List of top Mathematics Questions asked in AP EAMCET

If the roots of the quadratic equation \( x^2 - 35x + c = 0 \) are in the ratio 2:3 and \( c = 6K \), then \( K \) is:
If real parts of \( \sqrt{-5 - 12i} \), \( \sqrt{5 + 12i} \) are positive values, the real part of \( \sqrt{-8 - 6i} \) is a negative value. If \[ a + ib = \frac{\sqrt{-5 - 12i} + \sqrt{5 + 12i}}{\sqrt{-8 - 6i}} \] then \( 2a + b \) is:
The set of all real values of \( c \) for which the equation \[ zz' + (4 - 3i)z + (4+3i)z + c = 0 \] represents a circle is:
If \( Z = x + iy \) is a complex number, then the number of distinct solutions of the equation \[ z^3 + \bar{z} = 0 \] is:
If the determinant of a 3rd order matrix \( A \) is \( K \), then the sum of the determinants of the matrices \( (AA^T) \) and \( (A - A^T) \) is:
While solving a system of linear equations \( AX = B \) using Cramer’s rule, if \includegraphics[]{6.png}
If \( f(x) = \sqrt{x - 1 \) and \( g(f(x)) = x + 2\sqrt{x} + 1 \), then \( g(x) \) is:}
For all positive integers \( n \), if \( 3(5^{2n+1}) + 2^{3n+1 \) is divisible by \( k \), then the number of prime numbers less than or equal to \( k \) is:}
If \( \alpha, \beta, \gamma \) are the roots of the determinant equation: \[ \begin{vmatrix} 1-x & -2 & 1
-2 & 4-x & -2
1 & -2 & 1-x \end{vmatrix} = 0 \] then \( \alpha \beta + \beta \gamma + \gamma \alpha \) is:
If a function \( f: \mathbb{R} \to \mathbb{R} \) is defined by \( f(x) = x^3 - x \), then \( f \) is:
It is given that in a random experiment, events A and B are such that \( P(A) = \frac{1}{4} ,P(A|B) = \frac{1}{2} \) and \( P(B|A) = \frac{2}{3} \). Then \( P(B) \) is:
If the mean of the data 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of the data:
A unit vector perpendicular to the vectors \( \bar{a} = 2\bar{i} + 3\bar{j} + 4\bar{k} \) and \( \bar{b} = 3\bar{j} + 2\bar{k} \) is:
If \( \bar{a} = -4\bar{i} + 2\bar{j} + 4\bar{k} \), \( \bar{b} = \sqrt{2} \bar{i} - \sqrt{2} \bar{j} \) are two vectors, then the angle between the vectors \( 2\bar{a} \) and \( \frac{\bar{b}}{2} \) is:
The orthogonal projection vector of \( \bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k} \) on \( \bar{b} = \bar{i} - 2\bar{j} + \bar{k} \) is:
If \( AB = 2i + 3j - 6k \), \( BC = 6i - 2j + 3k \) are the vectors along two sides of a triangle ABC, then the perimeter of triangle ABC is:
If the vectors \(a\bar{i} + \bar{j} + \bar{k}\), \(\bar{i} + b\bar{j} + \bar{k}\), \(\bar{i} + \bar{j} + c\bar{k}\) (\(a \ne b \ne c \ne 1\)) are coplanar, then \(\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =\)
In \( \triangle ABC \), \( (r_2 + r_3) \csc^2 \frac{A}{2} =\)
In \( \triangle ABC \), evaluate: \[ \frac{r_2 (r_1 + r_3)}{\sqrt{r_1 r_2 + r_2 r_3 + r_3 r_1}}. \]
Evaluate \( \cosh (\log 4) \):
If \( 0<x<\frac{1}{2} \) and \( \alpha = \sin^{-1} x + \cos^{-1} \left(\frac{x}{2} +\frac{\sqrt{3} - 3x^2}{2} \right) \), then \( \tan \alpha + \cot \alpha = \):
The general solution of \( \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} \) is:
If A, B, C are the angles of a triangle, then \(\frac{\sin A + \sin B + \sin C}{\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} - 1} =\)
Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]
Evaluate the sum: \[ \tan^2 \frac{\pi}{16} + \tan^2 \frac{2\pi}{16} + \tan^2 \frac{3\pi}{16} + \tan^2 \frac{4\pi}{16} + \tan^2 \frac{5\pi}{16} + \tan^2 \frac{6\pi}{16} + \tan^2 \frac{7\pi}{16} \]