List of practice Questions

If \( z = e^{i\theta} \), then which of the following complex numbers is of unit modulus?

For the matrix \( A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \), the matrix \( A^{2n} \) has the form

For any positive integer \( n \), the value of \( 1 + 1! + 2.2! + 3.3! + \cdots + n.n! \) will be

If the straight line \( \frac{x}{p} - \frac{y}{q} = 1 \) touches the curve \( \left( \frac{x}{a} \right)^n - \left( \frac{y}{b} \right)^n = 1 \), then

3 moles of an ideal gas expands isothermally against a constant pressure of 2 Pascal from 20 L to 60 L. The amount of work involved is

A galvanic cell consists of the following: \[ \text{Zn(s)} | \text{Zn}^{2+}(0.01M) || \text{Cu}^{2+}(0.1M) | \text{Cu(s)} \] The standard reduction potentials of the two electrodes are given as \( E^0(\text{Zn}^{2+}/\text{Zn}) = -0.763 \, \text{V} \) and \( E^0(\text{Cu}^{2+}/\text{Cu}) = 0.337 \, \text{V} \). The emf of the above cell will be:

3 moles of an ideal gas expands isothermally against a constant pressure of 2 Pascal from 20 L to 60 L. The amount of work involved is

18 g of glucose was dissolved in 360 g of water. The vapor pressure of the solution at 100°C will be

Gold crystallizes in a face-centered cubic lattice with unit cell length of 4.07 Å. Relative atomic mass of gold is 197.0. The density of gold will be

The molar conductivity \( \Lambda^0_m \) at infinite dilution for HCl, NaCl, and \( \text{CH}_3\text{COONa} \) at 25°C are 426, 126, and 91 S cm\(^2\) respectively. The \( \Lambda^0_m \) for acetic acid at the same temperature will be

For which of the following is the adsorption theory applicable?

An aqueous solution of CuSO4 solution is electrolyzed for 193 s with a current of 2.5 amp. Given that the atomic mass of Cu is 63.5 and \( F = 96500 \) coulombs, the amount of copper deposited at the anode is

A colloidal solution is subjected to an electric field. The colloidal particles move toward the anode. In the coagulation of this solution using NaCl, BaCl2, and AlCl3 separately, which one is the correct order of coagulation power?

A 0.02(M) NaOH solution and a 0.01(M) HCl solution are mixed in the volume ratio of 2:3. The pH of the mixed solution will be

A man of height \( H \) is standing on level road where because of temperature variation, the refractive index of air is varying as \( \mu = (1 + \alpha y)^{1/2 \), where \( y \) is the height from the level road and \( \alpha \) is a positive constant. Find the distant point that man can see on the road.}

The thickness of the ice layer on the surface of a lake is 20 m. A hole is made in the ice layer. What is the minimum length of the rope required to take a bucket full of water?

An enclosed container filled with gas is moving in a horizontal direction with some acceleration. Neglecting the gravitational force, the pressure of the gas inside the container will be

The following forces are acting on a particle: (1) \( 2i + 3j - 2k \), (2) \( 3i + j + 3k \), and (3) \( -5i + 2j + k \). Now the particle will move in

The flow velocity of water from a tap is 3 liters/min. If the diameter of the tap is 1.25 cm and the viscosity of water is \( 10^{-3} \) Poise, then the value of Reynolds number is approximately

The speed of a projectile is half of its initial speed at maximum height. Then, the angle of projection will be

A diatomic gas expands adiabatically so that its density becomes \( \frac{1}{32} \) part the earlier value. If the initial pressure be \( P \), then the final pressure will be

A body is thrown vertically upward. It passes from a point at times \( t_1 \) and \( t_2 \), then the height of that point will be

Which of the following combination of properties would be most desirable for a cooking pot?

A force \( F \) is applied upon a square with side \( L \). Errors in \( L \) and \( F \) are 2% and 4% respectively. Error in measuring pressure will be

Teratogenicity is caused by