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**Hint:**In this question, we need to find the input resistance. For this, we will use the formula of power gain for a common emitter transistor amplifier. After simplification, we will get the final result.

**Formula used:**

The formula for power gain for a common emitter transistor amplifier is given below.

Power gain \[ = {\beta ^2} \times \dfrac{{{R_o}}}{{{R_i}}}\]

Here, \[\beta \] is the current gain, \[{R_o}\] is the output resistance and \[{R_i}\] is the input resistance.

**Complete step by step solution:**

We know that the power gain for a common emitter transistor amplifier is Power gain \[ = {\beta ^2} \times \dfrac{{{R_o}}}{{{R_i}}}\]

But the current gain \[\left( \beta \right)\]is 49.

Also, the output resistance is \[\left( {{R_o}} \right) = 500{\text{ k}}\Omega \]

But \[1{\text{ k}}\Omega = 1000{\text{ }}\Omega = {10^3}{\text{ }}\Omega \]

So, \[\left( {{R_o}} \right) = 500 \times 1000 = 500 \times {10^3}{\text{ }}\Omega \]

Also, power gain is \[5 \times {10^6}\]

So, we get

\[5 \times {10^6} = {\left( {49} \right)^2} \times \dfrac{{500 \times {{10}^3}{\text{ }}}}{{{R_i}}}\]

\[5 \times {10^6}\left( {{R_i}} \right) = {\left( {49} \right)^2} \times 500 \times {10^3}\]

By simplifying, we get

\[\left( {{R_i}} \right) = \dfrac{{{{\left( {49} \right)}^2} \times 500 \times {{10}^3}}}{{5 \times {{10}^6}}}\]

\[\Rightarrow \left( {{R_i}} \right) = {\left( {49} \right)^2} \times 100 \times {10^{3 - 6}}\]

\[\Rightarrow \left( {{R_i}} \right) = {\left( {49} \right)^2} \times {10^2} \times {10^{ - 3}}\]

\[\Rightarrow \left( {{R_i}} \right) = {\left( {49} \right)^2} \times {10^{2 - 3}}\]

By simplifying further, we get

\[\left( {{R_i}} \right) = 2401 \times {10^{2 - 3}}\]

\[\Rightarrow \left( {{R_i}} \right) = 2401 \times {10^{ - 1}}\]

\[\Rightarrow \left( {{R_i}} \right) = \dfrac{{2401}}{{10}}\]

This gives, \[\left( {{R_i}} \right) = 240.1{\text{ }}\Omega \]

That is \[\left( {{R_i}} \right) \approx 240{\text{ }}\Omega \]

Hence, the value of input resistance is approximately \[240{\text{ }}\Omega \].

**Therefore, the correct option is (D).**

**Additional information**: We know that an amplifier is a type of electronic circuit often used to boost the strength of a poor input signal in terms of voltage, current, or power. So, the common emitter amplifier is a voltage amplifier that consists of three basic single-stage bipolar junction transistors. This amplifier's input is captured from the base terminal, its output is gathered from the collector terminal, and both terminals share the emitter terminal.

**Note**: Many students generally make mistakes in writing the formula of power gain of an amplifier. They generally write \[{\beta ^2} \times \dfrac{{{R_i}}}{{{R_o}}}\] instead of \[{\beta ^2} \times \dfrac{{{R_o}}}{{{R_i}}}\]. Also, while doing calculations, they may get confused with the power of 10.

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