List of top Questions asked in TS EAMCET- 2025

If \( x = \frac{t^2}{1+t^5} \), \( y = \frac{2t^3}{1+t^5} \) and \( t \neq -1 \) is a parameter then \( \frac{dy}{dx} = \)

If x and y are two positive real numbers such that xy=4 then the minimum value of \( \sqrt{x+\frac{y^2}{2}} \) is

Let ABC be a triangle right angled at B. If a = 13 and c = 84, then r + R =

If $0 \le x \le \frac{3}{4}$, then the number of values of $x$ satisfying the equation $\text{Tan}^{-1}(2x-1) + \text{Tan}^{-1}2x = \text{Tan}^{-1}4x - \text{Tan}^{-1}(2x+1)$ is

If $\frac{x^2+1}{(x^2+2)(x^2+3)} = \frac{Ax+B}{x^2+2} + \frac{Cx+D}{x^2+3}$, then $A+B+C+D=$

If $\frac{3x+1}{(x-1)^2(x^2+1)} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{Cx+D}{x^2+1}$, then $2(A-C+B+D)=$

If $C_0, C_1, C_2, \dots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then $\sum_{r=1}^{n} \frac{r C_r}{C_{r-1}} =$

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 \( y = f(\cosh x) \) and \( f'(x) = \log(x + \sqrt{x^2-1}) \) then \( \frac{d^2 y}{dx^2} = \)

If $C_0, C_1, C_2, \dots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then the value of $\sum r^3 \cdot C_r$ when $n = 5$ is

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$

If A, B are the points of contact of the tangents drawn from the point (-3,1) to the circle \( x^2+y^2-4x+2y-4=0 \), then the equation of the circumcircle of the triangle PAB is

1+(1+3)+(1+3+5)+(1+3+5+7)+... to 10 terms =

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

5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is

The value of the greatest integer k satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in N$ is

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

Consider the following statements
Statement-I: $\cosh^{-1}x = \tanh^{-1}x$ has no solution
Statement-II: $\cosh^{-1}x = \coth^{-1}x$ has only one solution
The correct answer is

Optical communication using fibres is performed in the frequency range of:

In several fungi and plants, the bisexual condition is denoted by

The layer of the atmosphere which efficiently reflects high frequency waves particularly at night is

A metal crystallises in two cubic phases, fcc and bcc with edge lengths 3.5 Å and 3 Å respectively. The ratio of densities of fcc and bcc is approximately

Two wires A and B made of same material and areas of cross-section in the ratio $1:2$ are stretched by same force. If the masses of the wires A and B are in the ratio $2:3$, then the ratio of the elongations of the wires A and B is

Identify ``X'' name of enzyme; and ``Y'' enzyme class number by observing the reaction given below:
\[ \text{Glutamic acid} + NH_3 + \text{ATP} \xrightarrow{X} \text{Glutamine} + \text{ADP} + \text{iP} \]

Agaricus basidiocarp is having 60 basidia. Find out number of nuclear fusions, meiotic divisions and basidiospores formed from that basidiocarp