List of top Mathematics Questions asked in AP EAPCET

If \( \alpha = \log_e(2 + \sqrt{3}) \), then evaluate: \[ \frac{\cosh \alpha }{1 - \tanh \alpha} + \frac{\sinh \alpha}{1 - \coth \alpha} \]
If \( \sec(\theta + \alpha) \), \( \sec(\theta) \), and \( \sec(\theta - \alpha) \) are in arithmetic progression, then \( \sin^2 \theta = \)
Evaluate the following expression: \[ \sin 21^\circ \cos 9^\circ - \cos 84^\circ \cos 6^\circ \]
If the values of \( k \) for which the equation \( x^2 + 2(k+2)x + 6k + 7 = 0 \) has equal roots are \( k_1 \) and \( k_2 \), then \( k_1^2 + k_2^2 \) is:
The number of all possible solutions of the equation \( z^3 + z = 0 \) is:
If \( (3 + 2\sqrt{2})^{x^2 - 4} + (3 - 2\sqrt{2})^{x^2 - 4} = 6 \), then \( x^4 + x^2 + 5 = \)?
If \( z_1 = (2, -1) \) and \( z_2 = (6, 3) \), then find the amplitude of the expression \[ \text{amp}\left(\frac{z_1 - z_2}{z_1 + z_2}\right) \]
If \( A = \begin{bmatrix} i & 0 \\ 0 & -i \end{bmatrix}, B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}, C = \begin{bmatrix} 0 & i \\ -i & 0 \end{bmatrix} \), then the expression \( A^2 + B^2 + C^2 \) is:
If \( f(x) = x^3 - x \) and \( g(x) = \sin(2x) \), then \( f(g\left(\frac{\pi}{12}\right)) \) is:
If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is \( ( \alpha, \beta, \gamma ) \), then find the value of \( \alpha^2 + \beta^2 + \gamma^2 \).
If \( f(x) \) is the signum function, then in terms of \( f(x) \), the constant function \( g(x)=1, \ \forall x \in \mathbb{R} \) is:
If \[ \begin{vmatrix} x & 4 & -1 \\ 2 & 1 & 0 \\ 0 & 2 & 4 \end{vmatrix} = 0, \text{ then find the value of } x. \]
For real numbers \( a \) and \( b \), if \[ 4a + i(3a - b) = b - 6i \] and \[ z = a + \frac{b}{4}i, \] then find \[ \frac{|z|}{a}. \]
If \( z = (1 - i^3)(x + i) \) is a purely imaginary number for \( x = x_1 \), and if \( z \) is a purely real number for \( x = x_2 \), then find \( x_1, x_2 \).
If \( \omega, \omega^2 \) are the cube roots of unity, \( k \) is a positive integer, and \[ (1 - \omega^2)^{3k} + (1 - \omega^2 + 0)^{3k+1} + (1 + \omega - 0)^{3k+1}, \] then find \( k \).
If \( \alpha, \beta \) are the two real roots of the 4th roots of unity, and \( \gamma, \delta \) are the other two roots of it, then the sum of the eccentricities of the conics \( |z - \alpha| + |z - \beta| = 4 \) and \( |z - \gamma| + |z - \delta| = 6 \) is:
If \( \frac{17x - 2}{12x^2 - x - 20} = \frac{A}{ax + 5} + \frac{B}{3x + b} \), then \( a \cdot A + b \cdot B \) is:
Let \( \vec{a}, \vec{b}, \vec{c} \) be any three non-coplanar vectors. If \( m, n \) are scalars such that \( \vec{a} + \vec{b} = m\vec{c} \) and \( \vec{b} + \vec{c} = n\vec{a} \), then \( 3\vec{a} + 2\vec{b} + 2\vec{c} = \):
In \( \Delta ABC \), \( A, B, C \) are in arithmetic progression and \( a : c = 1 : 2 \). If \( b = 4\sqrt{3} \) cm, then the area of \( \Delta ABC \) (in sq. cm) is:
If \( \sinh x = \frac{5}{12} \), then \( \cosh \frac{x}{2} \) is:
If \( \alpha, \beta \) are acute angles such that \( \sin \beta = 2 \sin \alpha \) and \( 3 \cos \beta = 2 \cos \alpha \), then \( \sec (\alpha + \beta) \) is:
In \( \Delta ABC \), \( \left( \tan \frac{A}{2} + \tan \frac{B}{2} \right) \tan \frac{C}{2} = \):
Match the ranges of the functions given in List - A with those of the items given in List - B.
Match the ranges of the functions given
If \( \frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} = \):
Find the value of \( \cos 12^\circ \cdot \cos 24^\circ \cdot \cos 36^\circ \cdot \cos 48^\circ \cdot \cos 72^\circ \cdot \cos 84^\circ \):