List of top Mathematics Questions asked in AP EAPCET

The distance of the origin from the external centre of similitude for the circles \[ x^2 + y^2 - 8x - 10y - 8 = 0 \quad \text{and} \quad x^2 + y^2 + 2x - 2y - 2 = 0 \] is:
Let the circle \( S \) be concentric with the circle \( x^2 + y^2 - 2x + ky + 4 = 0 \). If one of the diameters of \( S \) lies along the line \( 3x - 2y + 4 = 0 \) and the length of the diameter is 6, then the radius of the circle \( S \) is
If \( 2x^2 - 3xy + y^2 = 0 \) represents two sides of a triangle and \( x + y - 1 = 0 \) is its third side, then the distance between the orthocenter and the circumcenter of that triangle is:
If \( S \) is the set of all real values of \( a \) such that a plane passing through the points \( (-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2) \) also passes through the point \( (-1, -1, 1) \), then \( S = \dots \)
The lines \( L_1: y - x = 0 \) and \( L_2: 2x + y = 0 \) intersect the line \( L_3: y + 2 = 0 \) at points \( P \) and \( Q \) respectively. The bisector of the acute angle between \( L_1 \) and \( L_2 \) intersects \( L_3 \) at \( R \). Statement-1: \( PR : RQ = 2\sqrt{2} : \sqrt{5} \) Statement-2: In any triangle, the bisector of an angle divides the triangle into two similar triangles.
The lines \( p(x^2 + 1) + x - y + q = 0 \) and \( (p^2 + 1)x^2 + (p^2 + 1)y + 2q = 0 \) are perpendicular to a line L. Then the equation of the line L is:
If the plane \( 56x + 4y + 9z = 2016 \) meets the coordinate axes in \( A, B \) and \( C \), then the centroid of the \( \triangle ABC \) is
Let the length of the latus rectum of an ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) be equal to the length of its semi-major axis. If the radius of its director circle is \( \sqrt{3} \) and \( e \) is its eccentricity, then the length of its latus rectum is:
If the length of the chord \( 2x + 3y + k = 0 \) of the circle \( x^2 + y^2 - 6x - 8y + 9 = 0 \) is \( 2\sqrt{5} \), then one of the values of \( k \) is
The locus of the point which is equidistant from the point \( (1, 1) \) and the line \( x + y + 1 = 0 \) is:
A point on the straight line \( 3x + 5y = 15 \) which is equidistant from the coordinate axes will lie in
If the tangent drawn at \( A(2, 1) \) to the curve \( x = 1 + \frac{1}{y^2} \) meets the curve again at \( B \), then
Let \( A(2, 3) \), \( B(3, -1) \), and \( C(-3, 2) \) be three points. If the centre of the circle passing through A, B, and C is \( (h, k) \), then \( 2k - 4 = \):
In $ \triangle ABC $, if $ r = 1 $, $ R = 4 $, and $ \Delta = 8 $, then \[ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \]
The locus of the poles of the tangents to the circle \( x^2 + y^2 - 2x + 2y - 2 = 0 \) with respect to the circle \( x^2 + y^2 = 4 \) is
Let \( [x] \) represent the greatest integer not more than \( x \). The discontinuous points of the function \[ f(x) = \frac{5 + [x]}{\sqrt{11 + [x]} - 6x + 2 + [x]} \] lie in the interval:
If \(\vec{r}\) is the position vector of the centroid \(G\) of triangle \(ABC\) and \[ 2\hat{i} + \hat{j} - \hat{k} \quad \text{and} \quad 2\hat{i} + 4\hat{j} - 4\hat{k} \] are respectively the position vectors of its vertices \(A\) and \(B\), then \[ AG^2 + BG^2 + CG^2 =\ ? \]
If \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \), then \( A^{-1} \) = ?
The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1, 2, and 6, then the other two observations are:
If a function $ f(x) $ defined on $ [a, b] $ is discontinuous at $ x = \alpha \in (a, b) $, then:
Let \( \vec{a}, \vec{b}, \vec{c} \) be any three non-coplanar vectors. If \( m, n \) are scalars such that \( \vec{a} + \vec{b} = m\vec{c} \) and \( \vec{b} + \vec{c} = n\vec{a} \), then \( 3\vec{a} + 2\vec{b} + 2\vec{c} = \):
The range of the expression: \[ \frac{1}{\sin^2x + 3\sin x \cos x + 5\cos^2x} \] is:
If the position vectors of the points \( A \) and \( B \) are \( 2i + 3j - k \) and \( i - j + 2k \) respectively, then the unit vector along \( \overrightarrow{BA} \) and in the direction of \( AB \) is:
If the roots of the equation \[ 6x^3 - 11x^2 + 6x - 1 = 0 \] are in harmonic progression, then the roots of \[ x^3 - 6x^2 + 11x - 6 = 0 \] will be in
In \( \triangle ABC \), if \( \frac{1}{r_1}, \frac{1}{r_2}, \frac{1}{r_3} \) are in arithmetic progression, then \( r_1 : r_2 : r_3 = \)?