The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero
 

The thermo e.m.f E in volts of a certain thermocouple is found to vary with temperature difference θ in ºC between the two junctions according to the relation
$E=30$ $\theta -\frac{{\theta }^2}{15}$ The neutral temperature for the thermo-couple will be:

1. 400ºC

2. 225ºC

3. 30ºC

4. 450ºC

A particle having a mass of \(10^{-2}\) kg carries a charge of \(5\times 10^{-8}~\mathrm{C}\). The particle is given an initial horizontal velocity of \(10^5~\mathrm{ms^{-1}}\) in the presence of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) . To keep the particle moving in a horizontal direction, it is necessary that:
 

Which one of the following pairs of statements is possible?

When monochromatic radiation of intensity I falls on a metal surface, the number of photoelectrons and their maximum kinetic energy are N and T respectively. If the intensity of radiation is 2I, the number of emitted electrons and their maximum kinetic energy are respectively:

1. 2N and T

2. 2N and 2T

3. N and T

4. N and 2T

The electrons in the hydrogen atom jump from the excited state (n = 3) to its ground state (n = 1) and the photons thus emitted irradiate a photosensitive material. If the work function of the material is 5.1 eV, the stopping potential is estimated to be (the energy of the electron in nth state $E_n=-\frac{13.6}{n^2}eV$):
1. 12.1 V

2. 17.2 V

3. 7 V

4. 5.1 V

The binding energy per nucleon in deuterium and helium nuclei are \(1.1\) MeV and \(7.0\) MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is:
1. \(2.2\) MeV
2. \(28.0\) MeV
3. \(30.2\) MeV
4. \(23.6\) MeV

The decay constant of a radioisotope is λ. If A₁ and A₂ are its activities at times t₁ and t₂ respectively, the number of nuclei which have decayed during the time (t₁ – t₂):

1. A₁ – A₂

2. (A₁ – A₂) / λ

3. λ (A₁ – A₂)

4. A₁t₁ – A₂t₂

For transistor action:
 

Which one of the following pairs of statements is correct?

1. (a), (b)

2. (b), (c)

3. (c), (d)

4. (d), (a)

The following figure shows a logic gate circuit with two inputs \(A\) and \(B\), and the output \(Y\). The voltage waveforms of \(A,B\) and \(Y\) are as given.
 

The logic gate is: