List of top Questions asked in AP EAPCET

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 $NH_3$?

A block of mass m is connected to one end of a spring of spring constant k. The other end of the spring is fixed to a rigid support. Tile mass is released slowly so that the total energy of the system is then constituted by only the potential energy, then d is the maximum extension of the spring. Instead, if the mass is released suddenly from the same initial position, the maximum extension of the spring now is (g = acceleration due to gravity)

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A): The velocity of a projectile at a point on its trajectory is equal to the slope at that point.
Reason (R): The velocity vector at a point is always along the tangent to the trajectory at that point.
In the light of the above statements, choose the correct answer from the options given below

Three masses $m,\, 2\, m$ and $3\, m$ are arranged in two triangular configurations as shown in figure $1$ and figure $2$ . Work done by an external agent in changing, the configuration from figure $1$ to figure $2$ is

A man moves 20 m North, then 10 m East and then 10 $ \sqrt{2} $ m South-West, his displacement is

A body of mass m strikes another body at rest of mass $ \frac{m}{9} $ . Assuming the impact to be inelastic the fraction of the initial kinetic energy transformed into heat during the contact is

A sphere of mass m moving with constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, aid the ratio of velocities of the two spheres after die collision will be

Water rises to a height of 10 cm in a capillary tube and mercury falls to a depth of 3.5 cm in the same capillary tube. If the density of mercury is 13.6 g/cc and its angle of contact is $ 135{}^\circ $ and density of water is 1 g/cc and its angle of contact is $ 0{}^\circ $ , then the ratio of surface tensions of the two liquids is: $ \left( \text{cos }135{}^\circ =0.7 \right) $

$f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is

$D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$