List of practice Questions

If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
The half-life of a radioactive substance is 4 hours. If initially there are 256 grams, how much remains after 10 hours?
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?
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?
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 $)
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?
How much water must be added to 500 mL of 2 M $ \mathrm{H_2SO_4} $ solution to make it 0.5 M?
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} $
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?
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 $.
The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
The value of $ \sin^2 30^\circ + \cos^2 60^\circ $ is:
The sum of the infinite geometric series $ S = \frac{a}{1-r} $ is 24, and the sum of the first three terms is 21. Find $ a $ and $ r $.
Find the value of $ \sin 75^\circ \cos 15^\circ + \cos 75^\circ \sin 15^\circ $.
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
The area of a triangle with vertices at points $ A(1,2) $, $ B(4,6) $, and $ C(k, 8) $ is 5. Find the value of $ k $.
A block of mass 5 kg is placed on a frictionless incline of angle $30^\circ$. What is the acceleration of the block down the incline? (Take $g = 9.8\, m/s^2$)
Two resistors, 4 $\Omega$ and 6 $\Omega$, are connected in parallel to a 12 V battery. What is the total current drawn from the battery?
The work function of a metal is 2 eV. What is the threshold frequency for the photoelectric emission? (Take Planck's constant $ h = 6.63 \times 10^{-34} \, \text{Js} $, $ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} $)
A 2 kg object is moving with a velocity of 5 m/s on a frictionless surface. It collides elastically with a stationary object of mass 3 kg. Find the velocity of the 3 kg object after the collision.
The number of moles of CO$_2$ produced when 2 moles of C$_2$H$_6$ are completely burnt is:
What volume of CO$_2$ gas at STP is produced by the reaction of 10 g of CaCO$_3$ with excess HCl?
How many grams of $ \mathrm{Al_2(SO_4)_3} $ are required to produce 10 L of a 0.5 M solution? (Molar mass = 342 g/mol)