List of top Mathematics Questions asked in TS EAMCET

A line segment joining a point A on x-axis to a point B on y-axis is such that AB = 15. If P is a point on AB such that \(\frac{AP}{PB} = \frac{2}{3}\), then the locus of P is

A circle S given by \(x^2 + y^2 - 14x + 6y + 33 = 0\) cuts the X-axis at A and B (OB \(>\) OA). C is midpoint of AB. L is a line through C and having slope \((-1)\). If L is the diameter of a circle S' and also the radical axis of the circles S and S', then the equation of the circle S' is

The angle between the tangents drawn from the point P(k, 6k) to the circle \(x^2+y^2+6x-6y+2=0\) is \(2\tan^{-1}(\frac{4}{3})\). If the coordinates of P are integers, then k =

A normal chord PQ drawn at a point P on the parabola \(y^2=5x\) subtends a right angle at the vertex. If P lies in the first quadrant, then the other end Q of the normal chord is

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

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 $P(X=3) =$

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

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 \( \frac{1}{p_1^2} + \frac{1}{p_2^2} + \frac{1}{p_3^2} = \)

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

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

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

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

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

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

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 \( a:b:c = \)

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

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 $\hat{i}+\hat{j}+\hat{k}$, $a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$, $a_2\hat{i}+b_2\hat{j}+c_2\hat{k}$, $a_3\hat{i}+b_3\hat{j}+c_3\hat{k}$ 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 $2\alpha+\beta+\gamma =$