List of top Questions asked in TS EAMCET

The circumcenter of the equilateral triangle having the three points $\theta_1, \theta_2, \theta_3$ lying on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ as its vertices is $(r,s)$. Then the average of $\cos(\theta_1-\theta_2), \cos(\theta_2-\theta_3)$ and $\cos(\theta_3-\theta_1)$ is

The normal at a point on the parabola $y^2=4x$ passes through a point P. Two more normals to this parabola also pass through P. If the centroid of the triangle formed by the feet of these three normals is G(2,0), then the abscissa of P is

If the angle between the tangents drawn to the parabola $y^2=4x$ from the points on the line $4x-y=0$ is $\frac{\pi}{3}$, then the sum of the abscissae of all such points is

If a tangent to the circle $x^2+y^2+2x+2y+1=0$ is radical axis of the circles $x^2+y^2+2gx+2fy+c=0$ and $2x^2+2y^2+3x+8y+2c=0$, then

If the circle $S=0$ intersect the three circles $S_1 = x^2+y^2+4x-7=0$, $S_2 = x^2+y^2+y=0$ and $S_3 = x^2+y^2+\frac{3}{2}x+\frac{5}{2}y-\frac{9}{2}=0$ orthogonally, then the radical axis of $S=0$ and $S_1=0$ is

If $P(\frac{7}{5}, \frac{6}{5})$ is the inverse point of $A(1,2)$ with respect to a circle with centre $C(2,0)$, then the radius of that circle is

The equation of the circle which touches the circle $S \equiv x^2+y^2-10x-4y+19=0$ at the point (2,3) internally and having radius equal to half of the radius of the circle S=0 is

The radius of the circle having three chords along y-axis, the line $y=x$ and the line $2x+3y=10$ is

If the equations $3x^2+2hxy-3y^2=0$ and $3x^2+2hxy-3y^2+2x-4y+c=0$ represent the four sides of a square, then $\frac{h}{c}= $

Two non parallel sides of a rhombus are parallel to the lines $x+y-1=0$ and $7x-y-5=0$. If (1,3) is the centre of the rhombus and one of its vertices $A(\alpha, \beta)$ lies on $15x-5y=6$, then one of the possible values of $(\alpha+\beta)$ is

Two families of lines are given by $ax+by+c=0$ and $4a^2+9b^2-c^2-12ab=0$. Then the line common to both the families is

$y-x=0$ is the equation of a side of a triangle ABC. The orthocentre and circumcentre of the triangle ABC are respectively (5,8) and (2,3). The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle is

When the coordinate axes are rotated about the origin through an angle $\frac{\pi}{4}$ in the positive direction, the equation $ax^2+2hxy+by^2=c$ is transformed to $25x'^2+9y'^2=225$, then $(a+2h+b-\sqrt{c})^2=$

A(2,0), B(0,2), C(-2,0) are three points. Let a, b, c be the perpendicular distances from a variable point P on to the lines AB, BC and CA respectively. If a, b, c are in arithmetic progression, then the locus of P is

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three times by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is

A and B are two events of a random experiment such that $P(B)=0.4$, $P(A \cap \bar{B}) = 0.5$, $P(A \cup B) + P(A|B) = 1.15$, then $P(A)=$

Functions are formed from the set $A = \{a_1, a_2, a_3\}$ to another set $B = \{b_1, b_2, b_3, b_4, b_5\}$. If a function is selected at random, the probability that it is a one-one function is

The mean deviation about median of the numbers $3x, 6x, 9x, ..., 81x$ is 91, then $|x|=$

Consider the following
Assertion (A): The two lines $\vec{r} = \vec{a}+t(\vec{b})$ and $\vec{r}=\vec{b}+s(\vec{a})$ intersect each other.
Reason (R): The shortest distance between the lines $\vec{r}=\vec{p}+t(\vec{q})$ and $\vec{r}=\vec{c}+s(\vec{d})$ is equal to the length of projection of the vector $(\vec{p}-\vec{c})$ on $(\vec{q}\times\vec{d})$.
The correct answer is

$\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar and mutually perpendicular vectors of same magnitude K. $\vec{r}$ is any vector satisfying $\vec{a}\times((\vec{r}-\vec{b})\times\vec{a}) + \vec{b}\times((\vec{r}-\vec{c})\times\vec{b}) + \vec{c}\times((\vec{r}-\vec{a})\times\vec{c}) = \vec{0}$, then $\vec{r} =$

In a quadrilateral ABCD, $\angle A = \frac{2\pi}{3}$ and AC is the bisector of angle A. If $15|AC| = 5|AD| = 3|AB|$, then the angle between $\vec{AB}$ and $\vec{BC}$ is

Two adjacent sides of a triangle are represented by the vectors $2\vec{i}+\vec{j}-2\vec{k}$ and $2\sqrt{3}\vec{i}-2\sqrt{3}\vec{j}+\sqrt{3}\vec{k}$. Then the least angle of the triangle and perimeter of the triangle are respectively

In a triangle ABC, $a=5, b=4$ and $\tan\frac{C}{2} = \sqrt{\frac{7}{9}}$, then its inradius r =

If the angular bisector of the angle A of the triangle ABC meets its circumcircle at E and the opposite side BC at D, then $DE\cos\frac{A}{2} =$

Consider the following statements
Statement-I: $\cosh^{-1}x = \tanh^{-1}x$ has no solution
Statement-II: $\cosh^{-1}x = \coth^{-1}x$ has only one solution
The correct answer is