List of top Questions asked in TS EAMCET

A circle C passing through the point (1,1) bisects the circumference of the circle \( x^2+y^2-2x=0 \). If C is orthogonal to the circle \( x^2+y^2+2y-3=0 \) then the centre of the circle C is

If A, B are the points of contact of the tangents drawn from the point (-3,1) to the circle \( x^2+y^2-4x+2y-4=0 \), then the equation of the circumcircle of the triangle PAB is

If \( x-2y=0 \) is a tangent drawn at a point P on the circle \( x^2+y^2-6x+2y+c=0 \), then the distance of the point (6,3) from P is

If the equation of the circle passing through the points (-1,0), (-1,1), (1,1) is \( ax^2+ay^2+2gx+2fy-2=0 \) then \( a = \)

If \( 4x^2+12xy+9y^2+2gx+2fy-1=0 \) represent a pair of parallel lines then

If a line L passing through a point A(2,3) intersects another line \( 4x-3y-19=0 \) at the point B such that \( AB=4 \), then the angle made by the line L with positive X-axis in anti-clockwise direction is

If \( (h,k) \) is the new origin to be chosen to eliminate first degree terms from the equation \( S = 2x^2 - xy - y^2 - 3x + 3y = 0 \) by translation and if \( \theta \) is the angle with which the axes are to be rotated about the origin in anticlockwise direction to eliminate xy-term from \( S = 0 \), then \( \tan 2\theta = \)

If the points A(2,3), B(3,2) form a triangle with a variable point \( p(t, t^2) \), where t is a parameter, then the equation of the locus of the centroid of triangle ABC is

If three dice are thrown, then the mean of the sum of the numbers appearing on them is

Urn A contains 6 white and 2 black balls; urn B contains 5 white and 3 black balls and urn C contains 4 white and 4 black balls. If an urn is chosen at random and a ball is drawn at random from it, then the probability that the ball drawn is white is

If three cards are drawn randomly from a pack of 52 playing cards then the probability of getting exactly one spade card, exactly one king and exactly one card having a prime number is

If three smallest squares are chosen at random on a chess board then the probability of getting them in such a way that they are all together in a row or in a column is

If \( \bar{a} \) and \( \bar{b} \) are two vectors such that \( |\bar{a}|=5 \), \( |\bar{b}|=12 \) and \( |\bar{a}-\bar{b}|=13 \) then \( |2\bar{a}+\bar{b}| = \)

The point of intersection of the line joining the points \( \bar{i} + 2\bar{j} + \bar{k} \), \( 2\bar{i} - \bar{j} - \bar{k} \) and the plane passing through the points \( \bar{i}, 2\bar{j}, 3\bar{k} \) is

The position vectors of two points A and B are \( \bar{i} + 2\bar{j} + 3\bar{k} \) and \( 7\bar{i} - \bar{k} \) respectively. The point P with position vector \( -2\bar{i} + 3\bar{j} + 5\bar{k} \) is on the line AB. If the point Q is the harmonic conjugate of P, then the sum of the scalar components of the position vector of Q is

Let the angles A, B, C of a triangle ABC be in arithmetic progression. If the exradii \( r_1, r_2, r_3 \) of triangle ABC satisfy the condition \( r_3^2 = r_1 r_2 + r_2 r_3 + r_3 r_1 \), then \( b = \)

If \( 2\tanh^{-1}x = \sinh^{-1}\left(\frac{4}{3}\right) \) then \( \cosh^{-1}\left(\frac{1}{x}\right) = \)

The general solution of the equation \( \sqrt{6 - 5\cos x + 7\sin^2 x} - \cos x = 0 \) also satisfies the equation

If \( A+B+C = 4S \) then \( \sin(2S-A) + \sin(2S-B) + \sin(2S-C) - \sin 2S = \)

The period of the function \( f(x) = \frac{2\sin\left(\frac{\pi x}{3}\right) \cos\left(\frac{2\pi x}{5}\right)}{3\tan\left(\frac{7\pi x}{2}\right) - 5\sec\left(\frac{5\pi x}{3}\right)} \) is

If \( \frac{x^3+3}{(x-3)^3} = a + \frac{b}{x-3} + \frac{c}{(x-3)^2} + \frac{d}{(x-3)^3} \), then \( (a+d)-(b+c) = \)

If the expression \( 5^{2n} - 48n + k \) is divisible by 24 for all \( n \in \mathbb{N} \), then the least positive integral value of k is

If the coefficient of \(3^{\text{rd}}\) term from the beginning in the expansion of \( \left(ax^2 - \frac{8}{bx}\right)^9 \) is equal to the coefficient of \(3^{\text{rd}}\) term from the end in the expansion of \( \left(ax - \frac{2}{bx^2}\right)^9 \) then the relation between \( a \) and \( b \) is

If all the letters of the word 'HANDLE' are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word 'HELAND' is

Number of triangles whose vertices are the points \( (x, y) \) in the XY-plane with integer coordinates satisfying \( 0 \le x \le 4 \) and \( 0 \le y \le 4 \) is