List of top Questions asked in TS EAMCET- 2025

A straight line passing through a point (3,2) cuts X and Y-axes at the points A and B respectively. If a point P divides AB in the ratio 2:3, then the equation of the locus of point P is

The number of normals that can be drawn through the point (2,0) to the parabola $y^2 = 7x$ is

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point (1,4) to the parabola $y^2 = 11x$ then $2(m_1^2 + m_2^2) =$

The length of the chord of the ellipse $\frac{x^2}{4} + y^2 = 1$ formed on the line $y = x+1$ is

Let P, Q, R, S be the points of intersection of the circle $x^2 + y^2 = 4$ and the hyperbola $xy = \sqrt{3}$. If P = $(\alpha,\beta)$ and $\alpha>\beta>0$, then the equation of the tangent drawn at P to the hyperbola is

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 ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ($b>a$) is an ellipse with eccentricity $\frac{1}{\sqrt{2}}$. If the angle of intersection between the ellipse and parabola $y^2=4ax$ is $\theta$, then the coordinates of the point $\frac{20}{3}$ on the ellipse is

The number of common tangents that can be drawn to the curves $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $x^2+y^2=16$ is

$\int \frac{x\text{Tan}^{-1}x}{(1+x^2)^2}dx =$

If $\int_0^{\pi/2}\tan^{14}(x/2)dx = 2\left[\sum_{n=1}^7 f(n) - \frac{\pi}{4}\right]$, then $f(n)=$

$\int \frac{\log x}{(1+x)^2}dx = $

If $\int \frac{\sqrt{1-\sqrt{x}}}{\sqrt{x(1+\sqrt{x})}}dx = 2f(x)-2\sin^{-1}\sqrt{x}+c$, then $f(x)=$

$\int_{-2}^{4} |2-x^2| dx =$

$\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =$

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

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

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

$\int \frac{3^x(x\log 3 - 1)}{x^2} dx =$

$\lim_{n \to \infty} \frac{(2n(2n-1)...(n+2)(n+1))^{1/n}}{n} =$

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

The area of the region bounded by $y=x^3$, x-axis, $x=-2$ and $x=4$ is

Consider the following
Assertion (A): $\int \sqrt{x-3}(\sin^{-1}(\log x) + \cos^{-1}(\log x))dx = \frac{\pi}{3}(x-3)^{3/2}+c$
Reason (R): $\sin^{-1}(f(x))+\cos^{-1}(f(x))=\frac{\pi}{2}$, $|f(x)|\le 1$
The correct answer is

If $I_1 = \int \frac{e^x}{e^{4x}+e^{2x}+1}dx$, $I_2 = \int \frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx$, then $I_2-I_1=$

If $\int \frac{3x+2}{4x^2+4x+5}dx = A\log(4x^2+4x+5)+B\tan^{-1}(\frac{2x+1}{2})+c$, then $A+B=$

$\int \frac{1}{(2\cos x + \sin x)^2} dx =$