with an ideal gas and Compartment \(3\) is filled with a real gas. Compartments \(2\) and \(4\) are vacuum . A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum Statement \(-1\) : No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum Statement \(-2\) : The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by \(5 \times 10^{-2} \,m\) towards the slits, the change in fringe width is \(3 \times 10^{-3} \,cm\). If the distance between the slits is \(1 \,mm\), then the wavelength of the light will be_______ \(nm\)

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is :

A perfectly dimagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field \(\overrightarrow{ B }\). Then the field inside the paramagnetic substance is:

If \(\mu_0\) and \(\varepsilon_0\) are the permeability and permittivity of free space, respectively, then the dimension of \(\left(\frac{1}{\mu_0 \varepsilon_0}\right)\) is :

The decay constant for a radioactive nuclide is \(1.5 \times 10^{-5} s ^{-1}\). Atomic of the substance is \(60\,g\) mole \(^{-1},\left( N _{ A }=6 \times 10^{23}\right)\). The activity of \(1.0\,\mu g\) of the substance is \(.......\,\times 10^{10}\,Bq\)

Diameter of a steel ball is measured using a Vernier callipers which has divisions of \(0. 1\,cm\) on its main scale \((MS)\) and \(10\) divisions of its vernier scale \((VS)\) match \(9\) divisions on the main scale. Three such measurements for a ball are given as

S.No.	\(MS\;(cm)\)	\(VS\) divisions
\((1)\)	\(0.5\)	\(8\)
\((2)\)	\(0.5\)	\(4\)
\((3)\)	\(0.5\)	\(6\)

If the zero error is \(- 0.03\,cm,\) then mean corrected diameter is  ........... \(cm\)

Ten charges are placed on the circumference of a circle of radius \(R\) with constant angular separation between successive charges. Alternate charges \(1,3,5,7,9\) have charge \((+q)\) each, while \(2,4,6,8,10\) have charge \((-q)\) each. The potential \(V\) and the electric field \(E\) at the centre of the circle are respectively (Take \(V =0\) at infinity \()\)

A uniform thin rod \(AB\) of length \(L\) has linear mass density \(\mu \left( x \right) = a + \frac{{bx}}{L}\) , where \(x\) is measured from \(A\). If the \(CM\) of the rod lies at a distance of \(\left( {\frac{7}{12}} \right)L\) from \(A\), then \(a\) and \(b\) are related as

In a simple pendulum experiment for determination of acceleration due to gravity \((g)\), time taken for \(20\) oscillations is measured by using a watch of \(1\, second\) least count. The mean value of time taken comes out to be \(30\,s\). The length of pendulum is measured by using a meter scale of least count \(1\, mm\) and the value obtained is \(55.0\, cm\). The percentage error in the determination of \(g\) is close to  ........... \(\%\)

A gas can be taken from \(A\) to \(B\) via two different processes \(ACB\) and \(ADB\). When path \(ACB\) is used \(60\, J\) of heat flows into the system and \(30\, J\) of work is done by the system. If path \(ADB\) is used work down by the system is \(10\, J\). the heat flow into the system in path \(ADB\) is ..... \(J\)

A regular hexagon is formed by six wires each of resistance \(r \Omega\) and the corners are joined to centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be