List of top Mathematics Questions asked in AP EAPCET

If a polygon of \( n \) sides has 275 diagonals, then \( n \) is:
The coefficient of \( x^5 \) in the expansion of \( \left( 2x^3 - \frac{1}{3x^2} \right)^5 \) is:
If the point \( P \) represents the complex number \( z = x + iy \) in the Argand plane and if \[ \frac{z\bar{z} + 1}{z - 1} \] is a purely imaginary number, then the locus of \( P \) is:
The set \( S = \{ z \in \mathbb{C} : |z + 1 - i| = 1 \} \) represents:
Evaluate the sum: \[ \frac{1}{3 \cdot 7} + \frac{1}{7 \cdot 11} + \frac{1}{11 \cdot 15} + \dots \text{ up to 50 terms=} \]
If the solution of the system of simultaneous linear equations: \[ x + y - z = 6, \] \[ 3x + 2y - z = 5, \] \[ 2x - y - 2z + 3 = 0 \] is \( x = \alpha, y = \beta, z = \gamma \), then \( \alpha + \beta = ? \)
In \( \triangle ABC \), if \( a = 13 \), \( b = 14 \), and \( \cos \frac{C}{2} = \frac{3}{\sqrt{13}} \), then \( 2r_1 = \):

The range of the real valued function \( f(x) =\) \(\sin^{-1} \left( \frac{1 + x^2}{2x} \right)\) \(+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)\) is:

The real valued function \( f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) \) defined by \( f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| \) is:
If \( 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots \) (n terms) = \( n(n + 1)f(n) - 3n \), then \( f(1) = \):

If \(3A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & -2 \\[0.3em] a & 2 & b \end{bmatrix}\) and \(AA^T = I\), then\(\frac{a}{b} + \frac{b}{a} =\):

\(\begin{vmatrix} a+b+2c & a & b \\[0.3em] c & b+c+2c & b \\[0.3em] c & a & c+a2b \end{vmatrix}\)

Assertion (A): If \( B \) is a \( 3 \times 3 \) matrix and \( |B| = 6 \), then \( | \text{Adj}(B) | = 36 \). Reason (R): If \( B \) is a square matrix of order \( n \), then \( |\text{Adj}(B)| = |B|^n \).
Imaginary part of \( \frac{(1 - i)^3}{(2 - i)(3 - 2i)} \) is:
The square root of \( 7 + 24i \) is:

If \(n\) is an integer and \(Z = \cos \theta + i \sin \theta\), \(\theta \neq (2n + 1)\) \(\frac{\pi}{2}\), then: \(\frac{1 + Z^{2n}}{1 - Z^{2n}}\) = ?

If \( x \) is real and \( \alpha, \beta \) are maximum and minimum values of \( \frac{x^2 - x + 1}{x^2 + x + 1} \) respectively, then \( \alpha + \beta = \):
If \( a \) is a common root of \( x^2 - 5x + \lambda = 0 \) and \( x^2 - 8x - 2\lambda = 0 \) (\( \lambda \neq 0 \)) and \( \beta, \gamma \) are the other roots of them, then \( a + \beta + \gamma + \lambda = \):
The equation \( x^4 - x^3 - 6x^2 + 4x + 8 = 0 \) has two equal roots. If \( \alpha, \beta \) are the other two roots of this equation, then \( \alpha^2 + \beta^2 = \):
The condition that the roots of \( x^3 - bx^2 + cx - d = 0 \) are in arithmetic progression is:

If the ratio of the terms equidistant from the middle term in the expansion of \((1 + x)^{12}\) is \(\frac{1}{256}\), then the sum of all the terms of the expansion \((1 + x)^{12}\) is:

In the expansion of \(\frac{2x+1}{(1+x)(1-2x)}\), the sum of the coefficients of the first 5 odd powers of \(x\) is:
If \[ \frac{x + 2}{(x^2 + 3)(x^4 + x^2)(x^2 + 2)} = \frac{Ax + B}{x^2 + 3} + \frac{Cx + D}{x^2 + 2} + \frac{Ex^3 + Fx^2 + Gx + H}{x^4 + x^2}, \] then \[ (E + F)(C + D)(A) = \]
If \( A, B, C \) are the angles of a triangle, then \[ \sin 2A - \sin 2B + \sin 2C = \]
Assertion (A): If \( A = 10^\circ, B = 16^\circ, C = 19^\circ \), then: \[ \tan(2A) \tan(2B) + \tan(2B) \tan(2C) + \tan(2C) \tan(2A) = 1. \] Reason (R): If \( A + B + C = 180^\circ \), then: \[ \cot\left(\frac{A}{2}\right) + \cot\left(\frac{B}{2}\right) + \cot\left(\frac{C}{2}\right) = \cot\left(\frac{A}{2}\right) \cot\left(\frac{B}{2}\right) \cot\left(\frac{C}{2}\right). \]