List of top Questions asked in AP EAPCET- 2025

If two sides of a triangle are represented by \( 3x^2 - 5xy + 2y^2 = 0 \) and its orthocentre is (2,1), then the equation of the third side is
If the normal drawn at the point P on the curve \(y = x \log x\) is parallel to the line \(2x - 2y = 3\), then P =
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 \( |m_1 - m_2| + a\sqrt{2} = \):
If the tangent drawn at the point \( (x_1,y_1) \), \(x_1,y_1 \in N \) on the curve \( y = x^4 - 2x^3 + x^2 + 5x \) passes through origin, then \( x_1+y_1 = \)
The equation \((2p - 3)x^2 + 2pxy - y^2 = 0\) represents a pair of distinct lines
The slope of the non-vertical tangent drawn from the point $(3,4)$ to the circle $x^2 + y^2 = 9$ is:
Problem: From a point \( P \) on the circle \( x^2 + y^2 = 4 \), two tangents are drawn to the circle \( x^2 + y^2 - 6x - 6y + 14 = 0 \). If \( A \) and \( B \) are the points of contact of those lines, then the locus of the center of the circle passing through the points \( P \), \( A \), and \( B \) is: Identify the correct option from the following:
If \( \left(\frac{1}{10}, \frac{-1}{5}\right) \) is the inverse point of a point (-1, 2) with respect to the circle \( x^2+y^2-2x+4y+c=0 \) then c =
If the function $y = g(x)$ represents the slopes of the tangents drawn to the curve $y = 3x^3 - 5x^2 - 12x^2 + 18x - 3$ strictly increasing then the domain of $g(x)$ is
Identify the correct option from the following:
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 \( \cos \alpha = \)
Circles are drawn through the point \( (2, 0) \) to cut intercepts of length 5 units on the X-axis. If their centre lies in the first quadrant, then their equation is
Assertion (A): The length of the latus rectum of an ellipse is 4. The focus and its corresponding directrix are respectively \( (1, -2) \) and the line \( 3x + 4y - 15 = 0 \). Then its eccentricity is \( \dfrac{1}{2} \). Reason (R): Length of the perpendicular drawn from focus of an ellipse to its corresponding directrix is \( \dfrac{a(1 - e^2)}{e} \)
Then which one of the following is correct?
If the locus of a point that divides a chord of slope 2 of the parabola \( y^2 = 4x \) internally in the ratio 1 : 2 is a parabola, then its vertex is
A hyperbola passes through the point \( P(\sqrt{2}, \sqrt{3}) \) and has foci at \( (\pm 2, 0) \). Then the point that lies on the tangent drawn to this hyperbola at \( P \) is
If the angle between the asymptotes of a hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) is \(2 \tan^{-1} \left(\frac{1}{3}\right)\) and \(a^2 - b^2 = 45\), then find \(ab\).
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 \( l+m+n= \):
The triangle formed by the lines \( 2x^2 + xy - 6y^2 = 0 \) and \( x+y-1=0 \) is:
The radius of the circle passing through the points of intersection of the circles \( x^2+y^2+2x+4y+1=0 \), \( x^2+y^2-2x-4y-4=0 \), and intersecting the circle \( x^2+y^2=6 \) orthogonally is:
If the slopes of both the lines given by \[ x^2 + 2hxy + 6y^2 = 0 \] are positive and the angle between these lines is \[ \tan^{-1} \left(\frac{1}{7}\right), \] then the product of the perpendiculars drawn from the point \((1,0)\) to the given pair of lines is:
If \( \beta \) is an angle between the normals drawn to the curve \( x^2+3y^2=9 \) at the points \( (3\cos\theta, \sqrt{3}\sin\theta) \) and \( (-3\sin\theta, \sqrt{3}\cos\theta) \), \( \theta \in \left(0, \frac{\pi}{2}\right) \), then
A line \(L_1\) passing through the point of intersection of the lines \(x-2y+3=0\) and \(2x-y=0\) is parallel to the Line \(L_2\). If \(L_2\) passes through origin and also through the point of intersection of the lines \(3x-y+2=0\) and \(x-3y-2=0\), then the distance between the lines \(L_1\) and \(L_2\) is
If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
The radius of a sphere is increased by 20%. What is the percentage increase in its volume?
A straight line passing through the origin \( O \) meets the parallel lines \( 4x + 2y = 9 \) and \( 2x + y + 6 = 0 \) at the points \( P \) and \( Q \) respectively. Then the point \( O \) divides the line segment \( PQ \) in the ratio
If Q \( (\alpha, \beta, \gamma) \) is the harmonic conjugate of the point P(0,-7,1) with respect to the line segment joining the points (2,-5,3) and (-1,-8,0), then \( \alpha - \beta + \gamma = \)