A cell \(E _{1}\) of \(emf 6 V\) and internal resistance \(2 \Omega\) is connected with another cell \(E _{2}\) of \(emf 4 V\) and internal resistance \(8 \Omega\) (as shown in the figure). The potential difference across points \(X\) and \(Y\) is............ \(V\)

A force \(\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}\) acts on a particle in a plane \(\mathrm{x}+\mathrm{y}=10\). The work done by this force during a displacement from \((0,0)\) to \((4 \mathrm{~m}, 2 \mathrm{~m})\) is Joule (round off to the nearest integer)

A ball is projected vertically upward with an initial velocity of \(50 \; ms ^{-1}\) at \(t =0 \; s\). At \(t =2 \,s\). another ball is projected vertically upward with same velocity. At \(t= \; \dots \; s\), second ball will meet the first ball \(\left( g =10 \; ms ^{-2}\right)\).

A parallel plate capacitor with width \(4\,cm\), length \(8\,cm\) and separation between the plates of \(4\,mm\) is connected to a battery of \(20\,V\). A dielectric slab of dielectric constant \(5\) having length \(1\,cm\), width \(4\,cm\) and thickness \(4\,mm\) is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be......... \(\in_{0}\,J\). (Where \(\epsilon_{0}\) is the permittivity of free space)

In an experiment to verify Stokes law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of \(h\) is proportional to : (ignore viscosity of air)

In the figure shown \(ABC\) is a uniform wire . If centre of mass of wire lies vertically below point \(A\) , then \(\frac{{BC}}{{AB}}\) is close to 

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \(V ^q\), where \(V\) is the volume of the gas. The value of \(q\) is \(\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)\)

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

In a meter bridge experiment to determine the value of unknown resistance, first the resistances \(2 \Omega\) and \(3 \Omega\) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \(l cm\) from the left. Now when an unknown resistance \(x \Omega\) is connected in parallel to \(3 \Omega\) resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance \(x\) is _________ \(\Omega\).