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

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

Find the area bounded by the curve \( y^2 = 4x \) and its latus rectum.

• (A) \( \frac{4}{3} \) sq units
• (B) \( \frac{8}{3} \) sq units
• (C) \( \frac{16}{3} \) sq units
• (D) \( \frac{2}{3} \) sq units

What happens to the magnetic field at the center of a circular coil if the number of turns is doubled while current remains constant?

• (A) It becomes half \( \left(\frac{B}{2}\right) \)
• (B) It remains the same \( (B) \)
• (C) It doubles \( (2B) \)
• (D) It becomes four times \( (4B) \)

An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the position and nature of the image.

• (A) \(20\) cm in front, real and inverted
• (B) \(30\) cm in front, real and inverted
• (C) \(30\) cm behind, virtual and erect
• (D) \(15\) cm behind, virtual and erect

Identify the IUPAC name for the coordination compound \( [Co(NH_3)_6]Cl_3 \).

• (A) Hexaamminecobalt(II) chloride
• (B) Hexaamminecobalt(III) chloride
• (C) Hexaamminecobalt(IV) chloride
• (D) Amminecobalt(III) chloride

Which of the following is an example of a condensation polymer?

• (A) Polyethylene
• (B) PVC
• (C) Nylon 6,6
• (D) Polystyrene

Find the missing number in the series: \(2, 6, 12, 20, 30, \_\_\).

• (A) \(38\)
• (B) \(40\)
• (C) \(42\)
• (D) \(44\)

If 'FRIEND' is coded as 'HUMJTK', how is 'CANDLE' coded?

• (A) EDRJRI
• (B) EDQJRI
• (C) EDSJRI
• (D) EDRKRI

Choose the correct synonym for ``Benevolent''.

• (A) Cruel
• (B) Kind/Generous
• (C) Angry
• (D) Selfish