Find the value of \(k\) if the lines \[ \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} \]
and \[ \frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{k} \]
are coplanar.

• (A) \(0\)
• (B) \(1\)
• (C) \(-1\)
• (D) \(2\)

If \(A\) is a square matrix of order \(3\) such that \( |adj\,A| = 64 \), then find the value of \( |A| \).

• (A) \(4\)
• (B) \(\pm 4\)
• (C) \(8\)
• (D) \(\pm 8\)

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

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

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

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

If the sum of the first \(n\) terms of an A.P. is \(S_n = 3n^2 + 5n\), find the \(10^{th}\) term.

• (A) \(60\)
• (B) \(61\)
• (C) \(62\)
• (D) \(63\)

Calculate the equivalent resistance between two diametrically opposite points of a circular wire of total resistance \(12\,\Omega\).

• (A) \(2\,\Omega\)
• (B) \(3\,\Omega\)
• (C) \(4\,\Omega\)
• (D) \(6\,\Omega\)

A capacitor of \(10\,\mu F\) is charged to \(50\,V\). Calculate the energy stored in the capacitor.

• (A) \(0.00125\,J\)
• (B) \(0.0125\,J\)
• (C) \(0.125\,J\)
• (D) \(1.25\,J\)

If the speed of light in a medium is \(2 \times 10^8 \, m/s\), what is the refractive index of the medium?

• (A) \(1.2\)
• (B) \(1.3\)
• (C) \(1.5\)
• (D) \(2\)

A proton \((q = 1.6 \times 10^{-19}\,C)\) enters a magnetic field of \(2\,T\) with a velocity of \(3 \times 10^6\,m/s\) perpendicular to the field. Find the magnetic force acting on the proton.

• (A) \(9.6 \times 10^{-14}\,N\)
• (B) \(9.6 \times 10^{-13}\,N\)
• (C) \(9.6 \times 10^{-12}\,N\)
• (D) \(9.6 \times 10^{-11}\,N\)

Determine the de Broglie wavelength of an electron accelerated through \(100\,V\).

• (A) \(0.1227\,\AA\)
• (B) \(1.227\,\AA\)
• (C) \(12.27\,\AA\)
• (D) \(0.01227\,\AA\)

Which compound undergoes Cannizzaro reaction: Formaldehyde, Acetaldehyde, or Benzophenone?

• (A) Formaldehyde
• (B) Acetaldehyde
• (C) Benzophenone
• (D) Both (A) and (B)

What is the coordination number of Fe in the complex \([Fe(C_2O_4)_3]^{3-}\)?

• (A) 3
• (B) 4
• (C) 6
• (D) 9

Calculate the pH of a \(0.01\,M\) \(HCl\) solution.

• (A) 1
• (B) 2
• (C) 3
• (D) 4

Identify the monomers for Nylon-6,6.

• (A) Adipic acid and Hexamethylenediamine
• (B) Ethylene glycol and Terephthalic acid
• (C) Styrene
• (D) Caprolactam

Which group contains the most electronegative elements in the periodic table?

• (A) Group 1
• (B) Group 2
• (C) Group 16
• (D) Group 17

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

• (A) EDRIRJ
• (B) EDRJRI
• (C) FESJRL
• (D) DCRHQI

A man walks \(5\) km East, then turns right and walks \(4\) km, and then turns left and walks \(5\) km. In which direction is he finally moving?

• (A) North
• (B) South
• (C) East
• (D) West

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

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

Choose the synonym of the word `ABANDON'.

• (A) Retain
• (B) Forsake
• (C) Protect
• (D) Defend

Fill in the blank: Neither of the two candidates ______ qualified.

• (A) are
• (B) were
• (C) is
• (D) have