Two identical cells each of emf \(1.5 \,V\) are connected in parallel across a parallel combination voltmeter connected in the circuit measures \(1.2 \,V\). The internal resistance of each cell is.................\(\Omega\)

Two tubes of radii \(r_1\) and \(r_2\), and lengths \(l_1\) and \(l_2\), respectively, are connected in series and a liquid flows through each of them in streamline conditions. \(P_1\) and \(P_2\) are pressure differences across the two tubes. If \(P_2\) is \(4P_1\) and \(l_2\) is \( \frac{l_1}{4}\) , then the radius \(r_2\) will be equal to

Let \(B_1\) be the magnitude of magnetic field at center of a circular coil of radius \(R\) carrying current \(I\). Let \(B_2\) be the magnitude of magnetic field at an axial distance ' \(x\) ' from the center. For \(x: R=3: 4, \frac{B_2}{B_1}\) is :

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\)

A swimmer wants to cross a river from point \(A\) to point \(B\). Line \(A B\) makes an angle of \(30^{\circ}\) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \(\theta\) with the line \({AB}\) should be \(^{\circ}\), so that the swimmer reaches point \({B}\).

The least count of the main scale of a vernier callipers is \(1\, mm\). Its vernier scale is divided into \(10\) divisions and coincide with \(9\) divisions of the main scale. When jaws are touching each other, the \(7\) th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between \(3.1\, cm\) and \(3.2\, cm\) and \(4^{th}\) \(VSD\) coincides with a main scale division.The length of the cylinder is \(.....cm\) (\(VSD\) is vernier scale division)

Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is _________ cm .

If the angular momentum of a planet of mass \(m\), moving a round the Sun in a circular orbit its \(L\), about the center of the Sun, its areal velocity is

A pendulum is suspended by a string of length \(250\,cm\). The mass of the bob of the pendulum is \(200\,g\). The bob is pulled aside until the string is at \(60^{\circ}\) with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ \(ms ^{-1}\). (if \(g=10\,m / s ^{2}\) )