List of top Mathematics Questions asked in TS EAMCET

If the equation of the circumcircle of the triangle formed by the lines $L_1=x+y=0$, $L_2=2x+y-1=0$, $L_3=x-3y+2=0$ is $\lambda_1 L_2 L_3 + \lambda_2 L_3 L_1 + \lambda_3 L_1 L_2 = 0$, then $\frac{7\lambda_1+\lambda_3}{\lambda_2} =$

The lines $x-2y+1=0$, $2x-3y-1=0$ and $3x-y+k=0$ are concurrent. The angle between the lines $3x-y+k=0$ and $mx-3y+6=0$ is $45^\circ$. If m is an integer, then $m-k=$

If $\text{Tan}^{-1}(2\sqrt{10})$ is the angle between the lines $ax^2+4xy-2y^2=0$ and $a \in \mathbb{Z}$, then the product of the slopes of given lines is

The radius of a circle $C_1$ is thrice the radius of another circle $C_2$ and the centres of $C_1$ and $C_2$ are (1,2) and (3,-2) respectively. If they cut each other orthogonally and the radius of the circle $C_1$ is 3r, then the equation of the circle with r as radius and (1,-2) as centre is

If the centre $(\alpha, \beta)$ of a circle cutting the circles $x^2+y^2-2y-3=0$ and $x^2+y^2+4x+3=0$ orthogonally lies on the line $2x-3y+4=0$, then $2\alpha+\beta=$

In a triangle ABC, if $c^2 - a^2 = b(\sqrt{3}c - b)$ and $b^2 - a^2 = c(c-a)$, then $\angle ACB =$

The sum of all the roots of the equation $\begin{vmatrix} x & -3 & 2 \\ -1 & -2 & x-1 \\ 1 & x-2 & 3 \end{vmatrix} = 0$ is

If the normals drawn at the points $P\left(\frac{3}{4}, \frac{3}{2}\right)$ and $Q(3,3)$ on the parabola $y^2 = 3x$ intersect again on $y^2=3x$ at R, then R =

The equation of the locus of a point which is at a distance of 5 units from a fixed point (1,4) and also from a fixed line 2x+3y-1=0 is

If $\text{Sinh}^{-1}x = \text{Cosh}^{-1}y = \log(1+\sqrt{2})$ then $\text{Tan}^{-1}(x+y) =$

A real valued function
$f:[4, \infty) \to \mathbb{R}$ is defined as $f(x) = (x^2+x+1)^{(x^2-3x-4)}$, then f is

Let ABC be a triangle right angled at B. If a = 13 and c = 84, then r + R =

If the tangent drawn at the point $P(3\sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in the fourth quadrant then $\beta = $

$\frac{\cos 15^\circ \cos^2 22\frac{1}{2}^\circ - \sin 75^\circ \sin^2 52\frac{1}{2}^\circ}{\cos^2 15^\circ - \cos^2 75^\circ} =$

If $\frac{1}{2.7} + \frac{1}{7.12} + \frac{1}{12.17} + \dots$ to 10 terms = k, then k =

If $\vec{a} = (x+2y-3)\hat{i} + (2x-y+3)\hat{j}$ and $\vec{b} = (3x-2y)\hat{i} + (x-y+1)\hat{j}$ are two vectors such that $\vec{a} = 2\vec{b}$, then $y-5x=$

If A(2,1,-1), B(6,-3,2), C(-3,12,4) are the vertices of a triangle ABC and the equation of the plane containing the triangle ABC is $53x+by+cz+d=0$, then $\frac{d}{b+c}=$

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

Let P be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and let the perpendicular drawn through P to the major axis meet its auxiliary circle at Q. If the normals drawn at P and Q to the ellipse and the auxiliary circle respectively meet in R, then the equation of the locus of R is

If $0 \le x \le \frac{3}{4}$, then the number of values of $x$ satisfying the equation $\text{Tan}^{-1}(2x-1) + \text{Tan}^{-1}2x = \text{Tan}^{-1}4x - \text{Tan}^{-1}(2x+1)$ is

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$

If X is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$, $k=0,1,2,\dots,\infty$, then $P(X=3) =$

If a normal is drawn at a variable point P(x, y) on the curve $9x^2+16y^2-144=0$, then the maximum distance from the centre of the curve to the normal is

If $(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from a point $(-1,2,-1)$ to the line joining the points $(2,-1,1)$ and $(1,1,-2)$, then $\alpha+\beta+\gamma=$

If the domain of the real valued function $f(x) = \frac{1}{\sqrt{\log_{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a,b)$, then $2b =$