List of top Mathematics Questions asked in TS EAMCET

The area of the triangle formed by the line L with the coordinate axes is 12 sq. units. If L passes through the point (12,4) and the product P of X-intercept of L and square of the Y-intercept of L is negative, then P =
Two families of lines are given by $ax+by+c=0$ and $4a^2+9b^2-c^2-12ab=0$. Then the line common to both the families is
The equation of the circle which touches the circle $S \equiv x^2+y^2-10x-4y+19=0$ at the point (2,3) internally and having radius equal to half of the radius of the circle S=0 is
A line L perpendicular to the line \( 5x-12y+6=0 \) makes positive intercept on the Y-axis. If the distance from the origin to the line L is 2 units and the angle made by the perpendicular drawn from the origin to the line L with positive X-axis is \( \theta \), then \( \tan \theta + \cot \theta = \)
Every point on the curve \(3x + 2y - 3xy = 0\) is the centroid of a triangle formed by the coordinate axes and a line (L) intersecting both the coordinate axes. Then all such lines (L)
The value of 'a' for which the equation \((a^2-3)x^2 + 16xy - 2ay^2 + 4x - 8y - 2 = 0\) represents a pair of perpendicular lines is
O(0,0,0), A(3,1,4), B(1,3,2) and C(0,4,-2) are the vertices of a tetrahedron. If G is the centroid of the tetrahedron and \(G_1\) is the centroid of its face ABC, then the point which divides \(GG_1\) in the ratio 1:2 is
If the points \((1, 1, \lambda)\) and \((-3, 0, 1)\) are equidistant from the plane \(3x + 4y - 12z + 13 = 0\), then the values of \(\lambda\) are
If (-1,-1) is the point of intersection of the pair of lines \(2x^2+5xy-3y^2+2gx+2fy+c=0\) then g+f=
If $(\alpha,\beta)$ is the centre of the circle which passes through the point (1,-1) and cuts the circles $x^2 + y^2+2x-3y-5=0$, $x^2+y^2-3x+2y+1=0$ orthogonally, then $\alpha-5\beta =$
A circle C touches the X-axis and makes an intercept of length 2 units on the Y-axis. If the centre of this circle lies on the line $y=x+1$, then a circle passing through the centre of the circle C is
If the equation of the circumcircle of the triangle formed by the lines $L_1=x+y=0$, $L_2=2x+y-1=0$, $L_3=x-3y+2=0$ is $\lambda_1 L_2 L_3 + \lambda_2 L_3 L_1 + \lambda_3 L_1 L_2 = 0$, then $\frac{7\lambda_1+\lambda_3}{\lambda_2} =$
$y-x=0$ is the equation of a side of a triangle ABC. The orthocentre and circumcentre of the triangle ABC are respectively (5,8) and (2,3). The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle is
The curve represented by \(\frac{x^2}{12-\alpha} + \frac{y^2}{\alpha-10} = 1\) is
If A = (0,1), B = (1,2), C = (-2,1) then the equation of the locus of a point P such that area of triangle PAB = area of triangle PAC is
If the latus rectum through one of the foci of a hyperbola \( \frac{x^2}{9} - \frac{y^2}{b^2} = 1 \) subtends a right angle at the farther vertex of the hyperbola, then \(b^2 = \)
Two non parallel sides of a rhombus are parallel to the lines $x+y-1=0$ and $7x-y-5=0$. If (1,3) is the centre of the rhombus and one of its vertices $A(\alpha, \beta)$ lies on $15x-5y=6$, then one of the possible values of $(\alpha+\beta)$ is
A straight line through the point P(1,2) makes an angle $\theta$ with the positive X-axis in anti-clockwise direction and meets the line $x+\sqrt{3}y-2\sqrt{3}=0$ at Q. If $PQ = \frac{1}{2}$, then $\theta=$
If the circle $S=0$ intersect the three circles $S_1 = x^2+y^2+4x-7=0$, $S_2 = x^2+y^2+y=0$ and $S_3 = x^2+y^2+\frac{3}{2}x+\frac{5}{2}y-\frac{9}{2}=0$ orthogonally, then the radical axis of $S=0$ and $S_1=0$ is
If $2x^2+xy-6y^2+k=0$ is the transformed equation of $2x^2+xy-6y^2-13x+9y+15=0$ when the origin is shifted to the point $(a,b)$ by translation of axes, then k =
If $P(\frac{7}{5}, \frac{6}{5})$ is the inverse point of $A(1,2)$ with respect to a circle with centre $C(2,0)$, then the radius of that circle is
If any tangent drawn to the ellipse \(\frac{x^2}{16} + \frac{y^2}{9} = 1\) touches one of the circles \(x^2 + y^2 = \alpha^2\), then the range of \(\alpha\) is
If $\text{Tan}^{-1}(2\sqrt{10})$ is the angle between the lines $ax^2+4xy-2y^2=0$ and $a \in \mathbb{Z}$, then the product of the slopes of given lines is
If a tangent to the circle $x^2+y^2+2x+2y+1=0$ is radical axis of the circles $x^2+y^2+2gx+2fy+c=0$ and $2x^2+2y^2+3x+8y+2c=0$, then
If S and S' are the foci of an ellipse \( \frac{x^2}{169} + \frac{y^2}{144} = 1 \) and the point B lying on positive Y-axis is one end of its minor axis, then the incentre of the triangle SBS' is