List of top Questions asked in AP EAPCET- 2025

The points $ (2,3) $ and $ \left(-4, \frac{4}{3}\right) $ lie on opposite sides of the line $$ L = 5x - 6y + k = 0, $$ and $ k $ is an integer. If the points $ (1, 2) $ and $ (4, 5) $ lie on the same side of the line, then the perpendicular distance from the origin to the line $ L = 0 $ 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
The angle between the tangents drawn from a point \( (-3, 2) \) to the ellipse \( 4x^2 + 9y^2 - 36 = 0 \) is:
If \( A = (0, 4, -3),\ B = (5, 0, 12),\ C = (7, 24, 0) \), then \( \angle BAC = \)

If the equation of a straight line passing through the point (1,2) and perpendicular to the line $3x + 4y = 7$ is:

The equation of the circle passing through the points (1, 1), (2, 2), and (3, 1) is
PQR is a right angled isosceles triangle with right angle at $ P(2, 1) $. If the equation of the line $ QR $ is $$ 2x + y = 3, $$ then the equation representing the pair of lines $ PQ $ and $ PR $ is:
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
If a hyperbola has asymptotes \(3x-4y-1=0\) and \(4x-3y-6=0\), then the transverse and conjugate axes of that hyperbola are
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 one of the lines given by the pair of lines \( 3x^2 - 2y^2 + axy = 0 \) is making an angle \( 60^\circ \) with the x-axis, then \( a = \)
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 \(S\).
Evaluate the limit: \[ \lim_{x \to \frac{\pi}{4}} \frac{2\sqrt{2} - \left(\cos x + \sin x\right)^3}{1 - \sin 2x} \]
If the normal chord drawn at the point \(\left(\frac{15}{2\sqrt{2}}, \frac{15}{2\sqrt{2}}\right)\) to the parabola \(y^2 = 15x\) subtends an angle \(\theta\) at the vertex of the parabola, then \(\sin \frac{\theta}{3} + \cos \frac{2\theta}{3} - \sec \frac{4\theta}{3} =\) ?
If the line of intersection of the planes \(2x+3y+z=1\) and \(x+3y+2z=2\) makes an angle \( \alpha \) with the positive x-axis, then \( \cos \alpha = \)
If \((\alpha, \beta)\) is the external centre of similitude of the circles \[ x^2 + y^2 = 3 \] and \[ x^2 + y^2 - 2x + 4y + 4 = 0, \] then find \(\frac{\beta}{\alpha}\).
The equation of the base of an equilateral triangle is \( x + y = 2 \) and its opposite vertex is \( (2,1) \). If \( m_1, m_2 \) are the slopes of the other two sides and the length of its side is \( a \), then \( |m_1 - m_2| + a\sqrt{2} = \):
One of the latus recta of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ subtends an angle $2 \tan^{-1} \left(\frac{3}{2}\right)$ at the centre of the hyperbola. If $b^2 = 36$ and $e$ is the eccentricity of the hyperbola, then find $\sqrt{a^2 + e^2}$.
G(1,0) is the centroid of the triangle ABC. If A = (1, -4, 2) and B = (3, 1, 0), then AG$^2$ + CG$^2$ =
Identify the correct option from the following:
If the equation of the polar of the point \( (\alpha, -1) \) with respect to the circle \( x^2+y^2-4x-6y-12=0 \) is \( y = \beta \), then \( 4(\alpha+\beta) = \):
If the equation of the plane passing through the point (2, -1, 3) and perpendicular to each of the planes $3x - 2y + z = 8$ and $x + y + z = 6$ is $lx + my + nz = 1$, then $4m + 2n - 3l$ =
Identify the correct option from the following:
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:
A line \(L\) passes through point \(P(1, 2)\) and makes an angle of \(60^\circ\) with OX in positive direction. A and B are points on line \(L\), 4 units from P. If O is origin, then area of \(\triangle OAB\) is
If the eccentricity of the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] passing through the point \( (4, 6) \) is 2, then the equation of the tangent to this hyperbola at (4, 6) is
From a point \( P(-4, 0) \), two tangents are drawn to the circle \( x^2+y^2-4x-6y-12=0 \) touching the circle at \( A \) and \( B \). If the equation of the circle passing through \( P, A, B \) is \( x^2+y^2+2gx+2fy+c=0 \), then \( (g,f) = \):