In the given potentiometer circuit arrangement, the balancing length \({AC}\) is measured to be \(250\) \({cm}\). When the galvanometer connection is shifted from point \((1)\) to point \((2)\) in the given diagram, the balancing length becomes \(400\, {cm}\). The ratio of the emf of two cells, \(\frac{\varepsilon_{1}}{\varepsilon_{2}}\) is -

A capacitor of capacitance \(C=1\, \mu \,{F}\) is suddenly connected to a battery of \(100\, volt\) through a resistance \({R}=100\, \Omega\). The time taken for the capacitor to be charged to get \(50 \,{V}\) is \(....\,\times \,10^{-4}\,s.\) [Take \(\ln 2=0.69]\)

First, a set of \({n}\) equal resistors of \(10\; \Omega\) each are connected in series to a battery of emf \(20\; {V}\) and internal resistance \(10\; \Omega .\) A current \(I\) is observed to flow. Then, the \(n\) resistors are connected in parallel to the same battery. It is observed that the current is increased \(20\) times, then the value of \(n\) is .... .

Consider a rectangular sheet of solid material of length \(\ell=9 \mathrm{~cm}\) and width \(\mathrm{d}=4 \mathrm{~cm}\). The coefficient of linear expansion is \(\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}\) at room temperature and one atmospheric pressure. The mass of sheet \(\mathrm{m}=0.1 \mathrm{~kg}\) and the specific heat capacity \(\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\). If the amount of heat supplied to the material is \(8.1 \times 10^2 \mathrm{~J}\) then change in area of the rectangular sheet is :-

Inside a uniform spherical shell \((a)\) the gravitational field is zero \((b)\) the gravitational potential is zero \((c)\) the gravitational field is same everywhere \((d)\) the gravitation potential is same everywhere \((e)\) all of the above Choose the most appropriate answer from the options given below

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is \(30 \;\mathrm{cm}\) and the refractive index of the lens material is \(1.5 .\) then the focal length of the lens (in \(\mathrm{cm}\) ) is

In an experiment of \(CE\) configuration of \(n-p-n\) transistor, the transfer characteristics are observed as given in figure. If the input resistance is \(200 \Omega\) and output resistance is \(60 \Omega\) the voltage gain in this experiment will be..........

To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm . The least count of scale is 1 cm . The percentage error in the ratio of EMFs is ___________.

The machine as shown has \(2\) rods of length \(1\, m\) connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor  in a slot As the roller goes back and forth, a \(2\, kg\) weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a