List of top Mathematics Questions asked in TS EAMCET

The slope of a common tangent to the circles \( x^2 + y^2 - 4x - 8y + 16 = 0 \) and \( x^2 + y^2 - 6x - 16y + 64 = 0 \) is:
If \( A(1,2) \), \( B(2,1) \) are two vertices of an acute angled triangle and \( S(0,0) \) is its circumcenter, then the angle subtended by \( AB \) at the third vertex is
The line \( x + y + 1 = 0 \) intersects the circle \( x^2 + y^2 - 4x + 2y - 4 = 0 \) at the points A and B. If \( M(a, b) \) is the midpoint of AB, then \( a - b = \)?
(0, k) is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degree terms from the equation \( ax^2 - 2xy + by^2 - 2x + 4y + 1 = 0 \) and \( \frac{1}{2} \tan^{-1}(2) \) is the angle through which the coordinate axes are to be rotated about the origin to remove the \( xy \)-term from the given equation, then \( a + b = \):
The line \( 2x + y - 3 = 0 \) divides the line segment joining the points \( A(1,2) \) and \( B(2,-1) \) in the ratio \( a:b \) at the point \( C \). If the point \( C \) divides the line segment joining the points \( P\left( \frac{b}{3a}, -3 \right) \) and \( Q\left( -3, \frac{-b}{3a} \right) \) in the ratio \( p:q \), then \( \frac{p}{q} + \frac{q}{p} = \):
If the focal chord of the parabola \( x^2 = 12y \) drawn through the point \( (3, 0) \) intersects the parabola at the points P and Q, then the sum of the reciprocals of the abscissae of the points P and Q is:
The circles \(x^2 + y^2 + 2x - 6y - 6 = 0\) and \(x^2 + y^2 - 6x - 2y + k = 0\) are two intersecting circles and \(k\) is not an integer. If \( \theta \) is the angle between the two circles and \( \cos \theta = -\frac{5}{24} \), then find \( k \).
The slope of one of the pair of lines \(2x^2 + hxy + 6y^2 = 0\) is three times the slope of the other line, \(h = ?\)
Length of the common chord of the circles \(x^2 + y^2 - 6x + 5 = 0\) and \(x^2 + y^2 + 4y - 5 = 0\) is:
If \( A(1, -2), B(-2, 3), C(-1, -3) \) are the vertices of a triangle ABC. \( L_1 \) is the perpendicular drawn from \( A \) to \( BC \) and \( L_2 \) is the perpendicular bisector of \( AB \). If \( (l, m) \) is the point of intersection of \( L_1 \) and \( L_2 \), then \( 26m - 3 = \)
If the inverse point of the point \(P(3,3)\) with respect to the circle \(x^2 + y^2 - 4x + 4y + 4 = 0\) is \(Q(a,b)\), then \(a + 5b =\)
If \( x - 2y - 6 = 0 \) is a normal to the circle \( x^2 + y^2 + 2gx + 2fy - 8 = 0 \) and the line \( y = 2 \) touches this circle, then the radius of the circle can be:
If the ratio of the perpendicular distances of a variable point \( P(x,y,z) \) from the X-axis and from the YZ-plane is 2:3, then the equation of the locus of \( P \) is:
If \( \beta \) is the angle made by the perpendicular drawn from origin to the line \( L = x + y - 2 = 0 \) with the positive X-axis in the anticlockwise direction. If \( a \) is the X-intercept of the line \( L = 0 \) and \( p \) is the perpendicular distance from the origin to the line \( L = 0 \), then \( \tan \beta + p^2 = \):
If the ratio of the distances of a variable point \(P\) from the point \((1,1)\) and the line \(x - y + 2 = 0\) is \(1/\sqrt{2}\), then the equation of the locus of \(P\) is:
(-2, -1), (2,5) are two vertices of a triangle and \( \left(2, \frac{5}{3} \right) \) is its orthocenter. If \( (m, n) \) is the third vertex of that triangle, then \( m+n = \):
If the direction ratios of two lines are \( (3,0,2) \) and \( (0,2,k) \), and \( \theta \) is the angle between them, and if \( |\cos \theta| = \frac{6}{13} \), then \( k = \)
If the angle between the pair of lines given by the equation \(ax^2 + 4xy + 2y^2 = 0\) is \(45^\circ\), then the possible values of 'a' are
If \( (2, -1) \) is the point of intersection of the pair of lines \[ 2x^2 + axy + 3y^2 + bx + cy - 3 = 0 \quad \text{then} \quad 3a + 2b + c = \]
The lengths of two equal sides of an isosceles triangle are given by \(L_1 = 2x + y - 3 = 0\) and \(L_2 = ax + by + c = 0\). If \(L_3 = x + 2y + 1 = 0\) is the third side of this triangle and \((5, 1)\) is a point on \(L_2\), then \(b^2/|ac|\) is:
The direction cosines of two lines are connected by the relations \[ l - m + n = 0, \quad 2lm - 3mn + nl = 0. \] If \( \theta \) is the angle between these two lines, then \( \cos \theta \) is:
The slope of a line L passing through the point \((-2, -3)\) is not defined. If the angle between the lines L and \( ax - 2y + 3 = 0 \) (where \( a>0 \)) is 45°, then the angle made by the line \( x + ay - 4 = 0 \) with positive X-axis in the anticlockwise direction is:
When the origin is shifted to the point \( (2,b) \) by translation of axes, the coordinates of the point \( (4,4) \) have changed to \( (6,8) \). When the origin is shifted to \( (a,b) \) by translation of axes, if the transformed equation of \( x^2 + 4xy + y^2 = 0 \) is \( X^2 + 2HXY + Y^2 + 2GX + 2FY + C = 0 \), then \( 2H(G + F) = \) ?
If \(A(-2,4,a)\), \(B(1,3,b)\), \(C(0,4,c)\), and \(D(-5,6,1)\) are collinear points, then \(a+b+c=\)
The pole of the line \(x - 5y - 7 = 0\) with respect to the circle \(S \equiv x^2 + y^2 - 2x - 2y + 1 = 0\) is \(P(a,b)\). If \(C\) is the centre of the circle \(S = 0\) then \(PC =\):