1. Write the cell reaction

The cell is:

$\mathrm{Tl}\,|\,\mathrm{Tl}^+(0.001\,M)\,||\,\mathrm{Cu}^{2+}(0.01\,M)\,|\,\mathrm{Cu}$

At the anode, thallium is oxidized:

$\mathrm{Tl} \rightarrow \mathrm{Tl}^+ + e^-$

At the cathode, copper ion is reduced:

$\mathrm{Cu}^{2+} + 2e^- \rightarrow \mathrm{Cu}$

Balancing electrons, the overall reaction is:

$2\mathrm{Tl} + \mathrm{Cu}^{2+} \rightarrow 2\mathrm{Tl}^+ + \mathrm{Cu}$

So, the number of electrons transferred is:

$n=2$

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2. Write the reaction quotient

For the reaction

$2\mathrm{Tl} + \mathrm{Cu}^{2+} \rightarrow 2\mathrm{Tl}^+ + \mathrm{Cu}$

Solids are omitted, so

$Q = \frac{[\mathrm{Tl}^+]^2}{[\mathrm{Cu}^{2+}]}$

Given:

$[\mathrm{Tl}^+] = 0.001 = 10^{-3}$ $[\mathrm{Cu}^{2+}] = 0.01 = 10^{-2}$

Thus,

$Q = \frac{(10^{-3})^2}{10^{-2}} = \frac{10^{-6}}{10^{-2}} = 10^{-4}$

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3. Use the Nernst equation

At $298\,K$:

$E = E^\circ - \frac{0.0591}{n}\log Q$

Here,

$E = E^\circ - \frac{0.0591}{2}\log\left(\frac{[\mathrm{Tl}^+]^2}{[\mathrm{Cu}^{2+}]}\right)$

To increase emf, we must increase $E$.

Since

$E = E^\circ - \frac{0.0591}{2}\log Q$

$E$ increases when $Q$ decreases.

So we need:

$\frac{[\mathrm{Tl}^+]^2}{[\mathrm{Cu}^{2+}]} \text{ to decrease}$

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4. Check each option

Option A: Increasing concentration of $\mathrm{Tl}^+$ ions

This increases the numerator $[\mathrm{Tl}^+]^2$, so $Q$ increases. Hence $E$ decreases.

Option A is incorrect.

Option B: Increasing concentration of $\mathrm{Cu}^{2+}$ ions

This increases the denominator, so $Q$ decreases. Hence $E$ increases.

Option B is correct.

Option C: Increasing concentration of both $\mathrm{Tl}^+$ and $\mathrm{Cu}^{2+}$ ions

This is not निश्चितly increasing emf, because effect depends on relative changes. In general, increasing $\mathrm{Tl}^+$ tends to decrease emf, while increasing $\mathrm{Cu}^{2+}$ tends to increase emf. So it cannot be said with certainty that emf will increase.

Option C is incorrect.

Option D: Decreasing concentration of both $\mathrm{Tl}^+$ and $\mathrm{Cu}^{2+}$ ions

Again, this is not certain. Decreasing $\mathrm{Tl}^+$ increases emf, but decreasing $\mathrm{Cu}^{2+}$ decreases emf. Net effect is uncertain.

Option D is incorrect.

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5. Final answer

The emf can definitely be increased by:

$\boxed{\text{B: increasing concentration of } \mathrm{Cu}^{2+} \text{ ions}}$

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6. Comparison with stored correct answer

Stored correct answer: B

My derived answer: B

So, they agree.