The capacitance of an infinite circuit formed by the repetition of the same link consisting of two identical capacitors, each with capacitance \(C\), as shown in the figure is:

• (A) Zero
• (B) \( \dfrac{(\sqrt{5}-1)C}{2} \)
• (C) \( \dfrac{(\sqrt{5}+1)C}{2} \)
• (D) Infinite

A \(1.5\,kg\) block is attached to a spring with spring constant \(k=100\,N m^{-1}\) and displaced by \(0.2\,m\). Calculate the potential energy stored in the spring.

• (A) \(1\,J\)
• (B) \(2\,J\)
• (C) \(3\,J\)
• (D) \(4\,J\)

What product is formed when a ketone reacts with hydrazine \( (\mathrm{NH_2-NH_2}) \)?

• (A) Alcohol
• (B) Hydrazone
• (C) Amide
• (D) Ester

Evaluate the definite integral:
\[ \int_{0}^{\frac{\pi}{2}} \sin^2 x \, dx \]

• (A) \( \dfrac{\pi}{2} \)
• (B) \( \dfrac{\pi}{4} \)
• (C) \( \dfrac{\pi}{8} \)
• (D) \( \pi \)