List of top Mathematics Questions asked in AP EAPCET

If $ z_1 = 2 + 3i $, $ z_2 = 4 - 5i $, and $ z_3 $ are three points in the Argand plane such that $ 5z_1 + xz_2 + yz_3 = 0 $ (where $ x, y \in \mathbb{R} $) and $ z_3 $ is the midpoint of the line segment joining the points $ z_1 $ and $ z_2 $, then find $ x + y $.

If two angles $ \alpha, \beta $ are such that $ 0<\alpha, \beta<\frac{\pi}{4} $, $ \sqrt{1 + \cos 2\alpha} = \frac{3}{\sqrt{5}} $ and $ \frac{\sqrt{1 - \cos 2\beta}}{\sqrt{1 + \cos 2\beta}} = \frac{1}{7} $, then $ (2\alpha + \beta) = $

If $x_1, x_2, \ldots, x_n$ are 'n' observations and $\bar{x}$ is their mean. If \[ \sum_{i=1}^{n}(x_i - \bar{x})^2 \text{ is almost zero, then a true statement among the following is} \]

In $ \triangle ABC $, if $ r_1 : r_2 = 7:8 $ and $ r_1 : r_3 = 3:4 $, then $ a : b : c = $

If a Bernoulli trial is conducted n times, then which one of the following is not suitable to use Poisson distribution?

Let $[ \cdot ]$ denote the greatest integer function.
Assertion (A): $\lim_{x \to \infty} \frac{[x]}{x} = 1$
Reason (R): $f(x) = x - 1$, $g(x) = [x]$, $h(x) = x$ and $\lim_{x \to \infty} \frac{f(x)}{x} = \lim_{x \to \infty} \frac{h(x)}{x} = 1$:

In $ \triangle ABC $, if $ A, B, C $ are in arithmetic progression, then $ \frac{c}{a} \sin 2A + \frac{a}{c} \sin 2C = $:

Let $[t]$ represent the greatest integer not more than $t$. Then the number of discontinuous points of $f(x) = \left[\frac{1}{x}\right]$ in $(0, \infty)$ is

If $(l_1, m_1, n_1), (l_2, m_2, n_2)$ are the direction cosines of two lines, then \[ (l_2m_1 - l_1m_2)^2 + (m_1n_2 - m_2n_1)^2 + (n_1l_2 - n_2l_1)^2 + (l_1l_2 + m_1m_2 + n_1n_2)^2 = \]

If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is $ ( \alpha, \beta, \gamma ) $, then find the value of $ \alpha^2 + \beta^2 + \gamma^2 $.

The sum of the global minimum and global maximum values of the function \[ f(x) = \frac{4}{3}x^3 - 4x \quad \text{in } [0, 2] \text{ is} \]

If $ \overline{\mathbf{a}} = 2\overline{\mathbf{i}} + 3\overline{\mathbf{j}} + 4\overline{\mathbf{k}} $, $ \overline{\mathbf{b}} = 3\overline{\mathbf{i}} + 4\overline{\mathbf{k}} $, and $ \overline{\mathbf{c}} = 5\overline{\mathbf{i}} + 4\overline{\mathbf{k}} $ are three vectors, then a vector which is perpendicular to $ \overline{\mathbf{a}} $ and $ \overline{\mathbf{b}} \times \overline{\mathbf{c}} $ is

If the number of diagonals of a regular polygon of $ n $ sides is 104, then $ n = $

The greatest integer $ r $ such that $ 30^r $ divides $ 30! $ is:

The number of six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 is:

If $ -1 $ is a twice repeated root of the equation $ a(x^3 + x^2) + bx + c = 0 $, then the ratio $ a : b : c $ is:

Evaluate the following expression: \[ (1+i)^{2024} + (1-i)^{2024} \]

The combined equation of the lines passing through the point $ (3, 4) $ and each making an angle of 45° with the line $ x + y + 1 = 0 $ is:

The area (in sq. units) of the region bounded by the curves $ y = 4 \cos x $ and $ y = -|\cos x| $ from $ x = -\frac{\pi}{2} $ to $ x = \frac{\pi}{2} $ is:

If $ 2^n $ divides $ 16! $ and $ 2^{n+1} $ does not divide $ 16! $, then $ n = $

Let ABCD be a parallelogram and $ 2\bar{i} + \bar{j} $, $ 4\bar{i} + 5\bar{j} + 4\bar{k} $ and $ -\bar{i} - 4\bar{j} - 3\bar{k} $ be the position vectors of the vertices A, B, D respectively. Then the position vector of one of the points of trisection of the diagonal AC is

If \[ \frac{-x^2 + 6x + 1}{(x - 1)^2 (x^2 + 2)} = \frac{A}{x - 1} + \frac{B}{(x - 1)^2} + \frac{Cx - 3}{x^2 + 2}, \] then $A + B + C =$ ?