If \(A\) is a \(3\times3\) matrix such that \(|A| = 4\) and \(B = adj\,A\), find the value of \(|B|\).

• (A) \(4\)
• (B) \(8\)
• (C) \(16\)
• (D) \(64\)

Find the value of \(k\) if the function \(f(x) = \dfrac{k\sin x}{x}\) is continuous at \(x = 0\) and \(f(0)=3\).

• (A) \(1\)
• (B) \(2\)
• (C) \(3\)
• (D) \(6\)

The converse of the statement \( ((\sim p) \land q) \rightarrow r \) is:

• (A) \(r \rightarrow ((\sim p) \land q)\)
• (B) \(((\sim p) \land q) \rightarrow (\sim r)\)
• (C) \(r \rightarrow (\sim p)\)
• (D) \(q \rightarrow r\)

Find the value of \( \tan(105^\circ) \) using compound angle identities.

• (A) \(2+\sqrt3\)
• (B) \(-(2+\sqrt3)\)
• (C) \(1+\sqrt3\)
• (D) \(\sqrt3-2\)

What is the power factor of an AC circuit containing only a pure resistor?

• (A) \(0\)
• (B) \(0.5\)
• (C) \(1\)
• (D) \(-1\)

A ball is thrown upwards with a velocity of \(20\,m/s\). Find the maximum height reached \((g=10\,m/s^2)\).

• (A) \(10\,m\)
• (B) \(20\,m\)
• (C) \(30\,m\)
• (D) \(40\,m\)

A particle in SHM has a speed of \(6\,cm/s\) at the mean position and an amplitude of \(4\,cm\). Find its position when its velocity is \(2\,cm/s\).

• (A) \( \frac{8\sqrt{2}}{3} \,cm \)
• (B) \( \frac{4\sqrt{2}}{3} \,cm \)
• (C) \( \frac{8}{3} \,cm \)
• (D) \( 2\sqrt{2} \,cm \)

Identify the product formed when phenol reacts with bromine water.

• (A) Bromobenzene
• (B) \(o\)-Bromophenol
• (C) \(2,4,6\)-Tribromophenol
• (D) Chlorobenzene

What is the SI unit of molar conductivity?

• (A) \(S\,cm^{-1}\)
• (B) \(S\,cm^{2}\,mol^{-1}\)
• (C) \(S\,mol^{-1}\)
• (D) \(S\,cm\)

Which enzyme converts trypsinogen into active trypsin in the digestive system?

• (A) Pepsin
• (B) Amylase
• (C) Enterokinase
• (D) Lipase

What is the number of unit particles present in a Body-Centered Cubic (BCC) unit cell?

• (A) \(1\)
• (B) \(2\)
• (C) \(4\)
• (D) \(6\)