List of top Questions asked in AP EAPCET

The area of the region (in sq.units) bounded by the curves \(x^2 + y^2 = 16\) and \(x^2 + y^2 = 6x\) is?
If the sum of the roots of the quadratic equation $ x^2 - 5x + k = 0 $ is 5, find the value of $ k $.
If $2x - 3y + 1 = 0$ is the equation of the polar of a point $P(x_1, y_1)$ with respect to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$, then $3x_1 - y_1 =$
If \( A = (0, 4, -3),\ B = (5, 0, 12),\ C = (7, 24, 0) \), then \( \angle BAC = \)
In \( \triangle ABC \), if \( \sin^2 B = \sin A \) and \( 2\cos^2 A = 3\cos^2 B \), then the triangle is:
If the median AD of the triangle ABC is bisected at E and BE meets AC in F, then AF : AC =
Let \(P(a \sec \theta, b \tan \theta)\) and \(Q(a \sec \phi, b \tan \phi)\) where \(\theta + \phi = \frac{\pi}{2}\) be two points on the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\). If \((h,k)\) is the point of intersection of the normals drawn at \(P\) and \(Q\), then find \(k\).
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2x^2 - xy - y^2}{x^2 - y^2} \]
If $ A(0, 1, 2) $, $ B(2, -1, 3) $, and $ C(1, -3, 1) $ are the vertices of a triangle, then the distance between its circumcentre and orthocentre is
In a binomial distribution, if \(n=4\) and \( P(X=0) = \frac{16{81} \), then \( P(X=4) = \)}
If \(P(\alpha, \beta)\) is a point on the curve \(9x^2 + 4 y^2 = 144\) in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at \(P\) with the coordinate axes is \(S\), then find \(S\).
If the pair of lines $ax^2 - 7xy - 3y^2 = 0$ and $2x^2 + xy - 6y^2 = 0$ have exactly one line in common and '$a$' is an integer, then the equation of the pair of bisectors of the angles between the lines $ax^2 - 7xy - 3y^2 = 0$ is
The transformed equation of \( 3x^2 - 4xy = r^2 \) when the coordinate axes are rotated about the origin through an angle of \( \tan^{-1}(2) \) in positive direction is
If \( y = \tan^{-1}\left(\frac{x}{1+2x^2}\right) + \tan^{-1}\left(\frac{x}{1+6x^2}\right) \), then \( \frac{dy}{dx} = \)
If \( i = \sqrt{-1} \), then \[ \sum_{n=2}^{30} i^n + \sum_{n=30}^{65} i^{n+3} = \]
\[ \text{If } x = 2 \cos^3 \theta \text{ and } y = 3 \sin^2 \theta, \text{ then } \frac{dy}{dx} =\ ? \]
PQ is a focal chord of the parabola \( y^2 = 4x \) with focus S. If \( P = (4,4) \), then SQ = ?
If $ \vec{a}, \vec{b}, \vec{c} $ are three unit vectors such that $ \vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2} \vec{b} + \frac{1}{2} \vec{c} $, and $ \alpha, \beta $ are the angles between $ \vec{a}, \vec{c} $ and $ \vec{a}, \vec{b} $ respectively, then $ \alpha + \beta = ? $
The number of all possible positive integral solutions of the equation \(xyz = 30\) is:
The remainder obtained when \( (2m + 1)^{2n} \), \( m, n \in \mathbb{N} \) is divided by 8 is
\(f(x)\) is a quadratic polynomial satisfying the condition \( f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) \). If \(f(-1)=0\), then the range of \(f\) is
If $ S_n = 1^3 + 2^3 + \ldots + n^3 $ and $ T_n = 1 + 2 + \ldots + n $, then
If \( (a + \sqrt{2}b \cos x)(a - \sqrt{2}b \cos y) = a^2 - b^2 \), where \( a>b>0 \), then at \( \left( \dfrac{\pi}{4}, \dfrac{\pi}{4} \right) \), \( \dfrac{dy}{dx} = \)
The general solution of the differential equation \(xy(y + 2y') + (y^2 - y) \, dx = 0\) is?
The set of all real values of x satisfying the inequation \( \frac{8x^2-14x-9}{3x^2-7x-6}>2 \) is