Evaluate \(\int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx\).

• (A) \(\frac{\pi}{2}\)
• (B) \(\frac{\pi}{6}\)
• (C) \(\frac{\pi}{4}\)
• (D) \(\frac{\pi}{3}\)

If A is a 3 × 3 matrix such that \(|A| = 5\), find the value of \(|adj(A)|\).

• (A) 5
• (B) 10
• (C) 25
• (D) 125

Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).

• (A) \(\frac{4\sqrt{3}}{3}\)
• (B) \(\frac{6\sqrt{3}}{3}\)
• (C) \(\frac{8\sqrt{3}}{3}\)
• (D) \(\frac{12\sqrt{3}}{3}\)

If the current in a coil changes from 2A to 4A in 0.1s, inducing an EMF of 20V, find the self-inductance.

• (A) 0.5 H
• (B) 1 H
• (C) 2 H
• (D) 4 H

In a common emitter transistor, \(\beta = 100\), \(R_c = 2k\Omega\), and the output voltage is 2V. If \(R_b = 1k\Omega\), find the input voltage.

• (A) 0.02 V
• (B) 0.01 V
• (C) 0.1 V
• (D) 0.2 V

Two point charges \(q_1\) and \(q_2\) are \(r\) cm apart in a vacuum with force \(F\). What is the force if they are placed in a medium with dielectric constant \(K = 5\) at distance \(r/5\)?

• (A) \(F\)
• (B) \(2F\)
• (C) \(5F\)
• (D) \(25F\)

A compound is formed by elements X and Y. Y atoms make CCP and X atoms occupy all octahedral voids. What is the formula?

• (A) \(X_2Y\)
• (B) \(XY\)
• (C) \(XY_2\)
• (D) \(X_2Y_3\)

Which linkage joins the monosaccharide units in sucrose?

• (A) \(C_1 - C_4\) glycosidic linkage
• (B) \(C_1 - C_2\) glycosidic linkage
• (C) \(C_1 - C_6\) glycosidic linkage
• (D) \(C_2 - C_4\) glycosidic linkage

Which electrolyte is most effective in the coagulation of a negative sol like \(As_2S_3\)?

• (A) \(NaCl\)
• (B) \(MgCl_2\)
• (C) \(AlCl_3\)
• (D) \(KCl\)

Complete the series: 285, 253, 221, 189, ?

• (A) 165
• (B) 157
• (C) 149
• (D) 161

If ‘PLAYER’ is written as ‘543976’ and ‘DARE’ is ‘8367’, what is the code for ‘YELP’?

• (A) 9745
• (B) 9457
• (C) 9743
• (D) 9547