List of practice Questions

Let $ f(x) = 2x^3 - 3x \neq 4 $. Then the inverse function $ f^{-1}(x) $ is:

Let $ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $, then $ A^2 - 5A + 6I = ? $

For the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2\text{NH}_3(g)$ at 298 K, the enthalpy change $ \Delta H = -92.4 \, \text{kJ/mol} $. What happens to the equilibrium when temperature is increased?

In a redox titration, 25 mL of 0.1 M KMnO$_4$ is required to completely react with oxalic acid in acidic medium. The volume of 0.2 M oxalic acid used is:
(Balanced reaction: $ 2\text{MnO}_4^- + 5\text{C}_2\text{O}_4^{2-} + 16\text{H}^+ \rightarrow 2\text{Mn}^{2+} + 10\text{CO}_2 + 8\text{H}_2\text{O} $)

Calculate the volume occupied by 4.4 g of CO$_2$ gas at 27°C and 1 atm pressure. ($ R = 0.0821 \, \text{L-atm/mol-K} $, Molar mass of CO$_2$ = 44 g/mol)

A charged particle of mass $ m $ and charge $ q $ moves with a velocity $ \vec{v} $ perpendicular to a magnetic field $ \vec{B} $. The radius of the circular path it follows is:

Let a circle pass through the point $ (1, 2) $ and touch the $ x $-axis at $ (3, 0) $. Then the equation of the circle is:

If $ \tan \theta = \frac{3}{4} $ and $ \theta $ is in the first quadrant, find the value of $ \sin \theta + \cos \theta $.

If $ A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} $, find the determinant of $ A $.

Evaluate $ \int_{0}^{1} (2x + 1) \, dx $.

A body of mass 2 kg is moving with a velocity of 10 m/s. What is its kinetic energy?

Two charges $ +4 \, \mu\text{C} $ and $ -4 \, \mu\text{C} $ are placed 2 m apart. What is the magnitude of the electric force between them? (Take $k = 9 \times 10^9 \, \text{N.m}^2/\text{C}^2$.

What is the molarity of a solution prepared by dissolving 4 g of NaOH in 250 mL of solution? (Molar mass of NaOH = 40 g/mol)

The enthalpy change for the reaction
$2H_2(g) + O_2(g) → 2H_2O(l)$
is -572 kJ/mol. What is the enthalpy change for the formation of 1 mole of $H_2O(l)$}?

Which of the following is the IUPAC name for $CH_3CH_2CH_2OH$?

What is the hybridization of the central atom in $NH_3$?

Kanha, Resham, and Nisha were partners in a firm. Nisha had given a loan of \rupee 1,00,000 to the firm @ 10\% p.a. The accountant of the firm is emphasizing that interest on loan will be paid @ 6\% p.a. At what rate the interest on loan will be paid to Nisha?

Given the linear equation $2x + 3y – 8 = 0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines

Vapour pressure of water at 293 K is 17.535 mm Hg. Calculate the vapour pressure of water at 293 K when 25 g of glucose is dissolved in 450 g of water.

Which of the following is correct for A - B?

The mass of 60% HCl by mass required for the neutralisation of 10 L of 0.1 M NaOH is

For the matrix $A=\begin{bmatrix}1&1&1\\ 1&2&-3\\ 2&-1&3\end{bmatrix}$show that $A^3−6A^2+5A+11I=O$.Hence,find A−1.

Do you think the soldiers of the two armies are like each other, or different from each other? Find evidence from the story to support your answer.

The coefficient of $ {{a}^{5}}{{b}^{6}}{{c}^{7}} $ in the expansion of $ {{(bc+ca+ab)}^{9}} $ is

The acceleration due to gravity at a height h above the earths surface is $ 9m{{s}^{-2}}. $ If $ g=10\text{ }m{{s}^{-2}} $ on the earths surface, its value at a point at an equal distance h below the surface of the earth is