List of top Questions asked in AP EAPCET

If $$ \int \frac{dx}{1 - \sin^4 x} = A \tan x + B \tan^{-1}(\sqrt{2} \tan x) + C, $$ then find $ A^2 - B^2 $.
The total maximum number of electrons possible in 3d, 6d, 5s and 4f orbitals with \(m_l\) (magnetic quantum number) value -2 is
If \[ A = \begin{bmatrix} 1 & -1 & 2 \\ -2 & 3 & -3 \\ 4 & -4 & 5 \end{bmatrix} \] and \( A^T \) represents the transpose of \( A \), then calculate \( AA^T - A - A^T \).
If the angular velocity of a planet about its axis is halved, the distance of the stationary satellite of this planet from the centre of the planet becomes $2^n$ times the initial distance. Then the value of $n$ is
The number of ways of dividing 15 persons into 3 groups containing 3, 5 and 7 persons so that two particular persons are not included into the 5 persons group is
If \( 3\overline{i} + \overline{j} + \overline{k} \), \( 2\overline{i} + \overline{k} \), and \( \overline{i} + 5\overline{j} \) are the position vectors of three non-collinear points A, B, C respectively. If the perpendicular drawn from C onto \( \overline{AB} \) meets \( \overline{AB} \) at the point \( a\overline{i} + b\overline{j} + c\overline{k} \), then \( a + b + c = \)
If a constant force of \((2i + 3j + 4k) \, \text{N}\) acting on a body of mass \(5 \, \text{kg}\) displaces it from \((3i - 4k)\, \text{m}\) to \((2i + 2j + 3k)\, \text{m}\), then the work done by the force on the body is:
A parallel plate capacitor has plates of area 0.4 m$^2$ and spacing of 0.5 mm. If a slab of thickness 0.5 mm and dielectric constant 4.5 is introduced between the plates of the capacitor, then the capacitance of the capacitor is
The ratio of the efficiencies of two Carnot engines A and B is 1.25 and the temperature difference between the source and the sink is the same in both engines. The ratio of the absolute temperatures of the sources of the engines A and B is
The domain of the real valued function $ f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x) $ is
If the locus of a point which is equidistant from the coordinate axes forms a triangle with the line \(y = 3\), then the area of the triangle is
If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person, then the maximum acceleration with which the person can safely climb up the rope is (g - acceleration due to gravity)
Identify the compound which is least reactive towards nucleophilic substitution reactions.
In an element with atomic number (Z) 25, the number of electrons with (n + l) value equal to 3 and 4 are x and y respectively. The value of (x + y) is
A metal crystallizes in simple cubic lattice. The volume of one unit cell is \( 6.4 \times 10^{-7} \, \text{pm}^3 \). What is the radius of the metal atom in pm?
If the incentre of the triangle formed by lines $$ x - 2 = 0, \quad x + y - 1 = 0, \quad x - y + 3 = 0 $$ is $ (\alpha, \beta) $, then find $ \beta $.
If \( l, m \) represent any two elements (identical or different) of the set \( \{1, 2, 3, 4, 5, 6, 7\} \), then the probability that \( lx^2 + mx + 1>0 \,\, \forall x \in \mathbb{R} \) is
The elastic potential energy stored in a copper rod of length one meter and area of cross-section \(1 \, \text{mm}^2\) when stretched by 1 mm is:
If $ r_1 $ and $ r_2 $ are radii of two circles touching all the four circles $$ (x \pm r)^2 + (y \pm r)^2 = r^2, $$ then find the value of $$ \frac{r_1 + r_2}{r}. $$
The general solution of the differential equation \(\frac{dy}{dx} + xy = 4x - 2y + 8\) is
Which of the following enzymatic reaction is not correctly matched with enzyme shown against it in brackets?
\[ \left( \sqrt{2} + 1 + i \sqrt{2} - 1 \right)^8 = ? \]
For all $n \in \mathbb{N}$, if $n(n^2+3)$ is divisible by $k$, then the maximum value of $k$ is
The number of solutions of the equation $4 \cos 2\theta \cos 3\theta = \sec \theta$ in the interval $[0, 2\pi]$ is

The logic gate equivalent to the combination of logic gates shown in the figure is