List of practice Questions

The half-life of a radioactive substance is 4 hours. If initially there are 256 grams, how much remains after 10 hours?
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
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 $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
Calculate the empirical formula of a compound containing 40% carbon, 6.7% hydrogen, and 53.3% oxygen by mass.
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)
What volume of CO$_2$ gas at STP is produced by the reaction of 10 g of CaCO$_3$ with excess HCl?
The number of moles of CO$_2$ produced when 2 moles of C$_2$H$_6$ are completely burnt is:
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 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} $)
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?
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 $g = 9.8\, m/s^2$)
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 $.
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
Find the value of $ \sin 75^\circ \cos 15^\circ + \cos 75^\circ \sin 15^\circ $.
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 $.
The value of $ \sin^2 30^\circ + \cos^2 60^\circ $ is:
A first-order reaction is 25% complete in 30 minutes. What is its half-life?
The acidic character of the oxides increases in the order:
The standard electrode potential for $\text{Zn}^{2+}/\text{Zn}$ is $-0.76$ V and for $\text{Cu}^{2+}/\text{Cu}$ is $+0.34$ V. The EMF of the cell
$$ \text{Zn}|\text{Zn}^{2+}||\text{Cu}^{2+}|\text{Cu} $$ is:
The complex $[Cr(NH_3)_4Cl_2]^+$ shows how many geometrical isomers?
The pH of a 0.01 M solution of a weak acid HA is 4. Calculate its dissociation constant (Ka).