Introduction:
In a bipolar junction transistor (BJT), the base width is an important parameter that affects the performance of the transistor. By doubling the base width, certain characteristics of the BJT will be affected. Let's analyze each statement and determine which one is true.

a) Current gain will increase:
The current gain of a BJT is given by the ratio of the collector current (IC) to the base current (IB), denoted as β. Doubling the base width would not directly affect the current gain. The current gain is primarily determined by the doping levels and physical dimensions of the transistor, not the base width. Therefore, this statement is not true.

b) Unity gain frequency will increase:
The unity gain frequency (fT) is a measure of the high-frequency response of a transistor. It represents the frequency at which the current gain drops to unity (1). Doubling the base width would not directly affect the unity gain frequency. The unity gain frequency is determined by the transit time of carriers across the base region, which is primarily influenced by the doping levels and physical dimensions of the transistor. Therefore, this statement is not true.

c) Emitter-base junction capacitor will increase:
The emitter-base junction of a BJT forms a capacitor due to the depletion region between the two regions. This junction capacitance (Cje) is inversely proportional to the width of the depletion region, which is influenced by the base width. Doubling the base width would increase the depletion region width and, consequently, increase the emitter-base junction capacitor. Therefore, this statement is true.

d) Early Voltage will increase:
The Early Voltage (VA) is a parameter that represents the output characteristics of a BJT. It is a measure of the voltage at which the collector current reaches a certain value. The Early Voltage is primarily determined by the doping levels and physical dimensions of the transistor, not the base width. Therefore, doubling the base width would not directly affect the Early Voltage. Therefore, this statement is not true.

Conclusion:
Based on the analysis, the statement that is true is: c) Emitter-base junction capacitor will increase. Doubling the base width of a bipolar junction transistor will increase the emitter-base junction capacitor, while the current gain, unity gain frequency, and Early Voltage will not be directly affected.