The rms velocity of hydrogen molecules at \(27^{\circ}\)C is v. At what temperature will the rms velocity of oxygen molecules equal v?

• (A) 4800 K
• (B) \(4527^{\circ}\)C
• (C) 1200 K
• (D) \(27^{\circ}\)C

An ideal gas undergoes a cyclic process ABCA wherein AB is an isothermal expansion, BC is an isochoric pressure drop, and CA is an adiabatic compression. The work done by the gas in the complete cycle is:

• (A) Zero
• (B) Positive
• (C) Negative
• (D) Cannot be determined

A Carnot engine operates between temperatures \(T_1\) and \(T_2\) (\(T_1 > T_2\)). If \(T_1\) is increased by \(\Delta T\) and \(T_2\) is decreased by \(\Delta T\), its efficiency will:

• (A) Increase
• (B) Decrease
• (C) Remain constant
• (D) Depend on the working substance

A particle executes simple harmonic motion of amplitude A and time period T. The time taken by the particle to travel from the mean position to a distance of A/2 is:

• (A) T/4
• (B) T/8
• (C) T/12
• (D) T/6

A pendulum clock gives correct time at \(20^{\circ}\)C. If the coefficient of linear expansion of the pendulum’s material is \(\alpha = 1.2 \times 10^{-5}/^{\circ}\)C, the clock will lose time per day at \(40^{\circ}\)C by approximately:

• (A) 10.4 s
• (B) 5.2 s
• (C) 20.8 s
• (D) 2.6 s

Which of the following forces is involved in dinitrogen?

• (A) Dipole - dipole interaction
• (B) Dipole - induced dipole interaction
• (C) London dispersion force
• (D) Hydrogen bonding

Which from following compounds is NOT in gaseous phase at \(25^{\circ}\)C?

• (A) ClF
• (B) BrF
• (C) \(I F_3\)
• (D) \(Cl F_3\)

Which of the following equations gives combined relationship of Boyle’s law and Charle’s law?

• (A) \(\frac{P_1V_2}{T_1} = \frac{P_2V_1}{T_2}\)
• (B) \(n = \frac{RT}{PV}\)
• (C) \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)
• (D) \(p = \frac{RT}{nV}\)

Find the concentration of sodium acetate when added to 0.1 M solution of acetic acid to form a buffer solution of pH = 5.5 ? (\(p K_a\) of \(C H_3 C O O H\) = 4.5)

• (A) 0.1 M
• (B) 0.01 M
• (C) 1.0 M
• (D) 10.0 M

The solubility product of AgBr is \(4.9 \times 10^{-13}\) at a certain temperature. Calculate the solubility.

• (A) \(4 \times 10^{-6} mol \cdot dm^{-3}\)
• (B) \(4 \times 10^{-7} mol \cdot dm^{-3}\)
• (C) \(7 \times 10^{-7} mol \cdot dm^{-3}\)
• (D) \(3 \times 10^{-8} mol \cdot dm^{-3}\)

Let \(f(x) = \int \frac{\sqrt{x}}{(1+x)^2} d x(x \geq 0)\). Then \(f(3) - f(1)\) is equal to:

• (A) \(-\frac{\pi}{12} + \frac{1}{2} + \frac{\sqrt{3}}{4}\)
• (B) \(\frac{\pi}{12} + \frac{1}{2} - \frac{\sqrt{3}}{4}\)
• (C) \(-\frac{\pi}{6} + \frac{1}{2} + \frac{\sqrt{3}}{4}\)
• (D) \(\frac{\pi}{6} + \frac{1}{2} - \frac{\sqrt{3}}{4}\)

Gas is being pumped into a spherical balloon at the rate of \(30ft^3/min\). Then the rate at which the radius increases when it reaches the value 15 ft is:

• (A) \(\frac{1}{30\pi} ft/min\)
• (B) \(\frac{1}{15\pi} ft/min\)
• (C) \(\frac{1}{20} ft/min\)
• (D) \(\frac{1}{25} ft/min\)

Let the function \(f(x)\) defined as \(f(x) = \frac{x-|x|}{x}\), then:

• (A) the function is continuous everywhere
• (B) the function is not continuous
• (C) the function is continuous when x < 0
• (D) the function is continuous for all x except zero

If the direction ratio of two lines are given by \(l + m + n = 0\) and \(mn - 2ln + lm = 0\), then the angle between the lines is:

• (A) \(\frac{\pi}{4}\)
• (B) \(\frac{\pi}{3}\)
• (C) \(\frac{\pi}{2}\)
• (D) 0

The value of c of Lagrange’s mean value theorem for \(f(x) = \sqrt{25 - x^2}\) on [1, 5] is:

• (A) \(\sqrt{15}\)
• (B) 5
• (C) \(\sqrt{10}\)
• (D) 1