List of top Mathematics Questions asked in AP EAPCET

If the position vectors of the points \( A \) and \( B \) are \( 2i + 3j - k \) and \( i - j + 2k \) respectively, then the unit vector along \( \overrightarrow{BA} \) and in the direction of \( AB \) is:
If \( 10 \sin^4 \alpha + 15 \cos^4 \alpha = 6 \), then \( 16 \tan^6 \alpha + 27 \cot^6 \alpha \) is:
If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is not in the first quadrant, then \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) is:
Evaluate \( \left[ 1 + \sec 2\theta \right] \left[ 1 + \sec 40^\circ \right] \):
Evaluate \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \):
In \( \triangle ABC \), if \( \cos^2 A + \cos^2 B + \cos^2 C = 1 \), then \( \triangle ABC \) is:
If \( A = \{ (a, b) : 4a = 5b, a \in \{1, 2, 3, \dots, 30\} \}, \) then the number of such ordered pairs \( (a, b) \) is:
The number of arrangements of the word KANGAROO in which the A's do not appear together 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:
The coefficient of \( x^2 \) in the expansion of \( (1 - 3x)^{\frac{1}{3}} (1 + 2x)^{\frac{1}{2}} \) is:
If \( C_j \) stands for \( ^nC_j \), then \[ \frac{C_0}{2} + \frac{C_1}{2.2^2} + \frac{C_2}{3.2^3} + \dots + C_n = \frac{3^n}{2^{n+1} (n+1)} \]
Find the value of \( (3 + \sqrt{8})^5 + (3 - \sqrt{8})^5 \):
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 matrix \( D_1 = \text{diag}(a, b, c) \), matrix \( D_2 = \text{diag}(3, 3, 3) \) and \( A \) is a skew-symmetric matrix of order 3, then
\[ \text{Tr}(D_1 D_2 A + D_2 D_1 + D_1 A + D_2 A) - \text{Tr}(D_1 + D_2) = ? \]
For \( x \in \mathbb{R} \), the minimum value of \( \frac{x^2 + 2x + 5}{x^2 + 4x + 10} \) is:
The modulus of the conjugate of \( z = \frac{-2 + i}{(1 - 2i)^2} \) 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:
If \( \alpha \) is the real root and \( \beta \), \( \gamma \) are the other roots of the equation \( x^3 - a^3 = 0 \, (a>0) \), then the number of common points of the curves given by \( |z - \beta| = \frac{\sqrt{3a}}{2} \) and \( |z - \gamma| = \frac{\sqrt{3a}}{2} \) is:
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 \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \), then \( A^{-1} \) = ?
If \( f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x} \) for \( x \in \mathbb{R} \), then find \( f(2023) \).
The rank of the matrix \( A = \begin{bmatrix} 1 & 1 & 3 \\ 2 & 2 & 1 \\ 1 & 1 & 1 \end{bmatrix} \) is:
If \( f(x) = \begin{cases} x \left( 1 + \frac{1}{2} \sin(\log x^2) \right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \)