List of top Mathematics Questions asked in AP EAPCET

If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is
If \( A + B = \frac{\pi}{4} \), then \( \dfrac{\cos B - \sin B}{\cos B + \sin B} \) is equal to:
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 \( x \ne (2n+1)\frac{\pi{4} \), then the general solution of \( \cos x + \cos 3x = \sin x + \sin 3x \) is}
If \( \left(\frac{2}{3},0\right) \) is the centroid of the triangle formed by the lines \( 4x^2 - y^2 = 0 \) and \( lx + my + n = 0 \), then \( l+m+n= \):
By taking $ \sqrt{a \pm ib} = x + iy, x>0 $, if we get $$ \frac{\sqrt{21} + 12\sqrt{2}i}{\sqrt{21} - 12\sqrt{2}i} = a + ib, $$ then $ \frac{b}{a} = $ ?
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2x^2 - xy - y^2}{x^2 - y^2} \]
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 \(k\).
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
Area of the region (in sq. units) bounded by the curve $ y = x^2 - 5x + 4 $, $ x = 0 $, $ x = 2 $, and the X-axis is
If \( \theta \) is the acute angle between the tangents drawn from the point \( (1,1) \) to the hyperbola \( 4x^2-5y^2-20=0 \), then \( \tan\theta \) is:
The general solution of the differential equation \(xy(y + 2y') + (y^2 - y) \, dx = 0\) is?
If the curves \(y^2 = 16x \text{ and } 9x^2 + \alpha y^2 = 25\) intersect at right angles, then \(\alpha =\)
\( \int_{5\pi}^{25\pi} |\sin 2x + \cos 2x| \ dx = \)
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 $ S_n = 1^3 + 2^3 + \ldots + n^3 $ and $ T_n = 1 + 2 + \ldots + n $, then
The remainder obtained when \( (2m + 1)^{2n} \), \( m, n \in \mathbb{N} \) is divided by 8 is
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
PQ is a focal chord of the parabola \( y^2 = 4x \) with focus S. If \( P = (4,4) \), then SQ = ?
If \( i = \sqrt{-1} \), then \[ \sum_{n=2}^{30} i^n + \sum_{n=30}^{65} i^{n+3} = \]
The set of all real values of x satisfying the inequation \( \frac{8x^2-14x-9}{3x^2-7x-6}>2 \) is
If \( (a + \sqrt{2}b \cos x)(a - \sqrt{2}b \cos y) = a^2 - b^2 \), where \( a>b>0 \), then at \( \left( \dfrac{\pi}{4}, \dfrac{\pi}{4} \right) \), \( \dfrac{dy}{dx} = \)
\[ \text{If } x = 2 \cos^3 \theta \text{ and } y = 3 \sin^2 \theta, \text{ then } \frac{dy}{dx} =\ ? \]
\(f(x)\) 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