List of top Mathematics Questions asked in AP EAMCET

Roots of the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) are:
If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]
If the amplitude of \( (Z - 2) \) is \( \frac{\pi}{2} \), then the locus of \( Z \) is:
The complex conjugate of \( (4 - 3i)(2 + 3i)(1 + 4i) \) is:
The system \( x + 2y + 3z = 4, \, 4x + 5y + 3z = 5, \, 3x + 4y + 3z = \lambda \) is consistent and \( 3\lambda = n + 100 \), then \( n = ? \)
Let \( A \) be a \( 4 \times 4 \) matrix and \( P \) be its adjoint matrix. If \( |P| = \left| \frac{A}{2} \right| \), then \( |A^{-1}| = ? \)
If \( A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} \) is a singular matrix, then the quadratic equation having the roots \( k \) and \( \frac{1}{k} \) is:
The sum of the series \( \frac{1}{1.5} + \frac{1}{5.9} + \frac{1}{9.13} + \cdots \) up to \( n \) terms is:
The range of the real valued function \( f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} \) is:
The domain of the real-valued function \( f(x) = \log_2 \log_3 \log_5 (x^2 - 5x + 11) \) is:
If \( \vec{a} = i\hat{i} + j\hat{j} + 3k\hat{k} \), \( \vec{b} = i\hat{i} + 2k\hat{k} \), \( \vec{c} = -3i\hat{i} + 2j\hat{j} + k\hat{k} \) are linearly dependent vectors and the magnitude of \( \vec{a} \) is \( \sqrt{14} \), then if \( \alpha, \beta \) are integers, find \( \alpha + \beta \):
The line \( 21x + 5y = k \) touches the hyperbola \( 7x^2 - 5y^2 = 232 \), then \( k \) is:
Angle between the circles \( x^2 + y^2 - 4x - 6y - 3 = 0 \) and \( x^2 + y^2 + 8x - 4y + 11 = 0 \) is:
The triangle \( PQR \) is inscribed in the circle \[ x^2 + y^2 = 25. \] If \( Q = (3,4) \) and \( R = (-4,3) \), then \( \angle QPR \) is:
If the slope of one of the lines in the pair of lines \( 8x^2 + axy + y^2 = 0 \) is thrice the slope of the second line, then \( a = \) ?
A line \( L \) passing through the point \( P(-5,-4) \) cuts the lines \( x - y - 5 = 0 \) and \( x + 3y + 2 = 0 \) respectively at \( Q \) and \( R \) such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line \( L \) is:
If a random variable \( X \) has the following probability distribution, then its variance is nearly: 
random variable
If the vectors \( a\hat{i} + \hat{j} + 3\hat{k} \), \( 4\hat{i} + 5\hat{j} + \hat{k} \), and \( 4\hat{i} + 2\hat{j} + 6\hat{k} \) are coplanar, then \( a \) is:
If \( A = (1,2,3), B = (3,4,7) \) and \( C = (-3,-2,-5) \) are three points then the ratio in which the point C divides AB externally is
In a triangle ABC, if \( (r_1 + r_2) \csc^2 \frac{C}{2} = \)
If \(\sinh x = \dfrac{\sqrt{21}}{2}\) then \(\cosh 2x + \sinh 2x = \)
The set of all real values \( a \) for which \[ -1<\frac{2x^2 + ax + 2}{x^2 + x + 1}<3 \] holds for all real values of \( x \) is:
If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]
If \( P(x, y) \) represents the complex number \( z = x + iy \) in the Argand plane and \[ \arg \left( \frac{z - 3i}{z + 4} \right) = \frac{\pi}{2}, \] then the equation of the locus of \( P \) is:
If \( P \) is the greatest divisor of \( 49^n + 16n - 1 \) for all \( n \in \mathbb{N} \), then the number of factors of \( P \) is: