List of top Mathematics Questions asked in AP EAPCET

The terms containing \( x^r y^s \) (for certain r and s) are present in both the expansions of \( (x+y^2)^{13} \) and \( (x^2+y)^{14} \). If \( \alpha \) is the number of such terms, then the sum \( \sum_{r,s} \alpha (r+s) = \) (Note: The sum is over the common terms)
If $A = \{x \in \mathbb{R} \mid \sin^{-1}(\sqrt{x^2+x+1}) \in [-\frac{\pi}{2}, \frac{\pi}{2}]\}$ and $B = \{y \in \mathbb{R} \mid y = \sin^{-1}(\sqrt{x^2+x+1}), x \in A\}$, then
The number of positive integers less than 10000 which contain the digit 5 at least once is
The domain and range of a real valued function \( f(x) = \cos (x-3) \) are respectively.
For all \( n \in \mathbb{N} \), if \( 1^3 + 2^3 + 3^3 + \cdots + n^3>x \), then a value of \( x \) among the following is:
$\tan\left(\frac{2\pi}{7}\right)\tan\left(\frac{4\pi}{7}\right) + \tan\left(\frac{4\pi}{7}\right)\tan\left(\frac{\pi}{7}\right) + \tan\left(\frac{\pi}{7}\right)\tan\left(\frac{2\pi}{7}\right) =$
Let $ A(4, 3), B(2, 5) $ be two points. If $ P $ is a variable point on the same side of the origin as that of line $ AB $ and at most 5 units from the midpoint of $ AB $, then the locus of $ P $ is:
The equation of the normal drawn at the point \((\sqrt{2}+1, -1)\) to the ellipse \(x^2 + 2y^2 - 2x + 8y + 5 = 0\) is
The equation \((2p - 3)x^2 + 2pxy - y^2 = 0\) represents a pair of distinct lines
If \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ l & m & n \end{bmatrix} \] is a matrix such that $|A|>0$ and \[ Adj(A) = \begin{bmatrix} 0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4 \end{bmatrix}, \] then find the value of \[ \frac{cd}{fb} + \frac{ln}{em}. \]
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 $.
A family consists of 8 persons. If 4 persons are chosen at random and they are found to be 2 men and 2 women, then the probability that there are equal numbers of men and women in that family 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 \( AA^T - A - A^T \).
The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ (with $a \ne 0$) from the set $\{0,1,2,4\}$ 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 the equation of the circle having the common chord to the circles $$ x^2 + y^2 + x - 3y - 10 = 0 $$ and $$ x^2 + y^2 + 2x - y - 20 = 0 $$ as its diameter is $$ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, $$ then find $ \alpha + 2\beta + \gamma $.
The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
The domain of the real valued function $ f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x) $ is
If \(\alpha, \beta, \gamma\) are the roots of the equation \[ x^3 - 13x^2 + kx + 189 = 0 \] such that \(\beta - \gamma = 2\), then find the ratio \(\beta + \gamma : k + \alpha\).

Find the variance of the following frequency distribution:

Class Interval 
0--44--88--1212--16
Frequency1221
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 \( f : \mathbb{R} \to \mathbb{R} \) and \( g : \mathbb{R} \to \mathbb{R} \) are two functions defined by \( f(x) = 2x - 3 \) and \( g(x) = 5x^2 - 2 \), then the least value of the function \((g \circ f)(x)\) is:
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