List of top Mathematics Questions asked in AP EAPCET

The differential equation corresponding to the family of parabolas whose axis is along $x = 1$ is
Identify the correct option from the following:
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
The domain and range of a real valued function \( f(x) = \cos (x-3) \) are respectively.
If the line $$ 4x - 3y + 7 = 0 $$ touches the circle $$ x^2 + y^2 - 6x + 4y - 12 = 0 $$ at $ (\alpha, \beta) $, then find $ \alpha + 2\beta $.
The number of ways of selecting 3 numbers that are in Arithmetic Progression (A.P.) from the set \(\{1, 2, 3, \ldots, 100\}\) is:
The numerically greatest term in the expansion of $ (x + 3y)^{13} $, when $ x = \frac{1}{2},\ y = \frac{1}{3} $, is
The general solution of the differential equation \(\frac{dy}{dx} + xy = 4x - 2y + 8\) is
\[ \left( \sqrt{2} + 1 + i \sqrt{2} - 1 \right)^8 = ? \]
For all $n \in \mathbb{N}$, if $n(n^2+3)$ is divisible by $k$, then the maximum value of $k$ is
If \(\alpha\) is the angle made by the perpendicular drawn from origin to the line \(12x - 5y + 13 = 0\) with the positive X-axis in anti-clockwise direction, then \(\alpha =\)
If \[ A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}, \] where \( x \) and \( y \) are non-zero real numbers, trace of \( A = 0 \), and determinant of \( A = -6 \), then the minor of the element 1 of \( A \) is:}
If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2) =$
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:
The number of solutions of the equation $4 \cos 2\theta \cos 3\theta = \sec \theta$ in the interval $[0, 2\pi]$ is
If \( \log_2 3 = p \), express \( \log_8 9 \) in terms of \( p \):
All the values of \(k\) such that the quadratic expression \(2kx^2 - (4k+1)x + 2\) is negative for exactly three integral values of \(x\), lie in the interval:
The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE 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 \(\beta + \gamma : k + \alpha\).
The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse \( 9x^2 + 4y^2 = 72 \) at the point (2, 3) with the X-axis 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
If the distance of a variable point \(P\) from a point \(A(2,-2)\) is twice the distance of \(P\) from the Y-axis, then the equation of locus of \(P\) 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 \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
If \( i = \sqrt{-1} \), then \[ \sum_{n=2}^{30} i^n + \sum_{n=30}^{65} i^{n+3} = \]
If $ 0 \le x \le 3,\ 0 \le y \le 3 $, then the number of solutions $(x, y)$ for the equation: $$ \left( \sqrt{\sin^2 x - \sin x + \frac{1}{2}} \right)^{\sec^2 y} = 1 $$