List of top Mathematics Questions asked in AP EAPCET

If a polygon of $n$ sides has 560 diagonals, then $n$ = ?
If $f(x) = ax^2 + bx + c$ for some $a, b, c \in \mathbb{R}$ with $a + b + c = 3$ and \[ f(x+y) = f(x) + f(y) + xy,\quad \forall x, y \in \mathbb{R} \] Then $\sum_{n=1}^{10} f(n) = $ ?
If the identity $\cos^4\theta = a\cos4\theta + b\cos2\theta + c$ holds for some $a, b, c \in \mathbb{Q}$, then $(a, b, c) =$ ?
Let $A = \begin{bmatrix} 5 & \sin^2\theta & \cos^2\theta \\ -\sin^2\theta & -5 & 1 \\ \cos^2\theta & 1 & 5 \end{bmatrix}$, then the maximum value of $\det(A)$ is:
The number of positive real roots of the equation \[ 3^{x+1} + 3^{-x+1} = 10 \] is:
Solve: $iz^3 + z^2 - z + i = 0 \Rightarrow |z| = $ ?
If $\dfrac{x - 1}{3 + i} + \dfrac{y - 1}{3 - i} = i$, then the true statement among the following is:
The number of integer solutions of the equation $|1 - i|^x = 2^x$ is:
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
Given $a_i^2 + b_i^2 + c_i^2 = 1$ and $a_i a_j + b_i b_j + c_i c_j = 0$ for $i \neq j$, and
\[ A = \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix} \] Then $\det(AA^T) = $ ?
If $A = \frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\-6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}$, then $A^{-1} = $ ?
If $A = \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix}$ and $\det(A^{10}) = 1024$, then $\alpha =$ ?
The range of the real valued function \[ f(x) = \sqrt{\frac{x^2 + 2x + 8}{x^2 + 2x + 4}} \] is

Given: \[ \lim_{x \to a} \left\lfloor \left( \frac{x^3}{a} - \left\lfloor \frac{x}{a} \right\rfloor^3 \right) \right\rfloor = k, \quad \lim_{x \to a} \left( \left\lfloor \frac{x^3}{a} \right\rfloor - \left\lfloor \frac{x}{a} \right\rfloor^3 \right) = l \] Then: \[ \boxed{?} \]

The equation √5·y − √8 = 0 is the directrix of a hyperbola:

x² / a² − y² / b² = 1

and the eccentricity is e = √5 / 2. 

Find the value of a.

The mean deviation about the mean for the given data:  

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If \(\cosec\, x = \frac{4}{5}\), then \( \cosh x = \) ?

Let \[ f(x) = \begin{cases} \frac{1 - \sin^3 x}{3 \cos^2 x}, & x<\frac{\pi}{2} \\ \alpha, & x = \frac{\pi}{2} \\ \frac{\beta(1 - \sin x)}{(\pi - 2x)^2}, & x>\frac{\pi}{2} \end{cases} \] If \( f(x) \) is continuous at \( x = \frac{\pi}{2} \), find \( \alpha \beta \).

Let f : ℝ → ℝ be a function such that:

|f(x) − f(y)| ≤ ½ |x − y|, for all x, y ∈ ℝ 

f′(x) ≥ ½, for all x ∈ ℝ, and f(1) = ½

Find the number of points of intersection of the curves:

y = f(x) and y = x² − 2x − 5

The derivative of the function $f(x) = \sin(x^2)$ at $x = \sqrt{\pi}$ is
The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation
If the slope of the tangent at a point $(x,y)$ on a curve is $\frac{y-4}{x}$ and the curve passes through $(4,3)$, then the point where it cuts the line $y=x$ is
By multiplying with $e^{\int P dx}$ on both sides of the equation $\frac{dy}{dx} + P(x)y = Q(x)$, the left side of the equation takes the form $\frac{d}{dx} (y f(x))$, then $f(x) =$
Evaluate the integral \( \int \frac{x^2 - 2}{x^3 \sqrt{x^2 - 1}} \, dx \)
Let \( f(x) = \int \frac{e^{3x}}{4 + 8e^{2x} + e^{4x}} \, dx \), and \( g(x) = \int \frac{2\, dx}{e^{3x} + 8e^x + 4e^{-x}} \), then \( f(x) - g(x) = \) ?