List of top Questions asked in AP EAPCET- 2025

Match the following
List-I (Symbol of electrical property)List-II (Units)
A) \( \Omega \)I) S cm\(^{-1}\)
B) GII) m\(^{-1}\)
C) \( \kappa \)III) S cm\(^2\) mol\(^{-1}\)
D) G\(^*\)IV) S
If the half-life of a radioactive element is $12.5$ hours, then the time taken to disintegrate $256~g$ of the substance into $1~g$ is (in hours)
Evaluate the limit: \[ \lim_{x \to \infty} \frac{3x+4\cos^2x}{\sqrt{x^2-5\sin^2x}} \]
Evaluate: \( \int_0^{400\pi} \sqrt{1 - \cos 2x} \, dx \)
The following equation is obtained for a first order reaction at 300 K.
$\log_{10} \frac{k}{A} = 0.00174$ What is the activation energy (in J mol\(^{-1}\)) of the reaction ?
(R = 8.314 J mol\(^{-1}\) K\(^{-1}\))
Consider the following statements
Statement-I: A function \( f: A \rightarrow B \) is said to be one-one if and only if \[ f(x) = f(y) \Rightarrow x = y \]
Statement-II: A relation \( f: A \rightarrow B \) is said to be a function if \[ x = y \Rightarrow f(x) \neq f(y) \]
Then which one of the following is true?
A wire of resistance 10 \(\Omega\) is stretched to twice its original length. What is the new resistance?
If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then \[ (\alpha + \beta)(\beta + \gamma)(\gamma + \alpha) =\ ? \]
If \[ \int \frac{dx}{(x \tan x + 1)^2} = f(x) + c, \] then \(\lim_{x \to \frac{\pi}{2}} f(x)\) is?
Consider the following reaction A(g) + 3B(g) \( \longrightarrow \) 2C(g); \( \Delta H^\ominus = -24 \) kJ. At \(25 \, ^\circ\text{C}\) if \( \Delta G^\ominus \) of the reaction is -9 kJ, the standard entropy change (in JK\(^{-1}\)) of the same reaction at same temperature is
The minimum value of \( |z - 1| + |z - 5| \) is:
The slope of one of the direct common tangents drawn to the circles \(x^2 + y^2 - 2x + 4y + 1 = 0\) and \(x^2 + y^2 - 4x - 2y + 4 = 0\) is
The radius of the circle passing through the points of intersection of the circles \( x^2+y^2+2x+4y+1=0 \), \( x^2+y^2-2x-4y-4=0 \), and intersecting the circle \( x^2+y^2=6 \) orthogonally is:
If the average number of accidents occurring at a particular junction on a highway in a week is 5, then the probability that at most one accident occurs in a particular week is:
The general solution of the equation \( \cos(2x) = \frac{1}{2} \) is:
If the maximum and minimum amplitudes of a modulated wave are \( 25 \) V and \( 5 \) V respectively, then the modulation index is:
If P(\(\alpha, \beta\)) is the radical centre of the circles \(S=x^2+y^2+4x+7=0\), \(S'=2x^2+2y^2+3x+5y+9=0\) and \(S''=x^2+y^2+y=0\), then the length of the tangent drawn from P to S' = 0 is
If \( x \ne (2n+1)\frac{\pi}{4} \), then the general solution of \( \cos x + \cos 3x = \sin x + \sin 3x \) is
If all letters of the word COMBINATION are arranged to form 11-letter words with \( C \) and \( N \) at the ends and no vowel in the middle position, find the number of such words.
If \( x \) satisfies the equation \( 3x^2 - 7x + 2 = 0 \), then what is the value of \( \frac{1}{x_1} + \frac{1}{x_2} \), where \( x_1 \) and \( x_2 \) are the roots?
White phosphorus on heating with concentrated NaOH solution in an inert atmosphere of CO\(_2\) gives a salt 'X' and gas 'Y'. The oxidation state of central atom in X and Y is respectively
Observe the following (Products = .........):
P₄ + SOCl₂ → Products
P₄ + SO₂Cl₂ → Products
In both the reactions, a common product 'X' is obtained. The number of lone pair of electrons on the central atom of 'X' is:
In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectively: