List of practice Questions

What is the molecular geometry of the water molecule (H₂O)?
Calculate the rate constant of a reaction with a given half-life.
What is a primary key in a relational database?
Find the focal length of a lens in a compound lens system.
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 \(3 \times 10^8 \, \text{m/s}\)?
A concave mirror produces an image that is real, inverted, and diminished. What is the position of the object in relation to the mirror?
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?
The rate of a reaction doubles when the temperature is increased by 10°C. What is the approximate value of the activation energy?
What is the major product when 1-bromopropane undergoes nucleophilic substitution with \(OH^-\)?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
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 angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
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?
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 gas expands isothermally and reversibly from a volume V to 2V. If the initial pressure is P, what is the final pressure?
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?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
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 angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
If $ \tan \theta + \cot \theta = 4 $, then find the value of $ \tan^3 \theta + \cot^3 \theta $.
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.