List of top Questions asked in TS EAMCET- 2025

A block of mass $\sqrt{2}$ kg is placed on a rough horizontal surface. A force 'F' acting upwards at an angle of 45$^\circ$ with the horizontal causes the block to start motion. If the coefficient of static friction between the surface and the block is 0.25, the magnitude of the force 'F' is (Acceleration due to gravity = 10 ms$^{-2}$)

The vertical displacement (y in metre) of a projectile in terms of its horizontal displacement (x in metre) is given by $y=(\sqrt{3}x - 0.2x^2)$. The time of flight of the projectile is (Acceleration due to gravity = 10 ms$^{-2}$)

For a particle moving along a straight line path, the displacements in third and fifth seconds of its motion are 10 m and 18 m respectively. The speed of the particle at time t=4s is

The error in the measurement of force acting normally on a square plate is 3%. If the error in the measurement of the side of the plate is 1%, then the error in the determination of the pressure acting on the plate is

The force of mutual attraction between any two objects by virtue of their masses is

If the general solution of $(1+y^2)dx = (\tan^{-1}y - x)dy$ is $x = f(y)+ce^{-\tan^{-1}y}$, then $f(y)=$

The differential equation of the family of all circles of radius 'a' is

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

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

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

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

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 the percentage error in the radius of a circle is 3, then the percentage error in its area is

The function $f(x)=2x^3-9ax^2+12a^2x+1$ where $a>0$ attains its local maximum and local minimum at p and q respectively. If $p^2=q$ then a =

The height of a cone with semi vertical angle $\pi/3$ is increasing at the rate of 2 units/min. The rate at which the radius of the cone is to be decreased so as to have a fixed volume always is

For the curve $(\frac{x}{a})^n + (\frac{y}{b})^n = 2$, ($n \in N$ & $n>1$) the line $\frac{x}{a}+\frac{y}{b}=2$ is

If $x=t-\sin t, y=1-\cos t$ and $\frac{d^2y}{dx^2}=-1$ at $t=K, K>0$, then $\lim_{t \to K} \frac{y}{x} =$

If $y=f(x)^{g(x)}$ and $\frac{dy}{dx} = y[H(x)f'(x)+G(x)g'(x)]$, then $\int \frac{G(x)H(x)f'(x)}{g(x)}dx =$

The set of all values of x for which $f(x) = ||x|-1|$ is differentiable is

If \( f(x) = \begin{cases} x^2 \cos\left(\frac{\pi}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then at \( x = 0 \), \( f(x) \) is

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

$\lim_{x \to 0} \frac{\sqrt[3]{\cos x} - \sqrt{\cos x}}{\sin^2 x} =$

If the plane $-4x-2y+2z+\alpha=0$ is at a distance of two units from the plane $2x+y-z+1=0$, then the product of all the possible values of $\alpha$ is

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