List of top Questions asked in AP EAPCET- 2025

If the intercept of a line \(L\) made between the straight lines \(5x - y - 4 = 0\) and \(3x + 4y - 4 = 0\) is bisected at the point (1, 5), then the equation of \(L\) is
P and Q are the ends of a diameter of the circle \( x^2+y^2=a^2(a>\frac{1}{\sqrt{2}}) \). \( s \) and \( t \) are the lengths of the perpendiculars drawn from P and Q onto the line \( x+y=1 \) respectively. When the product \( st \) is maximum, the greater value among \( s, t \) is:
If the equation of the hyperbola having foci at \((8,3)\), \((0,3)\) and eccentricity \( \frac{4}{3} \) is \[ \frac{(x-\alpha)^2}{p} - \frac{(y-\beta)^2}{q} = 1, \] then find \( p + q \). Options:
If a tangent having slope \(\frac{1}{3}\) to the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a>b)\) is normal to the circle \((x+1)^2 + (y+1)^2 = 1\), then \(a^2\) lies in the interval?
If the power of the point \( (1,6) \) with respect to the circle \( x^2+y^2+4x-6y-a=0 \) is \( -16 \), then \( a \) is:
Let \( A_1 \) be the area of the given ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). Let \( A_2 \) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point P on the given ellipse, then \( A_1 : A_2 = \)
Consider the following functions
I) $f(x) = \left| \frac{1}{2 - x}, x<\frac{1}{2} \right|$
II) $f(x) = \left| \frac{1}{(2 - x)^2}, x \neq 2 \right|$
III) $f(x) = |x|$
IV) $f(x) = |x|$
Then on $[0, 1]$, Lagrange's mean value theorem is applicable to the functions Identify the correct option from the following:
The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
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 \((2, -1, 3)\) is the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to a plane then the equation of that plane is
If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
If the displacement \(S\) of a particle travelling along a straight line in \(t\) seconds is given by \[ S = 2t^3 + 2t^2 - 2t - 3, \] then the time taken (in seconds) by the particle to change its direction is?
If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are the tangents to the same circle, then the area of that circle (in sq. units) is
If the sum of the distances of the point (3, 4, 0), $\alpha \in \mathbb{R}$ from X-axis, Y-axis and Z-axis is minimum, then $\sec \alpha$ =
Identify the correct option from the following:
If the tangent to the curve \(xy + ax + by = 0\) at \((1,1)\) makes an angle \(\tan^{-1} 2\) with X-axis, then find \(\frac{ab}{a+b}\).
If tangents are drawn to the ellipse $x^2 + 2 y^2 = 2$, then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is:
Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) be such that \( x = 0 \) is the only real root of \( P'(x) = 0 \). If \( P(-1)<P(1) \), then in the interval \( [-1,1] \):
If the distance between the foci of a hyperbola H is 26 and distance between its directrices is \( \frac{50}{13} \), then the eccentricity of the conjugate hyperbola of the hyperbola H is
If the lengths of the tangent, subtangent, normal, and subnormal for the curve \( y = x^2 + x - 1 \) at the point \( (1,1) \) are \( a, b, c, \) and \( d \) respectively, then their increasing order is:
If the point of contact of the circles \( x^2+y^2-6x-4y+9=0 \) and \( x^2+y^2+2x+2y-7=0 \) is \( (\alpha, \beta) \), then \( 7\beta = \)
If the angles between the sides of triangle ABC formed by A(2,3,5), B(-1,2,3), and C(3,5,-2) are \(\alpha, \beta, \gamma\), then \(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma =\)
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 \( 4(\alpha+\beta) = \):
A circle passing through the point (1,0) makes an intercept of length 4 units on X-axis and an intercept of length \(2\sqrt{11}\) units on Y-axis. If the centre of the circle lies in the fourth quadrant, then the radius of the circle is
If \( A(2,-1,1) \), \( B(2,5,1) \) and \( C(0,-2,3) \) are the vertices of a triangle, and \( D \) is the point of intersection of the side \( BC \) and the internal angular bisector of angle \( A \), then \( AD = \):