List of top Questions asked in TS EAMCET- 2026

Let a tangent \(L_1\) with slope \(m\) drawn to the parabola \[ y^2=8x \] be perpendicular to a normal \(L_2\) drawn to the parabola \[ y^2=12x. \] If \(m=1\) and the point of intersection of \(L_1\) and \(L_2\) is \((\alpha,\beta)\), then \(\alpha+\beta=\)

The length of the common chord of the circles \[ x^2+y^2-8x-6y-11=0 \] and \[ x^2+y^2-6x+8y+9=0 \] is

Let \(\dfrac32\) be the eccentricity of the conjugate hyperbola of a hyperbola \(H\) and one of the foci of \(H\) lie on the straight line \[ x+y-3=0. \] If the transverse and conjugate axes of \(H\) are along \(X\)-axis and \(Y\)-axis respectively, then the length of the latus rectum of \(H\) is

If the length of a focal chord drawn to the parabola \[ y^2=64x \] is \(289\) and the angle made by this focal chord with the positive \(X\)-axis measured in the positive direction is an acute angle, then the slope of the focal chord is

If the points \[ (\alpha,4,2),\ (6,\beta,-1)\ \text{and}\ (8,\beta-7) \] are collinear, then \(\alpha+\beta=\)

For the ellipse \[ \frac{x^2}{36}+\frac{y^2}{25}=1, \] the straight line \[ 2x+y-5=0 \] is

If the straight line \[ x+by+1=0 \] is a polar with respect to the circle \[ x^2+y^2-8x+10y-8=0, \] but not a tangent and not a chord, then all the values of \(b\) lie in the interval

If the equation of a transverse common tangent drawn to the circles \[ x^2+y^2-2x-10y+1=0 \] and \[ x^2+y^2+8x+14y+1=0 \] is \[ 5x+by+c=0, \] then \(b+c=\)

If the circles \[ x^2+y^2-10x+8y+5=0 \] and \[ x^2+y^2+6x-4y+c=0 \] cut each other orthogonally, then the sum of the radii of these circles is

The parametric equation of a circle passing through origin are given by \[ x=-g+5\cos\theta, \qquad y=-f+5\sin\theta. \] If the straight line passing through origin with slope \[ -\frac43 \] is the diameter of this circle, then the sum of the intercepts made by this circle on the coordinate axes is

If the length of the chord of the line \[ x+y-1=0 \] of the circle \[ x^2+y^2-6x+2fy-2=0\qquad(f>0) \] is \[ \frac{6\sqrt7}{\sqrt2}, \] then the length of the intercept made by this circle on the \(Y\)-axis is

If the pair of lines joining the origin to the points of intersection of the curve \[ 2x^2-5xy-3y^2-10x+27y-8=0 \] and the straight line \[ ax+y=1 \] are perpendicular to each other and \(a\) is not an integer, then \(a=\)

If the difference of mean and variance of a binomial distribution \(B(n,p)\) is \(\dfrac{4}{7}\) and their product is \(\dfrac{20}{7}\), then \(P(X=1)=\)

Two straight lines are drawn parallel to the straight line \[ L\equiv 5x-12y-13=0 \] which are at a distance of \(13\) units from the given line. Among these lines, if \[ ax+by+c=0 \] is the line which is closest to \[ L=0, \] then \[ \frac{a-2b+c}{a+b} = \]

If \[ x+y-2=0 \] and \[ 2x-y-1=0 \] represent two adjacent sides of a parallelogram and \[ x+4y-14=0 \] represents one of its diagonals, then one of the vertices of the parallelogram is

When axes are rotated through an angle \(\theta\) about the origin in the positive direction, if the equation \[ 3x^2+\sqrt{3}xy-5=0 \] is transformed to the form \[ ax'^2+by'^2=10, \] then \(ab=\)

If the point \(M\) is the foot of the perpendicular drawn from the point \(P(0,9)\) to the straight line \[ 2x-5y+16=0, \] and \(Q=(12,8)\), then the orthocentre of \(\triangle MPQ\) is

If the distance of a variable point \(P\) from a fixed point \((3,-4)\) is \(\dfrac23\) times the distance of \(P\) from the fixed line \(x-y+2=0\), then the locus of \(P\) is \[ ax^2+4by+by^2-62x+80y+c=0, \] then \(2c=\)

If the vectors \[ \vec a=4\hat{i}+6\hat{j}+\lambda\hat{k},\qquad \vec b=\hat{i}-2\hat{j}-3\hat{k}, \qquad \vec c=4\lambda\hat{i}+\hat{j}-3\hat{k} \] are coplanar and \(\lambda\in\mathbb{Z}\), then \(\vec a\cdot\vec c=\)

Three persons A, B and C planned to have a running race among themselves. If the probability that A wins the race is three times that of B and the probability that B wins the race is \(\dfrac32\) times that of C, then the difference in probabilities of A and C to win the race is

Two persons A and B are playing a game of rolling 2 dice alternately. The person who first gets the sum of the numbers appearing on the dice as a prime number will win the game. If A starts the game, then the probability of B winning the game is

A dealer bought a fixed number of laptops from 3 different companies A, B and C. Among these laptops, \(28\%\) are bought from A, \(32\%\) are bought from B and \(40\%\) are bought from C. \(2.5\%\) of laptops bought from A, \(1.5\%\) bought from B and \(1\%\) bought from C are likely to be defective. If a customer found that the laptop bought by him is defective, then the probability that it was from B is

If \(\vec a\) is a vector perpendicular to the plane containing the vectors \[ 2\hat i-\hat j+3\hat k \quad\text{and}\quad -\hat i+3\hat j+2\hat k, \] then the magnitude of the projection of the vector \[ 3\hat i+2\hat j-\hat k \] on \(\vec a\) is

If \[ \vec a=\hat i+p\hat j-3\hat k,\qquad \vec b=2\hat i-3\hat j+q\hat k,\qquad \vec c=\hat i+2\hat j+2\hat k\;(p0) \] are three vectors such that the magnitude of projection of \(\vec a\) on \(\vec c\) is \(3\) and the magnitude of projection of \(\vec b\) on \(\vec c\) is \(2\), then the magnitude of projection of \(\vec a\) on \(\vec b\) is

The straight line given by the equation \[ \vec r=(4\hat{i}+5\hat{j}+\hat{k})+s(4\hat{i}+6\hat{j}+2\hat{k}) \] is coplanar with the straight line given below. Choose the correct option.