List of top Mathematics Questions asked in AP EAPCET

If $z = \frac{\sqrt{3} + i}{2}$, then $z^{101} + z^{103} =$
If the system of linear equations $x + y + z = 1$, $x + 2y + 4z = \eta$, $x + 4y + 10z = \eta^2$ has a solution, then the value of $\eta$ is:
The domain of the function $f(x) = \sqrt{\log_{10} \left(\frac{5x - x^2}{4}\right)}$ is:
If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of $\sum_{r=1}^{100} \left[ \frac{r}{5} \right]$ is:
If $a_n = \sum_{r=0}^n \frac{1}{^{n}C_r}$ and $b_n = \sum_{r=0}^n \frac{r}{^{n}C_r}$, then $\frac{b_n}{a_n} =$
If $f : [1, \infty) \to [1, \infty)$ is defined by $f(x) = 2^{x(x-1)}$, then $f^{-1}(x) =$
Points \( P \) and \( Q \) are given by \( \vec{OP} = \vec{i} - \vec{j} - \vec{k} \) and \( \vec{OQ} = -\vec{i} + \vec{j} + \vec{k} \). A line along the vector \( \vec{a} = \vec{i} + \vec{j} \) passes through point \( P \), and another line along the vector \( \vec{b} = \vec{j} - \vec{k} \) passes through point \( Q \). If a line along the vector \( \vec{c} = \vec{i} - \vec{j} + \vec{k} \) intersects both the lines along \( \vec{a} \) and \( \vec{b} \) at \( L \) and \( M \) respectively, then \( \vec{PM} = \) ?
In a shoe rack there are 4 pairs of shoes and 4 shoes are drawn one after the other at random without replacement. Then the probability of getting at least one correct pair of shoes among the four shoes drawn is:
If \( \alpha \) is the common root of the quadratic equations \( x^2 - 5x + 4a = 0 \) and \( x^2 - 2ax - 8 = 0 \), where \( a \in \mathbb{R} \), then the value of \( \alpha^4 - \alpha^3 + 68 \) is:
What is the distance between the points $(3, -2)$ and $(-1, 4)$?
The coefficient of $x^{10}$ in the expansion of $\left(x + \frac{2}{x} - 5 \right)^{12}$ is
\(\int \frac{\sqrt{x - 2}}{2x + 4} \, dx =\)
If the equation of the tangent of the hyperbola \( 5x^2 - 9y^2 - 20x - 18y - 34 = 0 \) which makes an angle \( 45^\circ \) with the positive X-axis in positive direction is \( x+by+c=0 \) then \( b^2+c^2 = \)
If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is
If \(k\) is a positive integer and \(10^k\) is a divisor of the number \(9^{11} + 11^9\), then the greatest value of \(k\) is:
If the vectors \(2\vec{i} + 3\vec{j} + k\), \(-3\vec{i} - 2\vec{j} - 4k\), and \(l\vec{i} - \vec{j} + 3\vec{k}\) form a right-angled triangle for a positive value of \(l\), then the length of its hypotenuse is
\[ \text{If } y = |\cos x - \sin x| + |\tan x - \cot x|, \text{ then } \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{3}} + \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{6}} = \]
The product of all the real roots of the equation $|x^2 - 5||x| + 6 = 0$ is
If \( \int x^2 \cos^3 x\, dx = \frac{1}{6}f(x) + g(x) \sin 2x + h(x) \cos 2x + c \), then \( f(1) + g(2) + h\left(\frac{1}{2}\right) = \)
All the letters of the word LETTER are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word TETLER is:
5 men and 4 women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $ \alpha $, and the number of arrangements in which they are not together is $ \beta $, then $ \frac{\alpha}{\beta} = $
Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \[ \lim_{x \to 2^+} \left( \frac{[x]^3}{3} - \left[ \frac{x^3}{3} \right] \right) \]
If \( \frac{3x+1}{(x-1)(x^2+2)} = \frac{A}{x-1} + \frac{Bx+C}{x^2+2} \), then \( 5(A-B) = \)?
If g is the inverse of the function f(x) and \( g(x) = x + \tan x \) then, \( f'(x) = \)
The general solution of the differential equation $\left( x \sin \frac{y}{x} \right) \frac{dy}{dx} = y \sin \frac{y}{x} - x$ is
Identify the correct option from the following: