List of top Mathematics Questions asked in AP EAPCET

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 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 \(\beta + \gamma : k + \alpha\).

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 $.

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:

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:

If $ x - y - 3 = 0 $ is a normal drawn through the point $ (5, 2) $ to the parabola $ y^2 = 4x $, then the slope of the other normal that can be drawn through the same point to the parabola 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 differential equation corresponding to the family of parabolas whose axis is along $x = 1$ is
Identify the correct option from the following:

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 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

\[ \left( \sqrt{2} + 1 + i \sqrt{2} - 1 \right)^8 = ? \]

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:}