List of top Mathematics Questions asked in AP EAMCET

Given the partial fraction decomposition: \[ \frac{4x^2 + 5}{(x - 2)^4} = \frac{A}{(x - 2)} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3} + \frac{D}{(x - 2)^4} \] then the value of \[ \sqrt{\frac{A}{C} + \frac{B}{C} + \frac{D}{C}} \] is:
For \(|x|<\frac{1}{\sqrt{2}}\) the coefficient of \(x\) in the expansion of \(\frac{(1-4x)^2(1-2x^2)^{1/2}}{(4-x)^{3/2}}\) is
The independent term in the expansion of \( (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 \) is:
The number of ways of selecting 3 numbers that are in GP from the set \( \{1, 2, 3, \dots, 100\} \) is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + 3x^2 - 10x - 24 = 0. \] If \( \alpha(\beta + \gamma), \beta(\gamma + \alpha) \), and \( \gamma(\alpha + \beta) \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then find the value of \( q \).
The cubic equation whose roots are the squares of the roots of the equation \( 12x^3 - 20x^2 + x + 3 = 0 \) is:
The set of all values of \(k\) for which the inequality \(x^2 - (3k+1)x + 4k^2 + 3k - 3>0\) is true for all real values of \(x\) is
If \( (r, \theta) \) denotes \( r (\cos \theta + i \sin \theta) \). If \[ x = (1, \alpha), \quad y = (1, \beta), \quad z = (1, \gamma) \] and \( x + y + z = 0 \), then \[ \sum \cos (2\alpha - \beta - \gamma) = \]
If \( \omega \) is a complex cube root of unity and if \( Z \) is a complex number satisfying \( |Z - 1| \leq 2 \) and \[ |\omega^2 Z - 1 - \omega| = a, \] then the set of possible values of \( a \) is:
If the system of equations: \[ a_1 x + b_1 y + c_1 z = 0, \quad a_2 x + b_2 y + c_2 z = 0, \quad a_3 x + b_3 y + c_3 z = 0 \] has only the trivial solution, then the rank of the matrix: \(\left[ \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right]\) is:
If the matrix is: 
\(\left| \begin{array}{ccc} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{array} \right|>0, \text{ then } abc>?\)
If \( A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] \), then \(\text{det} (A - A^T) = \): 
The \( n^{th} \) term of the series \[ 1 + (3+5+7) + (9+11+13+15+17) + \dots \] is:
Which of the following functions are odd? 
\[ \begin{aligned} \text{I. } & f(x) = x \left( \frac{e^x -1}{e^x +1} \right) \\[8pt] \text{II. } & f(x) = k^x + k^{-x} + \cos x \\[8pt] \text{III. } & f(x) = \log \left( x + \sqrt{x^2 +1} \right) \end{aligned} \]
If \( A \subseteq \mathbb{Z} \) and the function \( f: A \to \mathbb{R} \) is defined by \[ f(x) = \frac{1}{\sqrt{64 - (0.5)^{24+x- x^2} }} \] then the sum of all absolute values of elements of \( A \) is:
If \(f(x) = \begin{cases} ax^2 + bx - \frac{13}{8}, & x \le 1 \\ 3x - 3, & 1<x \le 2 \\ bx^3 + 1, & x>2 \end{cases}\)is differentiable \(\forall x \in \mathbb{R}\), then \( a - b = \)
\[ f(x) = \begin{cases} \frac{x - |x|}{x}, & x \neq 0 \\[8pt] 2, & x = 0 \end{cases} \] Which of the following is true for \( f(x) \)
Evaluate \( \int (\log x)^m x^n dx \).
If \[ \int \frac{\sqrt[4]{x}}{\sqrt{x} + \sqrt[4]{x}} \, dx = \frac{2}{3} \left[ A \sqrt[4]{x^3} + B \sqrt[4]{x^2} + C \sqrt[4]{x} + D \log \left( 1 + \sqrt[4]{x} \right) \right] + K \] then \( \frac{2}{3} (A + B + C + D) = \)}
Evaluate the integral: \[ \int \sin^{-1} \left( \sqrt{\frac{x - a}{x}} \right) dx \]
Find the domain of \( f(x) \) given: \[ \int \frac{\sin x \cos x}{\sqrt{\cos^4 x - \sin^4 x}} dx = -\frac{f(x)}{2} + C. \] then domain of f{x) is
Given the equation: \[ y = (\tan^{-1} 2x)^2 + (\cot^{-1} 2x)^2, \] find the expression: \[ (1+4x^2)^2 y'' - 16. \]
If \( \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx = K \int_0^\pi \sin^2 x \, dx + L \int_0^\frac{\pi}{2} \cos^2 x \, dx \) and \( K, L \in \mathbb{N} \), then the number of possible ordered pairs \( (K, L) \) is}
Evaluate the integral \( \int_0^{\pi} \frac{x \sin x}{4 \cos^2 x + 3 \sin^2 x} dx \):
If \( (a, b) \) is the stationary point of the curve \( y = 2x - x^2 \), then the area bounded by the curves \( y = 2x - x^2 \), \( y = x^2 - 2x \), and \( x = a \) is: