A galvanometer having coil resistance \(10 \ \Omega\) shows a full scale deflection for a current of \(3 \mathrm{~mA}\). For it to measure a current of \(8 \mathrm{~A}\), the value of the shunt should be:

The relation between root mean square speed \(\left( v _{ rms }\right)\) and most probable speed \(\left( v _{ p }\right)\) for the molar mass \(M\) of oxygen gas molecule at the temperature of \(300\, K\) will be

Asseretion \(A:\) If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \(5\, {mm}\) and there are \(50\) total divisions on circular scale, then least count is \(0.001\, {cm}\). Reason \(R:\) Least Count \(=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}\) In the light of the above statements, choose the most appropriate answer from the options given below:

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)

The value of current in the \(6 \,\Omega\) resistance is \(....\,A\)

Find the truth table for the function \(Y\) and \(A\) and \(B\) represented in the following figure.

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) For measuring the potential difference across a resistance of \(600\,\Omega\), the voltmeter with resistance \(1000\,\Omega\) will be preferred over voltmeter with resistance \(4000\,\Omega\). Reason \(R:\) Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance. In the light of the above statements, choose the most appropriate answer from the options given below.

In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ \(\mu \mathrm{C}\).

Match List \(I\) with List \(II\)

LIST\(-I\)	LIST\(-II\)
\((A)\) Surface tension	\((I)\) \(Kg m ^{-1} s ^{-1}\)
\((B)\) Pressure	\((II)\) \(Kg ms^{-1 }\)
\((C)\) Viscosity	\((III)\) \(Kg m ^{-1} s ^{-2}\)
\((D)\) Impulse	\((IV)\) \(Kg s ^{-2}\)

Choose the correct answer from the options given below :

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about \(150\, N/C\), directed inward towards the center of the Earth . This gives the total net surface charge carried by the Earth to be......\(kC\) [Given \({\varepsilon _0} = 8.85 \times {10^{ - 12}}\,{C^2}/N - {m^2},{R_E} = 6.37 \times {10^6}\,m\)]

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is \(\frac{4}{3}\),  and the diver's eyes are \(15\, cm\) below the surface of water. Then the radius of the circle is