List of top Questions asked in AP EAPCET

Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?
The value of $\dfrac{1 + \tanh x}{1 - \tanh x} =$ ?
The value of $\dfrac{\sin\theta + \sin3\theta}{\cos\theta + \cos3\theta}$ is:
In a triangle ABC, $a = 2,\ b = 3,\ c = 4$, then $\tan\left(\dfrac{A}{2}\right) = $ ?
In a triangle ABC, if $a \ne b$, then \[ \frac{a\cos A - b\cos B}{a\cos B - b\cos A} + \cos C = ? \]
How many chords can be drawn through 21 points on a circle?
If $4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1}$, then the value of $x$ is:
A person writes letters to 6 friends and addresses envelopes. In how many ways can the letters be placed so that at least two go to wrong envelopes?
If a polygon of $n$ sides has 560 diagonals, then $n$ = ?
If \[ \frac{x^4 + 24x^2 + 28}{(x^2 + 1)^3} = \frac{Ax + B}{x^2 + 1} + \frac{Cx + D}{(x^2 + 1)^2} + \frac{Ex + F}{(x^2 + 1)^3} \] then the value of $A + B + C + D + E + F =$ ?
The number of real roots of the equation \[ \frac{\sqrt{x}}{\sqrt{1 - x}} + \frac{\sqrt{1 - x}}{\sqrt{x}} = \frac{13}{6} \] is:
The total number of permutations of $n$ different things taken not more than $r$ at a time, when each thing may be repeated any number of times 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:
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) = $ ?
The number of integer solutions of the equation $|1 - i|^x = 2^x$ is:
The number of positive real roots of the equation \[ 3^{x+1} + 3^{-x+1} = 10 \] is:
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:
If $A = \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix}$ and $\det(A^{10}) = 1024$, then $\alpha =$ ?
If $A = \frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\-6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}$, then $A^{-1} = $ ?
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) = $ ?
The range of the real valued function \[ f(x) = \sqrt{\frac{x^2 + 2x + 8}{x^2 + 2x + 4}} \] is