Find the value of the integral \( \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \).

• (A) \( \pi \)
• (B) \( \pi/2 \)
• (C) \( \pi/4 \)
• (D) \( 0 \)

If \(A\) is a \(3 \times 3\) matrix and \( |A| = 5 \), find the value of \( |adj(A)| \).

• (A) \(5\)
• (B) \(25\)
• (C) \(125\)
• (D) \(15\)

Calculate the de Broglie wavelength of an electron accelerated through a potential difference of \(100\,V\).

• (A) \(1.227\,\AA\)
• (B) \(12.27\,\AA\)
• (C) \(0.1227\,\AA\)
• (D) \(122.7\,\AA\)

Calculate the work done in moving a charge of \(2\mu C\) between two points with a potential difference of \(5V\).

• (A) \(10\,J\)
• (B) \(10^{-5}\,J\)
• (C) \(2.5\,J\)
• (D) \(0.4\,J\)

Calculate the half-life of a first-order reaction if the rate constant is \(0.693\, min^{-1}\).

• (A) \(10\) min
• (B) \(1\) min
• (C) \(0.5\) min
• (D) \(6.93\) min

What is the major product formed when Propene reacts with \(HBr\) in the presence of peroxide?

• (A) \(2\)-Bromopropane
• (B) \(1\)-Bromopropane
• (C) \(1,2\)-Dibromopropane
• (D) Propane

Complete the series: \(3, 7, 15, 31, 63, \ldots\)

• (A) \(95\)
• (B) \(111\)
• (C) \(127\)
• (D) \(128\)