List of top Questions asked in AP EAPCET- 2025

If \(x^2 + y^2 = \dfrac{1}{t} \text{ and } x^4 + y^4 = t^2 + \dfrac{1}{t^2},\) then \(\dfrac{dy}{dx} =\)

A random variable \(X\) follows a binomial distribution in which the difference between its mean and variance is 1. If \(2P(x=2) = 3P(x=1)\), then \(n^2 P(x>1)\) is:

In \(\triangle ABC\), if \(r_1 = 2r_2 = 3r_3\), then find the ratio \(a : b\).

If \(\vec{a} = 2 \vec{i} - 3 \vec{j} + 4 \vec{k}, \vec{b} = \vec{i} + 2 \vec{j} - \vec{k}, \vec{c} = -3 \vec{i} - \vec{j} + 2 \vec{k}\) and \(\vec{d} = \vec{i} + \vec{j} + \vec{k}\) are four vectors, then evaluate \[ (\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) = ? \]

For \(\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), if \(2\cos \theta + \sin \theta = 1\), and \(7\cos \theta + 6 \sin \theta = k\), then the possible values of \(k\) are:

If $5f(x) + 3f \left( \frac{1}{x} \right) = x + 2$ and $y = x f(x)$, then $\frac{dy}{dx}$ at $x = 1$ is
Identify the correct option from the following:

If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true? \[ \begin{cases}

If \[ A = \begin{bmatrix} 1 & -1 & 2 \\ -2 & 3 & -3 \\ 4 & -4 & 5 \end{bmatrix} \] and \( A^T \) represents the transpose of \( A \), then calculate \( AA^T - A - A^T \).

$\lim_{x \to 0} \frac{(\sqrt{2})^{-\sqrt{1 + \cos x}}}{15 + \cos 2x - 4} =$
Identify the correct option from the following:

$\lim_{x \to 0} \frac{x \tan 2x - 2x \tan x}{(1 - \cos 3x) (\cos x - \cot x)^2} =$
Identify the correct option from the following\nobreakspace the following:

If \( i = \sqrt{-1} \), then \[ \sum_{n=2}^{30} i^n + \sum_{n=30}^{65} i^{n+3} = \]

If the area of triangle \(ABC\) is \(4\sqrt{5}\) sq. units, length of the side \(CA\) is 6 units and \(\tan \frac{B}{2} = \frac{\sqrt{5}}{4}\), then its smallest side is of length:

Match the following

Pickup the correctly matched pairs from the following.

Assertion (A) : Lactational amenorrhoea is a natural method of contraception.
Reason (R) : Ovulation in mother generally does not occurs during intense lactation following parturition. Identify the correct option from the following

Match the following

Study the following statements and pick up the incorrect statements.
I. Oriented locomotor movement of an organism towards or away from the direction of light is called photokinesis.
II. The influence of light on non-directional movement of organisms is called phototaxis.
III. UV-B and UV-C rays are more harmful than UV-A rays.
IV. Photoperiod influences the migration of birds.