List of top Mathematics Questions asked in AP EAPCET

Let the curve \(x^2 + 2y^2 = 2\) intersect the line \(x + y = 1\) at two points \(P\) and \(Q\) and \(O\) be the origin. If \(\theta\) is the acute angle between the lines \(OP\) and \(OQ\), then \(\tan \theta =\)
If \( (a^2 - 1)x + ay + (3 - a) = 0 \) is a normal to the curve \( xy = 1 \), then the interval in which ‘a’ lies is:
If $x+y-1=0$ and $2x - y + 1=0$ are conjugate lines with respect to the circle $x^2 + y^2 - 4x + 2fy - 1 = 0$, then $f=$
Let X-axis be the transverse axis and Y-axis be the conjugate axis of a hyperbola H. Let \( x^2 + y^2 = 16 \) be the director circle of H. If the perpendicular distance from the centre of H to its latus rectum is \( \sqrt{34} \), then \( a + b = \):
Two sides of a rhombus are along the lines \( x - y + 1 = 0 \) and \( 7x - y - 5 = 0 \). If its diagonals intersect at \( (-1, -2) \), then one of the vertices of this rhombus is:
In \( \triangle ABC \), the coordinates of the vertices are \( A(1,8,4) \), \( B(0,-11,4) \), and \( C(2,-3,1) \). If \( D \) is the foot of the perpendicular drawn from \( A \) to \( BC \), then the coordinates of \( D \) are:
If the chord through $(1,-2)$ cuts the curve $3x^2 - y^2 - 2x + 4y = 0$ at P and Q, then the angle subtended by PQ at the origin is
The line $3x+y-5=0$ touches a circle S at $(1,2)$. If $(h,k)$ is the ntre of the circle S such that $h^2+hk+k^2=37$ and radius is $\sqrt{10}$, then $k=$
The product of the slopes of the common tangents drawn to the circles $x^2+y^2+2x-2y-2=0$ and $x^2+y^2-2x+2y+1=0$ is
The number of straight lines that can be drawn through the point $ (-3, 4) $, which are at a distance of 5 units from the point $ (2, -8) $, is:
If a circle \(S\) passing through the points \(A(1, 2)\) and \(B(2, 1)\) has its centre \(C\) located in the third quadrant at a distance of \(\frac{7}{\sqrt{2}}\) units from \(AB\), then the point \(P(1, -2)\)
Tangent \( L_1 = 3x - 4y - 8 = 0 \) and the chord \( L_2 = x + y - 1 = 0 \) are at a distance of 2 and \( \sqrt{2} \) units respectively from the centre of a circle \( S \). \((h, k)\) is the centre of \( S \) such that \( h^2 + k^2 = 13 \). If the midpoint of the chord \( L_2 = 0 \) is \( (\alpha, \beta) \) and the radius of the circle is \( r \), then \( \alpha + \beta + r = \):
The distance between two parallel planes \( ax + by + cz + d_1 = 0 \) and \( ax + by + cz + d_2 = 0 \) is given by \( \frac{|d_1 - d_2|}{\sqrt{a^2 + b^2 + c^2}} \). If the plane \( 2x - y + 2z + 3 = 0 \) has the distances \( \frac{1}{3} \) units from the planes \( 4x - 2y + 4z + \lambda = 0 \) and \( 2x - y + 2z + \mu = 0 \) respectively, then the maximum value of \( \lambda + \mu \) is:
The equation of the line, passing through the point $(a\cos^3\theta, a\sin^3\theta)$ and perpendicular to the line $x\sec\theta - y\csc\theta = a$, is
Let $ PQR $ be a right-angled isosceles triangle, right-angled at $ P(2,1) $. If the equation of the side $ QR $ is $ 2x + y = 3 $, then the equation of one of its sides other than $ QR $ is:
The equal sides of an isosceles triangle are given by equations \( 7x - y + 3 = 0 \) and \( x + y - 3 = 0 \). If the slope \( m \) of the third side is an integer, then \( m = \):
The length of the chord of contact from point $(2,1)$ to the circle $x^2+y^2+4x+2y+1=0$ is
If the inverse point of the point $ (3, 2) $ with respect to the circle $ x^2 + y^2 - 2x + 4y - 4 = 0 $ is $ (l, m) $, then $ 2l + 19m = $:
If the focal chord drawn through the point $ P(5, 5) $ to the parabola $ y^2 = 5x $ meets the parabola again at the point $ Q $, then the tangent drawn to this parabola at $ Q $ meets the axis of the parabola at the point:
If \( A(2, 3, 5), B(\alpha, 3, 3), C(7, 5, \beta) \) are the vertices of a triangle. If the median through \( A \) is equally inclined with the coordinate axes, then \( \frac{\beta}{\alpha} = \):
If \( PS \) is the median of the triangle with vertices \( P(2, 2) \), \( Q(6, -1) \), and \( R(7, 3) \), then the equation of the line passing through \( (1, -1) \) and parallel to \( PS \) is:
If a focal chord of the ellipse \(\frac{x^2}{25} + \frac{y^2}{16} = 1\) meets its minor axis at the point \((0, 3)\), then the perpendicular distance from the centre of the ellipse to this focal chord is:
If the equation of the circle of radius 3 units which touches the circle \( x^2 + y^2 + 6x - 8y - 11 = 0 \) externally at (3, 0) is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then \( 3g - 4f + c = \):
Let $ M \left( \frac{-7}{2}, \frac{-5}{2} \right) $ be the midpoint of the chord $ AB $ of the circle. The equation of the circle is $ x^2 + y^2 + 10x + 8y - 23 = 0 $. If $ ax + by + 1 = 0 $ is the equation of $ AB $, then $ 3a + 3b = $:
If \( f(x) = \begin{cases} ax^2 - bx + 2, & x<3 \\ bx - 3, & x \geq 3 \end{cases} \) is differentiable at every \( x \in \mathbb{R} \), then the area (in sq units) of the triangle formed by the line \(\frac{x}{a} + \frac{y}{b} = 1\) with the coordinate axes is: