List of top Mathematics Questions asked in AP EAPCET

If \( 10 \sin^4 \alpha + 15 \cos^4 \alpha = 6 \), then \( 16 \tan^6 \alpha + 27 \cot^6 \alpha \) is:
In \( \triangle ABC \), if \( \cos^2 A + \cos^2 B + \cos^2 C = 1 \), then \( \triangle ABC \) is:
Find the value of \( (3 + \sqrt{8})^5 + (3 - \sqrt{8})^5 \):
If \( C_j \) stands for \( ^nC_j \), then \[ \frac{C_0}{2} + \frac{C_1}{2.2^2} + \frac{C_2}{3.2^3} + \dots + C_n = \frac{3^n}{2^{n+1} (n+1)} \]
If \( \alpha_1, \alpha_2, \alpha_3 \) are the roots of the equation \( x^3 + 3x + 2 = 0 \), then \( \alpha_1^5 + \alpha_2^5 + \alpha_3^5 \) is:
If \( \alpha \) and \( \beta \) are the roots of the equation \( 2x^3 - 3(2x^2) + 32 = 0 \) with \( \beta<1 \), then \( 2\alpha + 3\beta \) is:
If \( \alpha \), \( \beta \), and \( \gamma \) are the roots of the equation \( x^3 - ax^2 + bx - c = 0 \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is:
If \( z_1 = 2 + 5i \), \( z_2 = -1 + 4i \) and \( z_3 = i \), then
\[ \frac{|z_1 - z_3|}{|z_3 - z_2|} = ? \]
The locus of the variable point \( z = x + iy \) whose amplitude is always equal to \( \theta \), is:
For \( x \in \mathbb{R} \), the minimum value of \( \frac{x^2 + 2x + 5}{x^2 + 4x + 10} \) is:
The rank of the matrix \( A = \begin{bmatrix} 1 & 1 & 3 \\ 2 & 2 & 1 \\ 1 & 1 & 1 \end{bmatrix} \) is:
If \( f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x} \) for \( x \in \mathbb{R} \), then find \( f(2023) \).
If \( f(0) = 0, f(1) = 1, f(2) = 2 \) and \( f(x) = f(x-2) + f(x-3) \) for \( x = 3, 4, 5, \dots \), then find \( f(10) \).
If \( f(x) = \begin{cases} \sqrt{\pi - \cos^{-1} x}, & x = -1 \\ \frac{\sqrt{2(1 + x)}}{\pi + \cos^{-1} x}, & x \neq -1 \end{cases} \) is right continuous at \( x = -1 \), then \( \lambda = \)
If \( y = y(x) \) is the solution of \( \frac{dy}{dx} = \frac{x - y \cos x}{1 + \sin x} \), \( y\left(\frac{\pi}{2}\right) = \frac{\pi^2}{8} \), then \( y(\pi) = \)
\( \lim_{n \to \infty} \frac{1}{n} \left( \frac{1}{e^{1/n}} + \frac{1}{e^{2/n}} + \frac{1}{e^{3/n}} + \dots + \frac{1}{e^{n/n}} \right) = \)
\( \int_0^{1/2} \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx = \)
Given that \( \frac{d}{dx} \left[ \int_0^{\phi(x)} f(t) dt \right] = \phi'(x) f(\phi(x)) \). If \( \int_0^{x^3} f(t) dt = x^2 \sin 2\pi x \), then the value of \( f(8) \) is
\( \int \frac{x^2 - 1}{x^3 \sqrt{2x^4 - 2x^2 + 1}} dx = \)
The points on the curve \( y^2 = x + \sin x \) at which the normal is parallel to the Y-axis lie on
If the tangent drawn at \( A(2, 1) \) to the curve \( x = 1 + \frac{1}{y^2} \) meets the curve again at \( B \), then
Let \( f(x) = \max\{\cos x, \sin x, 0\} \). If the number of points at which \( f(x) \) is not differentiable in \( (0, 2024\pi) \) is \( 1012k \), then \( k = \)
If \( \theta \) is the angle between the asymptotes of the hyperbola \( \frac{x^2}{9} - \frac{(y - 2)^2}{16} = 1 \) and \( \cos \theta = \frac{a^2}{b^2} \), then \( a^2 = \)
\( \lim_{x \to 0} \left( \frac{(1 + y)^{1/x} - 1}{y} \right) = \)
Let \( f(x) = |x - 3| + |x + 5| \) and \( A = \left\{ a \in \mathbb{R} / \lim_{x \to a} \frac{f(x) - f(a)}{x - a} \text{ exists} \right\} \). Then the number of real numbers which are in \( [-8, 3] \cup [5, \infty) \) but not in \( A \) is