In a \(\mathrm{n\text{-}}\)type silicon, which of the following statement is true:

Carbon, silicon, and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by the energy bandgap respectively equal to \((E_g)_C, (E_g)_{Si}~\text{and}~(E_g)_{Ge}\). Which of the following statements is true?

In an unbiased \(\mathrm{p\text-n}\) junction, holes diffuse from the \(\mathrm{p\text-}\)region to the  \(\mathrm{n\text-}\)region because:

In a half-wave rectification, what is the output frequency if the input frequency is \(50~\text{Hz}?\)
1. \(50~\text{Hz}\)
2. \(100~\text{Hz}\)
3. \(25~\text{Hz}\)
4. \(60~\text{Hz}\)

A \(\text{p-n}\) photodiode is fabricated from a semiconductor with a bandgap of \(2.8~\text{eV}.\) The energy of the incident photon with a wavelength of \(6000~\text{nm}\) is:
1. \(0.207~\text{eV}\)
2. \(0.270~\text{eV}\)
3. \(0.027~\text{eV}\)
4. \(0.072~\text{eV}\)

The number of silicon atoms per \(\text m^3\) is  \(5 × 10^{28}.\) This is doped simultaneously with \(5 × 10^{22}\) atoms per \(\text m^3\) of Arsenic and \(5 × 10^{20}\) per \(\text m^3\) atoms of Indium. The number of holes is:
(given that \(n_{i} = 1 . 5 \times 10^{16} ~\text m^{- 3}\))
1. \(4.51\times 10^{9}\)
2. \(4.99\times 10^{22}\)
3. \(1.56\times 10^{22}\)
4. \(3.33\times 10^{23}\)

In an intrinsic semiconductor, the energy gap \(E_g\) is \(1.2~\text{eV}.\) Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at \(600~\text{K}\) and that at \(300~\text{K}?\) 
(assume that the temperature dependence of intrinsic carrier concentration \(n_{i}\) is given by; \(n_{i} = n_{0} \exp \left[\frac{- E_{g}}{2 k_{B} T}\right],\) where \(n_0\) is the constant)
1. \(1.01\times10^6:1\)
2. \(1.09\times10^5:1\)
3. \(1:1\)
4. \(1:2\)

Which statement is true for the given circuit:

A NAND gate is connected, as shown in the figure.

    
The circuit operates like a:
1. NOT gate
2. OR gate
3. AND gate
4. None of these