The \(I-V\) characteristics of a \(p - n\) junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltages of \(2 \; V\) and \(4 \; V\) respectively, is

A solid body of constant heat capacity \(1\ J/^o C\) is being heated by keeping it in contact with reservoirs in two ways : \((i)\) Sequentially keeping in contact with \(2\) reservoirs such that each reservoir supplies same amount of heat. \((ii)\) Sequentially keeping in contact with \(8\) reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature \(100^o C\) to final temperature \(200^o C\). Entropy change of the body in the two cases respectively is :

The threshold frequency of a metal with work function \(6.63\  \mathrm{eV}\) is:

Muon \((\mu ^{-1})\) is negatively charged \(\left( {\left| q \right| = \left| e \right|} \right)\) with a mass \(m_{\mu}\, = 200\,m_e\), where \(m_e\) is the mass of the electron and \(e\) is the electronic charge. If \(\mu ^{-1}\) is bound to a proton to form a hydrogen like atom, identify the correct statements \((A)\) Radius of the muonic orbit is \(200\) times smaller than that of the electron \((B)\) the speed of the \(\mu ^{-1}\) in the \(n^{th}\) orbit is \(\frac{1}{{200}}\) times that of the election in the \(n^{th}\) orbit \((C)\) The Ionization energy of muonic atom is \(200\) times more than that of an hydrogen atom \((D)\) The momentum of the muon in the \(n^{th}\) orbit is \(200\) times more than that of the electron

Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be

A meter bridge with two resistances \( R_{1} \) and \( R_{2} \) as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when 16 \( \Omega \) resistance is connected in parallel to \( R_{2} \). The values of resistances \( R_{1} \) and \( R_{2} \) are __________ .

The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth)

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y\left( {x,t} \right) = 0.5\sin\, \left( {\frac{{5\pi }}{4}x} \right)\,\cos\, \left( {200\,\pi t} \right)\). What is the speed of the travelling wave moving in the positive \(x\) direction .... \(m/s\) ? (\(x\) and \(t\) are in meter and second, respectively.)

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 ?

The frequency of revolution of the electron in Bohr's orbit varies with \(n\), the principal quantum number as _______.

Experimentally it is found that \(12.8\,eV\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{ x } \times 10^{-10}\,m\). The value of the \(x\) is \(\left(1\,eV =1.6 \times 10^{-19}\,J , \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\,Nm ^2 / C ^2\right.\) and electronic charge \(=1.6 \times 10^{-19}\,J\,C\) )