List of top Mathematics Questions asked in AP EAPCET

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 \( 3\vec{a} + 2\vec{b} + 2\vec{c} = \):
If \( 2i\hat{i} - j\hat{j} - 3j\hat{k} \) and \( -3i\hat{i} + 4j\hat{j} - 4k\hat{k} \) are the position vectors of three points A, B, and C respectively, then \( \Delta ABC \) is:
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 \( \Delta ABC \), \( \left( \tan \frac{A}{2} + \tan \frac{B}{2} \right) \tan \frac{C}{2} = \):
In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):
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
In \( \Delta ABC \), if \( \sin 2A + \sin 2B + \sin 2C = \frac{\cos A + \cos B + \cos C - 1}{\cos A + \cos B + \cos C - 1} \), then:
Find the value of \( \cos 12^\circ \cdot \cos 24^\circ \cdot \cos 36^\circ \cdot \cos 48^\circ \cdot \cos 72^\circ \cdot \cos 84^\circ \):
If \( \frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} = \):
If \( f(n) = n!(31-n)! \), where \( n \in \{ 0, 1, 2, \dots, 31 \} \), then the minimum value of \( f(n) \) is:
The number of all 8-digit odd numbers is:
The number of all four-digit numbers which begin with 4 and end with either zero or five is:
The degree of the polynomial \( \left( x + \sqrt{x^4 - 1} \right)^9 + \left( x - \sqrt{x^4 - 1} \right)^9 \) is:
If the numerically greatest term in the expansion of \( (2 - 3x)^9 \) when \( x = 1 \) is \( P_1^q P_2^r P_3^s P_4^t \) (where \( P_1 < P_2 < P_3 < P_4 \) are the first four prime numbers), then \( \alpha + \beta + \gamma + \delta = \):
If the sum of the cubes of the roots of the equation \( x^3 - ax^2 + bx - c = 0 \) is zero, then \( a^3 + 3c = \):
If \( \alpha, \beta, \gamma \) are the roots of \( x^3 + 2x + 5 = 0 \), then \( \sum \frac{\beta + \gamma}{\alpha^2} \) is:
The set \( \{ x \in \mathbb{R} : 4 + 11x - 3x^2>0 \} \) is the interval:

If \( \lim_{x \to 1} \frac{\sqrt[4]{x^3} + a\sqrt[4]{x^5} - 2}{x - 1} = -2 \), then the coefficient of \(x\) in the expansion of 
 \(\left( \sqrt[4]{x^3} + a\sqrt[4]{x^5} \right)^4 is:\)

Let \( E \) be an ellipse whose major axis is the X-axis and minor axis is the Y-axis. If the distance of a point \( \left(\frac{5}{2}, 2\sqrt{3}\right) \) on \( E \) from its foci are \( \frac{7}{2} \) and \( \frac{13}{2} \), then the eccentricity of the ellipse \( E \) is: