List of top Questions asked in TS EAMCET- 2025

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

Numerically greatest term in the expansion of $(3x-4y)^{23}$ when $x=\frac{1}{6}$ and $y=\frac{1}{8}$ is

The direction ratios of the line bisecting the angle between the x-axis and the line having direction ratios (3, -1, 5) are

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

The number of integral values of 'a' for which the quadratic equation \( ax^2 + ax + 5 = 0 \) cannot have real roots is

The substitution required to reduce the differential equation \(t^2 dx + (x^2 - tx + t^2) dt = 0\) to a differential equation which can be solved by variables separable method is

Let \(p_1, p_2, p_3\) be the altitudes of a triangle ABC drawn through the vertices A, B, C respectively. If \(r_1=4, r_2=6, r_3=12\) are the ex-radii of triangle ABC then \( \frac{1}{p_1^2} + \frac{1}{p_2^2} + \frac{1}{p_3^2} = \)

A student has to answer a multiple-choice question having 5 alternatives in which two or more than two alternatives are correct. Then the number of ways in which the student can answer that question is

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

The values of x at which the real valued function $f(x)=7|2x+1|-19|3x-5|$ is not differentiable is

The system of linear equations $(\sin\theta)x+y-2z=0$, $2x-y+(\cos\theta)z = 0$ and $-3x+(\sec\theta)y+3z=0$, where $\theta \neq (2n+1)\frac{\pi}{2}$, has non-trivial solution for

In a triangle ABC, if \( r_1=4 \), \( r_2=8 \) and \( r_3=24 \), then \( a:b:c = \)

$\coth^2 x - \tanh^2 x =$

If $\frac{x+3}{(x+1)(x^2+2)} = \frac{a}{x+1} + \frac{bx+c}{x^2+2}$ then $a-b+c =$

\((1-i\sqrt{3})^{2025}= \)

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 $2\alpha+\beta=$

\( \tan^{-1}\frac{3}{5} + \tan^{-1}\frac{6}{41} + \tan^{-1}\frac{9}{191} = \)

Let $f:[-1,2] \to \mathbb{R}$ be defined by $f(x) = [x^2-3]$ where $[.]$ denotes greatest integer function, then the number of points of discontinuity for the function $f$ in $(-1,2)$ is

The domain and range of $f(x) = \frac{1}{\sqrt{|x|-x^2}}$ are A and B respectively. Then $A \cup B = $ ?

If $\hat{i}+\hat{j}+\hat{k}$, $a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$, $a_2\hat{i}+b_2\hat{j}+c_2\hat{k}$, $a_3\hat{i}+b_3\hat{j}+c_3\hat{k}$ are the position vectors of the points A, B, C, D respectively, $\frac{2}{3}(\hat{i}+\hat{j}+\hat{k})$ is the position vector of the centroid of the triangular face BCD of the tetrahedron ABCD, and if $\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ is the position vector of the centroid of the tetrahedron, then $2\alpha+\beta+\gamma =$

A line makes angles 60$^\circ$, 45$^\circ$, $\theta$ with positive X, Y, Z-axes respectively. If $\theta$ is an acute angle, then $\tan\theta =$

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

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

Sum of all the roots of the equation $||2x-3|-4| = 2$ is

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