Two charges \(7 \mu \mathrm{c}\) and \(-4 \mu \mathrm{c}\) are placed at \((-7 \mathrm{~cm}, 0,0)\) and \((7 \mathrm{~cm}, 0,0)\) respectively. Given, \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\), the electrostatic potential energy of the charge configuration is :

A heat engine operates between a cold reservoir at temperature \({T}_{2}=400\, {K}\) and a hot reservoir at temperature \({T}_{1} .\) It takes \(300 \,{J}\) of heat from the hot reservoir and delivers \(240\, {J}\) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be \(....{K}\)

An air bubble of volume \(1\,cm ^3\) rises from the bottom of a lake \(40\,m\) deep to the surface at a temperature of \(12^{\circ}\,C\). The atmospheric pressure is \(1 \times 10^5 Pa\), the density of water is \(1000\,kg / m ^3\) and \(g =10\,m / s ^2\). There is no difference of the temperature of water at the depth of \(40\,m\) and on the surface. The volume of air bubble when it reaches the surface will be \(..........\,cm^{3}\)

Consider the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), where \(H=\) magnetic field; \(E=\) electric field, \(\epsilon=\) permittivity, \(x=\) distance, \(t=\) time. The values of \(p, q, r\) and \(s\) respectively are:

A moving proton and electron have the same deBroglie wavelength. If \({K}\) and \({P}\) denote the \({KE}\). and momentum respectively. Then choose the correct option :

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to \(\left|R_1\right|\) and \(\left|R_2\right|\), i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is :

A stone is dropped from the top of a building. When it crosses a point \(5\, m\) below the top, another stone starts to fall from a point \(25\, m\) below the top. Both stones reach the bottom of building simultaneously. The height of the building is ..... \(m\).

A plane polarized monochromatic \(EM\) wave is travelling a vacuum along \(z\) direction such that at \(t\, = t_1\) it is found that the electric field is zero at a spatial point \(z_1\) . The next zero that occurs in its neighbourhood is at \(z_2\). The frequency of the electromagnetic wave is:

A monoatomic gas of mass \(4.0\, u\) is kept in an insulated container. Container is moving with velocity \(30 \,m / s\). If container is suddenly stopped then change in temperature of the gas \(\left( R =\right.\) gas constant) is \(\frac{ x }{3 R } .\) Value of \(x\) is ..........

Refer to the logic circuit given below. For two inputs \((A=1, B=1)\) and \((A=0, B=1)\), output \((Y)\) will be __________.

Two bodies of masses \(m_{1}=5\,kg\) and \(m _{2}=3\,kg\) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass \(m _{1}\) will be\(....N\) [Take \(g=10\,ms ^{-2}\) ]

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.

For the given figures, choose the correct options: