List of top Questions asked in TS EAMCET- 2026

The foci of the ellipse \[ \frac{x^2}{25}+\frac{y^2}{16}=1 \] and that of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] are same. The greatest length of the transverse axis of the hyperbola such that the difference of the squares of their eccentricities is at least one is

The radical axis of the circles \[ x^2+y^2+4x+6y+7=0 \] and \[ 4x^2+4y^2+8x+12y-24=0 \] is a tangent to the circle \[ x^2+y^2=13 \] at a point \((\alpha,\beta)\), then \(\alpha+\beta=\)

If the locus of midpoints of the chords of the circle \[ S\equiv x^2+y^2-6x-8y-11=0 \] which subtend a right angle at \(A(1,2)\) is another circle \(S'=0\), then the centre of \(S'=0\)

If the latus rectum of the ellipse \[ \frac{x^2}{16}+\frac{y^2}{b^2}=1 \] subtends an angle \[ \frac{\pi}{3} \] at the centre of the ellipse, then \(b^2=\)

Let \(L=0\) be the chord of contact of \((5,1)\) with respect to the circle \[ S\equiv x^2+y^2+8x+10y-8=0. \] If the pole of \(L=0\) with respect to the circle \[ S'\equiv x^2+y^2+4y-21=0 \] is \((-k,-h)\), then \(k+h=\)

Let \[ S\equiv x^2+y^2-6x+4y+c=0,\qquad S'\equiv x^2+y^2-4x+6y+9=0, \] \[ S''\equiv x^2+y^2+5x+3y+k=0 \] be three circles. If the angles of intersection of the circle \(S'=0\) with the circles \(S=0\) and \(S''=0\) are respectively \[ \frac{\pi}{4} \quad\text{and}\quad \frac{\pi}{2}, \] then \(c+k=\)

If a normal drawn at the point \(t=1\) on the parabola \[ x^2+4y+2x-8=0 \] intersects the parabola again at a point \(A(\alpha,\beta)\), then \(4\alpha\beta=\)

If \[ P\equiv y^2+2y-x+6=0 \] is a parabola. \(S=0\) is another parabola such that the axes of \(S=0\) and \(P=0\) are same and the distance between their foci is \[ \frac54. \] If the foci of these parabolas are on either side of the vertex of \(S=0\) and the vertex of \(S=0\) is on the directrix of \(P=0\), then the length of latus rectum of \(S=0\) is

If the equation of the line joining the points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \[ ax+by=c \] and the distance between \(A\) and \(B\) is \(\sqrt{a^2+b^2}\), then \(c^2=\)

The locus of midpoints of the chords of the circle \[ x^2+y^2-2x-2y+1=0 \] which are parallel to the line \[ x+y+2=0 \] is

The line common to the two families of concurrent lines \[ x+y+\lambda(4x+3y-1)=0 \] and \[ 2x-3y+k(x+y-5)=0 \] is along the base of a triangle. If \((1,1)\) is the vertex of the triangle, then the perpendicular distance from that vertex to its base is

Two diagonal sides of a parallelogram \(ABCD\) are \[ x-y+1=0 \] and \[ 3x-y=9. \] If one of its diagonals is \[ 7x-5y+3=0, \] then the equation of the other diagonal is

Equation of the image of the pair of lines \[ ax^2+2hxy+by^2=0 \] with respect to \(y=0\) is

The locus of the centre of a circle touching the lines \[ x+2y=0 \] and \[ x-2y=0 \] is

Which of the following is not the correct data of a binomial distribution?

Let \(E\) and \(F\) be two events such that \[ P(\bar E)=\frac13,\qquad P(E\cap F)=\frac13,\qquad P(\overline{E\cup F})=\frac16. \] Which of the following is correct?

Let \(X\) be a discrete random variable. If \[ P(X=r)=\frac{3}{7}a^r,\qquad r=0,1,2,\ldots,\infty,\quad 0<a<1, \] then \(aP(X=2)=\)

The transformed equation of \[ 4x^2-4xy+7y^2-24=0 \] in the new coordinate system when the axes are rotated through an angle \(\theta\) about the origin in the positive direction is \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1. \] If \[ 0<\theta<\frac{\pi}{4}, \] then \[ 1+b^2\sin^2\theta= \]

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spade cards. The probability that the missing card is not a spade is

Let \(A(a,0)\) be a point on the \(X\)-axis. The locus of the midpoints of the line segments joining \(A\) and any point \(P\) on the parabola \[ y=16-x^2 \] is

If \[ \vec r=2\hat i-\hat j+2\hat k,\qquad \vec s=3\hat i-3\hat j+3\hat k,\qquad \vec t=\hat i+2\hat j+\hat k \] are three vectors and \(\vec a\) is a vector such that \[ \vec s\times\vec a=\vec r\times\vec a \] and \[ \left|\vec t\times\vec a\right|=\sqrt{128}, \] then \(|\vec t-\vec a|=\)

If \[ \vec r=\vec a+t\vec b \quad\text{and}\quad \vec r=\vec p+l\vec b \] are two lines, where \[ \vec a=\hat i+2\hat j,\qquad \vec b=\hat i+\hat j+\hat k,\qquad \vec p=2\hat i+\hat k. \] The position vector of a point \(A\) is \[ 5\hat i+\hat j-3\hat k. \] Let \(B,C\) be the feet of the perpendiculars drawn from \(A\) to the given two lines respectively, then \[ \overrightarrow{BA}+\overrightarrow{AC}= \]

Mean and variance of an ungrouped data of 15 numbers are \(12\) and \(14\) respectively. For another ungrouped data of 15 numbers the mean and variance are \(14\) and \(10\) respectively. If the two data are combined, then the variance of the combined data of 30 numbers is

If \(\alpha,\beta,\gamma\;(\alpha>\beta>\gamma)\) are roots of the equation \[ x^3-x^2-4x+4=0, \] the volume of the parallelepiped whose coterminous edges are \[ \alpha\hat i+\beta\hat j+\gamma\hat k,\; \beta\hat i+\gamma\hat j+\alpha\hat k,\; \gamma\hat i+\alpha\hat j+\beta\hat k \] is

Let \[ A=\{1,2,3,4,\ldots,20\}. \] If three distinct elements are drawn from the set \(A\) at random, then the probability that the three numbers drawn are in increasing G.P. with common ratio as a non integral rational value is