The rate of reaction A \(\to\) P is \(1.25 \times 10^{-2} mol dm^{-3} s^{-1}\) when \([A] = 0.5 M\). Calculate the rate constant if the reaction is second order in A.

• (A) 0.05
• (B) 0.04
• (C) 0.03
• (D) 0.01

Which of the following is a correct set of four quantum numbers for 4d orbital?

• (A) (4, 3, 2, +1/2)
• (B) (4, 2, 1, +1/2)
• (C) (4, 1, 2, +1/2)
• (D) None of these

Identify unit of rate constant for first order reaction from the following.

• (A) \(mol dm^{-3} s^{-1}\)
• (B) \(s^{-1}\)
• (C) \(mol^{-1} dm^3 s^{-1}\)
• (D) \(mol dm^{-3}\)

Which of the following mixtures of gases represent water gas?

• (A) \(CO + H_2\)
• (B) \(CO_2 + H_2\)
• (C) \(H_2O + CH_4\)
• (D) \(H_2 + O_2\)

Which of the following electrolytic solutions of the same electrolyte has Maximum electrolytic conductivity at the same temp?

• (A) 0.2 mole of solute is dissolved in 250 ml
• (B) 0.3 mol in 600 ml
• (C) 0.6 in 1000 ml
• (D) 0.8 mole in 2000 ml

If \(\sin x \cos x = \frac{1}{4}\), then the general solution is:

• (A) \(x = \frac{n\pi}{2} + (-1)^n \frac{\pi}{12}\)
• (B) \(x = n\pi + (-1)^n \frac{\pi}{12}\)
• (C) \(x = \frac{n\pi}{2} + (-1)^n \frac{\pi}{6}\)
• (D) \(x = n\pi + (-1)^n \frac{\pi}{6}\)

If \(n \in \mathbb{Z}\), then the expression \(\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}\) is equal to:

• (A) \(2i^n\)
• (B) 0
• (C) \(2^{n+1}\)
• (D) \(i^n\)

The value of \(\int \frac{x^2-1}{(x^4+3x^2+1)\tan^{-1}(x+\frac{1}{x})} dx\) is:

• (A) \(\ln |\tan^{-1}(x + 1/x)| + C\)
• (B) \(\tan^{-1}(x + 1/x) + C\)
• (C) \(\frac{1}{2}(\tan^{-1}(x + 1/x))^2 + C\)
• (D) \(\ln |x^4 + 3x^2 + 1| + C\)

If \(A = \begin{bmatrix} \sin \alpha & -\cos \alpha
\cos \alpha & \sin \alpha \end{bmatrix}\) and \(\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})\). If \(A + A^T = I\), then \(\alpha = \)

• (A) \(\frac{2\pi}{3}\)
• (B) \(\frac{5\pi}{6}\)
• (C) \(\pi\)
• (D) \(\frac{4\pi}{3}\)

The parametric equations of the circle \(x^2 + y^2 - 4x - 6y - 12 = 0\) are:

• (A) \(x = 2 + 5 \cos \theta, y = 3 + 5 \sin \theta\)
• (B) \(x = -2 + 5 \cos \theta, y = -3 + 5 \sin \theta\)
• (C) \(x = 2 + 25 \cos \theta, y = 3 + 25 \sin \theta\)
• (D) \(x = 5 + 2 \cos \theta, y = 5 + 3 \sin \theta\)

If the absolute temperature of a black body is doubled, the frequency corresponding to maximum emissive power becomes:

• (A) halved
• (B) doubled
• (C) four times
• (D) unchanged

The ratio of specific heats \(C_p/C_v\) for a mixture of 1 mole of helium and 1 mole of hydrogen is:

• (A) 1.5
• (B) 1.67
• (C) 1.4
• (D) 1.33

In an isothermal expansion of an ideal gas, the heat supplied to the gas is:

• (A) entirely used to increase internal energy
• (B) entirely used to do work
• (C) partly used to do work and partly to increase internal energy
• (D) none of the above

A refrigerator has a coefficient of performance of 5. If the temperature inside the freezer is \(-20^\circC\), the temperature of the surroundings to which it rejects heat is:

• (A) \(31^\circC\)
• (B) \(41^\circC\)
• (C) \(21^\circC\)
• (D) \(11^\circC\)

The displacement of a particle executing SHM is given by \(x = 0.01 \sin(100\pi t + 0.05)\). Its maximum velocity is:

• (A) \(\pi m/s\)
• (B) \(10\pi m/s\)
• (C) \(0.1\pi m/s\)
• (D) \(100\pi m/s\)