A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × 10⁻⁸ A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of:

Let G be the resistance of the galvanometer and Ig be the current required for full-scale deflection.
Given:
G = 50 Ω
Number of divisions = 25
Current for one division deflection, Ig = 4 × 10⁻⁸ A
Current for full-scale deflection (25 divisions) = Ig = 25 × 4 × 10⁻⁸ A = 10⁻⁶ A
Voltage for full-scale deflection, Vg = IgG = 10⁻⁶ A × 50 Ω = 5 × 10⁻⁵ V
To convert the galvanometer into a voltmeter of range 2.5 V, we need to connect a high resistance R in series with the galvanometer.
The total resistance of the voltmeter is R + G.
The current through the voltmeter is I = V / (R + G), where V is the voltage across the voltmeter.
For full-scale deflection, I = Ig and V = 2.5 V
Therefore, 10⁻⁶ A = 2.5 V / (R + 50 Ω)
R + 50 Ω = 2.5 V / 10⁻⁶ A = 2.5 × 10⁶ Ω
R = 2.5 × 10⁶ Ω - 50 Ω ≈ 2.5 × 10⁶ Ω = 2500000 Ω = 2.5 MΩ
However, this value is not among the options. Let's re-examine the calculation.
The current required for full-scale deflection is Ig = 25 × 4 × 10⁻⁸ A = 10⁻⁶ A
The voltage across the galvanometer for full-scale deflection is Vg = IgG = 10⁻⁶ A × 50 Ω = 5 × 10⁻⁵ V
To make this galvanometer a voltmeter with a range of 2.5V, we need to connect a resistor R in series such that the total voltage is 2.5 V when the current is 10⁻⁶ A.
The total resistance is RT = R + G = V / Ig = 2.5 V / 10⁻⁶ A = 2.5 × 10⁶ Ω
R = RT - G = 2.5 × 10⁶ Ω - 50 Ω ≈ 2.5 × 10⁶ Ω
Let's consider the options:
If R = 6250 Ω, then the total resistance is 6300 Ω. The current would be 2.5V / 6300 Ω ≈ 3.97 × 10⁻⁴ A which is much higher than Ig.
If R = 6250 Ω, total resistance = 6250 + 50 = 6300 Ω. Current = 2.5 / 6300 = 3.97 × 10⁻⁴ A. This is not correct.
Let's use the formula: V = Ig(R + G)
2.5 = 10⁻⁶ (R + 50)
R = 2.5 × 10⁶ - 50 ≈ 2500000 Ω
This is not among the options. There must be an error in the problem statement or options provided.