List of practice Questions

Calculate the electric field at a point due to a uniformly charged spherical shell.
Find the angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
What is the major product when 1-bromopropane undergoes nucleophilic substitution with \(OH^-\)?
The rate of a reaction doubles when the temperature is increased by 10°C. What is the approximate value of the activation energy?
In an isobaric process, 200 J of heat is supplied to a gas. The gas does 50 J of work. What is the change in internal energy?
A concave mirror produces an image that is real, inverted, and diminished. What is the position of the object in relation to the mirror?
A radio wave travels in a medium with refractive index 1.5. What is the speed of light in this medium if the speed of light in vacuum is \(3 \times 10^8 \, \text{m/s}\)?
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).
Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
For a reaction A → B, the concentration of A decreases from 0.8 M to 0.2 M in 10 minutes. If the rate constant is 0.1 min⁻¹, what is the order of the reaction?
A gas expands isothermally and reversibly from a volume V to 2V. If the initial pressure is P, what is the final pressure?
The electric field at a point on the axis of a uniformly charged ring of radius R at a distance x from its center is given by: \[ E = \frac{1}{4\pi\epsilon_0} \cdot \frac{2\pi kQx}{(x^2 + R^2)^{3/2}}. \] If x = 2R, what is the magnitude of the electric field?
A block of mass 2 kg slides on a frictionless horizontal surface with a velocity of 3 m/s. It collides elastically with another block of mass 3 kg initially at rest. What is the velocity of the 2 kg block after the collision?
For the reaction $ N_2 + 3H_2 \rightleftharpoons 2NH_3 $, if initially 1 mole of $ N_2 $ and 3 moles of $ H_2 $ are taken and at equilibrium 0.4 moles of $ NH_3 $ are formed, find the equilibrium concentration of $ H_2 $.
A 2 L container holds oxygen gas at 300 K and 2 atm pressure. If the temperature is increased to 600 K and the volume is doubled, what is the final pressure?
How many grams of $ \text{CO}_2 $ are produced when 10 g of $ \text{C}_2\text{H}_6 $ (ethane) is completely combusted? Reaction: $ 2\text{C}_2\text{H}_6 + 7\text{O}_2 \rightarrow 4\text{CO}_2 + 6\text{H}_2\text{O} $
How much water must be added to 500 mL of 2 M $ \mathrm{H_2SO_4} $ solution to make it 0.5 M?
A charged particle moves in a magnetic field with velocity $ v $ perpendicular to the field $ B $. The radius of the circular path is $ r $. Which of the following expressions gives the charge $ q $ of the particle?
Two identical charges $ q $ are placed 1 m apart. The electrostatic force between them is $ 9 \times 10^{-9} \, \text{N} $. What is the magnitude of each charge? (Take $ k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 $)
The escape velocity from the surface of a planet is 11.2 km/s. If the radius of the planet is doubled but the mass remains the same, what will be the new escape velocity?
A fluid flows through a pipe with varying cross-section. If the velocity at the narrow section is 3 m/s and the cross-sectional area is half of the wider section, what is the velocity in the wider section?