List of top Questions asked in TS EAMCET- 2025

If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

One of the values of $\sqrt{24-70i} + \sqrt{-24+70i}$ is

The set of all values of $\theta$ such that $\frac{1-i\cos\theta}{1+2i\sin\theta}$ is purely imaginary is

If $\cos\alpha+\cos\beta+\cos\gamma = 0 = \sin\alpha+\sin\beta+\sin\gamma$, then $\sin 2\alpha + \sin 2\beta + \sin 2\gamma =$

If $\alpha$ is a root of the equation $x^2-x+1=0$ then $(\alpha + \frac{1}{\alpha}) + (\alpha^2 + \frac{1}{\alpha^2}) + (\alpha^3 + \frac{1}{\alpha^3}) + \dots$ to 12 terms =

$\int e^x(x^3-2x^2+3x-4)dx =$

$\int(1+\tan^2 x)(1+2x\tan x)dx =$

$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$

$\int_4^{18} \frac{1}{(x+2)\sqrt{x-3}}dx = $

If $[\cdot]$ denotes the greatest integer function, then $\int_1^2 [x^2] dx =$

Number of all possible ways of distributing eight identical apples among three persons is

If $3\sin\theta + 4\cos\theta = 3$ and $\theta \neq (2n+1)\frac{\pi}{2}$, then $\sin 2\theta =$

$16 \sin 12^\circ \cos 18^\circ \sin 48^\circ =$

Number of solutions of the equation $\sin^2\theta + 2\cos^2\theta - \sqrt{3}\sin\theta\cos\theta = 2$ lying in the interval $(-\pi, \pi)$ is

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is

The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is

If $2x^2+xy-6y^2+k=0$ is the transformed equation of $2x^2+xy-6y^2-13x+9y+15=0$ when the origin is shifted to the point $(a,b)$ by translation of axes, then k =

The line L: $6x+3y+k=0$ divides the line segment joining the points (3,5) and (4,6) in the ratio -5:4. If the point of intersection of the lines L = 0 and $x-y+1=0$ is P(g,h) then h =

A straight line through the point P(1,2) makes an angle $\theta$ with the positive X-axis in anti-clockwise direction and meets the line $x+\sqrt{3}y-2\sqrt{3}=0$ at Q. If $PQ = \frac{1}{2}$, then $\theta=$

If $m_1, m_2$ are the slopes of the tangents drawn through the point $(-1,-2)$ to the circle $(x-3)^2+(y-4)^2=4$, then $\sqrt{3}|m_1-m_2|=$

A line meets the circle $x^2+y^2-4x-4y-8=0$ in two points A and B. If P(2,-2) is a point on the circle such that PA = PB = 2 then the equation of the line AB is