List of top Mathematics Questions asked in AP EAPCET

The number of solutions of \( \tan^{-1} 1 + \frac{1}{2} \cos^{-1} x^2 - \tan^{-1}\left(\frac{\sqrt{1+x^2} + \sqrt{1-x^2}}{\sqrt{1+x^2} - \sqrt{1-x^2}}\right) = 0 \) is
If \( \sqrt{3} \cos \theta + \sin \theta > 0 \), then the range of \( \theta \) is:
In triangle $ ABC $, if $ a = 5,\ b = 4,\ \cos(A - B) = \frac{31}{32} $, then $ c = ? $
In a triangle ABC, if $a, b, c$ are in arithmetic progression and the angle $A$ is twice the angle $C$, then $\cos A : \cos B : \cos C =$
If \( \tan(\theta - \phi) = \frac{3}{4} \) and \( \theta + \phi = \frac{\pi}{2} \), then the value of \[ \tan \left( \frac{\pi}{4} - \theta \right) + \tan \left( \frac{\pi}{4} - \phi \right) \] is:
The general solution satisfying both the equations \(\sin x = -\frac{3}{5}\) and \(\cos x = -\frac{4}{5}\) is:
If \(\cos\theta = -\frac{3}{5}\) and \(\theta\) does not lie in second quadrant, then \(\tan\frac{\theta}{2} =\)
In a $\triangle ABC$, $\frac{2(r_1 + r_3)}{a c (1 + \cos B)} =$
In triangle $ ABC $, if $ C = 120^\circ $, $ c = \sqrt{19} $, and $ b = 3 $, then $ a = ? $
Consider the following statements
Statement-I: A function \( f: A \rightarrow B \) is said to be one-one if and only if \[ f(x) = f(y) \Rightarrow x = y \]
Statement-II: A relation \( f: A \rightarrow B \) is said to be a function if \[ x = y \Rightarrow f(x) \neq f(y) \]
Then which one of the following is true?
Let \( [t] \) denote the greatest integer function and \( [t - m] = [t] - m \) when \( m \in \mathbb{Z} \). If \( k = 2[2x - 1] - 1 \) and \( 3[2x - 2] + 1 = 2[2x - 1] - 1 \), then the range of \( f(x) = [k + 5x] \) is:
Let \( g(x) = 1 + x - \lfloor x \rfloor \) and \[ f(x) = \begin{cases} -1, & x<0\\ 0, & x = 0 \\ 1, & x>0 \end{cases} \] where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \). Then for all \( x \), \( f(g(x)) = \)
The domain and range of a real valued function \( f(x) = \cos (x-3) \) are respectively.
If a real-valued function \( f : [-1, 2] \to B \) is defined by: \[ f(x) = \begin{cases} 1 - x, & \text{when } -1 \leq x \leq 1 \\ x - 1, & \text{when } 1 < x \leq 2 \end{cases} \] and if \( f \) is a surjection, then \( B = ? \)
If $ 0 \le x \le 3,\ 0 \le y \le 3 $, then the number of solutions $(x, y)$ for the equation: $$ \left( \sqrt{\sin^2 x - \sin x + \frac{1}{2}} \right)^{\sec^2 y} = 1 $$
For all \( n \in \mathbb{N} \), which of the following is less than or equal to \( \frac{3^n - 1}{2} \)?
The sum of the least positive integer and the greatest negative integer in the range of the function \( f(x) = \dfrac{x^2 - 5x + 7}{x^2 - 5x - 7} \) is:
If \( f : \mathbb{R} \to A \), defined by \( f(x) = \cos x + \sqrt{3}\sin x - 1 \), is an onto function, then \( A = \)
The set of all real values of \(x\) for which \(f(x) = \sqrt{\frac{|x|-2}{|x|-3}}\) is a well defined function is
Consider the following statements
Statement-I: A function \( f: A \rightarrow B \) is said to be one-one if and only if \[ f(x) = f(y) \Rightarrow x = y \]
Statement-II: A relation \( f: A \rightarrow B \) is said to be a function if \[ x = y \Rightarrow f(x) \neq f(y) \]
Then which one of the following is true?
The range of the real valued function \( f(x) = \cos^{-1} \left( \dfrac{3}{\sqrt{9x^2 - 12x + 22}} \right) \) is
If \( \frac{3x+1}{(x-1)(x^2+2)} = \frac{A}{x-1} + \frac{Bx+C}{x^2+2} \), then \( 5(A-B) = \)?
\[ \text{If the function } f(x) = \begin{cases} 1 + \cos x, & x \leq 0 \\ a - x, & 0 < x \leq 2 \\ x^2 - b^2, & x > 2 \end{cases} \text{ is continuous everywhere, then } a^2 + b^2 =\ ? \]
If the extreme value of the function \( f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x} \) in \(\left[0, \frac{\pi}{2}\right]\) is \(m\) and it exists at \(x = k\), then \(\cos k =\)}
Let $[x]$ represent the greatest integer less than or equal to $x$, $\{x\} = x - [x]$. Given \[ \sqrt{2} = 1.414
\text{and}
\sqrt{3} = 1.732. \] If \[ f(x) = x + \frac{x}{1 + x^2} \] is a real valued function, then find \[ f(\sqrt{2}) + f(-\sqrt{3}). \]