From the given transfer characteristic of a transistor in \(CE\) configuration, the value of power gain of this configuration is \(10^{ x }\), for \(R_B=10\,k \Omega\), and \(R _C=1\,k \Omega\). The value of \(x\) is \(.....\).

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant \(\varepsilon_1\) and \(\varepsilon_2\), as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are \(C_1\) and \(C_2\) respectively, then \(\frac{C_1}{C_2}\) is :

An amount of ice of mass \(10^{-3} \mathrm{~kg}\) and temperature \(-10^{\circ} \mathrm{C}\) is transformed to vapour of temperature \(110^{\circ} \mathrm{C}\) by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice \(=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), specific heat of water \(=4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), specific heat of steam \(=1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), Latent heat of ice \(=3.35 \times 10^5 \mathrm{Jkg}^{-1}\) and Latent heat of steam \(=2.25 \times 10^6\) \(\mathrm{Jkg}^{-1}\) )

An object of mass 1000 g experiences a time dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N\). The power generated by the force at time \(t\) is :

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

Two point dipoles of dipole moment \({\vec P_1}\) and \({\vec P_2}\) are at a distance \(x\) from each other and  \({\vec P_1}\) || \({\vec P_2}\). The force between the dipoles is

A current of \(10\, A\) exists in a wire of crosssectional area of \(5\, mm ^{2}\) with a drift velocity of \(2 \times 10^{-3}\, ms ^{-1}\). The number of free electrons in each cubic meter of the wire is ..........

If force \(\vec{F}=3 \hat{i}+4 \hat{j}-2 \hat{k}\) acts on a particle having position vector \(2 \hat{i}+\hat{j}+2 \hat{k}\) then, the torque about the origin will be

A particle of charge \(-q\) and mass \(m\) moves in a circle of radius \(r\) around an infinitely long line charge of linear density \(+\lambda\). Then time period will be given as _______. (Consider \(k\) as Coulomb's constant)

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and \(2 \sqrt{3}\) (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is _________ .

The disintegration rate of a certain radioactive sample at any instant is \(4250\) disintegrations per minute.\(10\) minutes later, the rate becomes \(2250\) disintegrations per minute. The approximate decay cons \(.........\min^{-1}\)

Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\)

A triangular plate is shown. A force \(\overrightarrow{ F }=4 \hat{ i }-3 \hat{ j }\) is applied at point \(P\). The torque at point \(P\) with respect to point \('O'\) and \('Q'\) are