List of top Mathematics Questions asked in TS EAMCET

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 \( 2H(G + F) = \) ?
Area of the triangle bounded by the lines given by the equations: \[ 12x^2 - 20xy + 7y^2 = 0 \quad \text{and} \quad x + y - 1 = 0 \]
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:
(-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 distance from a variable point \( P \) to the point \( (4,3) \) is equal to the perpendicular distance from \( P \) to the line \( x + 2y - 1 = 0 \), then the equation of the locus of the point \( P \) is:
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 \( \frac{p}{q} + \frac{q}{p} = \):
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:
The area of the parallelogram formed by the lines \( L_1: \lambda x + 4y + 2 = 0 \), \( L_2: 3x + 4y - 3 = 0 \), \( L_3: 2x + \mu y + 6 = 0 \), and \( L_4: 2x + y + 3 = 0 \), where \( L_1 \) is parallel to \( L_2 \) and \( L_3 \) is parallel to \( L_4 \), is
A, B, C are the vertices of a triangle ABC. If the bisector of \( \angle BAC \) intersects the side BC at D\((p,q,r)\), then \( \sqrt{2p+q+r} = ? \)
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:
P and Q are the points of trisection of the line segment joining the points \( (3, -7) \) and \( (-5,3) \). If line PQ subtends a right angle at a variable point R, then the locus of R 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
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:
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 \(PC =\):
If \( (4,3) \) and \( (1,-2) \) are the endpoints of a diagonal of a square, then the equation of one of its sides is:
If the equation of the transverse common tangent of the circles \(x^2 + y^2 - 4x + 6y + 4 = 0\) and \(x^2 + y^2 + 2x - 2y - 2 = 0\) is \(ax + by + c = 0\), then \(\frac{a}{c} =\)
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
A circle passing through the points \( (1, 1) \) and \( (2, 0) \) touches the line \( 3x - y - 1 = 0 \). If the equation of this circle is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then a possible value of \( g \) is
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 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 equation of the pair of transverse common tangents drawn to the circles \( x^2 + y^2 + 2x + 2y + 1 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is:
P and Q are the extremities of a focal chord of the parabola \( y^2 = 4ax \). If \( P = (9,9) \) and \( Q = (p, q) \), then \( p - q \) is:
(a,b) is the point of concurrency of the lines \(x-3y+3=0\), \(Kx+y+k=0\) and \(2x+y-8=0\). If the perpendicular distance from the origin to the line \(L: ax-by+2k=0\) is \(p\), then the perpendicular distance from the point \((2,3)\) to \(L=0\) is:
If the line \( 4x - 3y + p = 0 \) (where \( p + 3>0 \)) touches the circle \( x^2 + y^2 - 4x + 6y + 4 = 0 \) at the point \( (h,k) \), then the value of \( h - 2k \) is:
A(1, -2, 1) and B(2, -1, 2) are the end points of a line segment. If \(D(\alpha, \beta, \gamma)\) is the foot of the perpendicular drawn from \(C(1, 2, 3)\) to AB, then \(\alpha^2 + \beta^2 + \gamma^2 =\)