List of top Questions asked in AP EAPCET- 2025

If \( \frac{1}{2} \sin^{-1} \left( \frac{3\sin 2\theta}{5+4\cos 2\theta} \right) = \tan^{-1 x \) then \( x = \)}

If $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos^2 \frac{x{4} + \sin \frac{x}{4}$, $x \in \mathbb{R}$, then $\alpha-\beta=$}

If the volume of a sphere is increasing at the rate of 12 \( \text{cm}^3/\text{sec} \), then the rate (in \( \text{cm}^2/\text{sec} \)) at which its surface area is increasing when the diameter of the sphere is 12 cm is:

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 + ax^2 + bx + c = 0 \), then \( (\alpha + \beta - 2\gamma)(\beta + \gamma - 2\alpha)(\gamma + \alpha - 2\beta) = \)

The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is

If the power of the point \( (1,6) \) with respect to the circle \( x^2+y^2+4x-6y-a=0 \) is \( -16 \), then \( a \) is:

Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]

Lines \(L_1\) and \(L_2\) have slopes 2 and \(-\frac{1}{2}\) respectively. If both \(L_1\) and \(L_2\) are concurrent with the lines \(x - y + 2 = 0\) and \(2x + y + 3 = 0\), then the sum of the absolute values of the intercepts made by the lines \(L_1\) and \(L_2\) on the coordinate axes is?

The point in the \(xy\)-plane which is equidistant from the points \(A(2,0,3), B(0,3,2)\) and \(C(0,0,1)\) has the coordinates?

Evaluate \[ \lim_{n \to \infty} \frac{1}{2n} \left( \sin \frac{\pi}{2n} + \sin \frac{\pi}{n} + \sin \frac{2\pi}{2n} + \dots \right) = ? \]

\[ \lim_{y \to 0} \frac{\sqrt{1 + \sqrt{1 + y^4}} - \sqrt{2}}{y^4} = \ ? \]

If the inverse of $$ \begin{bmatrix} -x & 14x & 7x \\ 0 & 1 & 0 \\ x & -4x & -2x \end{bmatrix} $$ is $$ \begin{bmatrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1 \end{bmatrix} $$ then the value of $$ \begin{vmatrix} x & x+1 & x+2 \\ x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \end{vmatrix} $$

In triangle $ ABC $, if $ a = 5,\ b = 4,\ \cos(A - B) = \frac{31}{32} $, then $ c = ? $

If a real valued function \[ f(x) = \begin{cases} \frac{x^2 (a + 3) x (a + 1)}{x + 3}, & x \neq -3
-\frac{5}{2}, & x = -3 \end{cases} \] is continuous at $x = -3$, then $\lim_{x \to -3} [x^2 x + 1] =$ Identify the correct option from the following:

If the tangents of the parabola $ y^2 = 8x $ passing through the point $ P(1, 3) $ touch the parabola at points $ A $ and $ B $, then the area (in sq. units) of $ \triangle ABC $ is

If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed is

In triangle \(ABC\), if \(\cos A \cos B + \sin A \sin B \sin C = 1\), then \(\sin A + \sin B + \sin C =\)

The triangle formed by the lines \( 2x^2 + xy - 6y^2 = 0 \) and \( x+y-1=0 \) is:

If \( A(2,-1,1) \), \( B(2,5,1) \) and \( C(0,-2,3) \) are the vertices of a triangle, and \( D \) is the point of intersection of the side \( BC \) and the internal angular bisector of angle \( A \), then \( AD = \):