List of top Questions asked in AP EAPCET- 2022

In a triangle \(ABC\), \[ \frac{a-b}{a+b}= \]

Let \(\theta\in \mathbb{R}\) such that \[ 3\sinh(2\theta)=13-3e^{2\theta}, \] then \(\theta=\)

Simplify: \[ \frac{1}{1+\sin\theta}+\frac{1}{1-\sin\theta}= \]

Evaluate: \[ \cos^2 45^\circ+\cos^2 135^\circ+\cos^2 225^\circ+\cos^2 315^\circ= \]

If \(\theta\) is any angle, then \[ \sin^2\theta \cos^2\theta= \]

Let \(T_n\) be the number of all possible triangles formed by joining vertices of an \(n\)-sided regular polygon. If \[ T_{n+1}-T_n=10, \] then the value of \(n\) is

If the equivalent partial fraction of \[ \frac{x^3}{(2x-1)(x+2)(x-3)} \] is given by \[ A+\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}, \] then the value of \(C\) is

How many numbers between \(10\) and \(10,000\) can be formed by using the digits \(1,2,3,4,5\), if no digit is repeated in any number?

Evaluate: \[ (4\cos^2 9^\circ-3)(4\cos^2 27^\circ-3)= \]

The number of numbers between \(2000\) and \(5000\) that can be formed with the digits \(0,1,2,3,4\), repetition of digits not allowed, and are multiples of \(3\), is

If one root of the quadratic equation \[ ax^2+bx+c=0 \] is equal to the \(n^{th}\) power of the other, then \[ (ac^n)^{\frac{1}{n+1}}+(a^nc)^{\frac{1}{n+1}}= \]

If \(a\), \(b\), \(c\) are distinct positive real numbers and \[ a^2+b^2+c^2=1, \] then the value of \(ab+bc+ca\) is

In how many ways can the letters of the word ``ASSASSINATION'' be arranged so that all \(S\)'s are together?

If \(a\), \(b\), \(c\), \(d\) are real numbers such that \[ a\lt b\lt c\lt d, \] then the roots of the equation \[ (x-a)(x-c)+2(x-b)(x-d)=0 \] are

The sum of squares of roots of the equation \[ x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0 \] is

Evaluate: \[ (-1+\sqrt{3})^{60}= \]

For any complex number \(z\), the minimum value of \[ |z|+|z-1| \] is

If the vertices \(A\), \(B\) and \(C\) of an isosceles triangle \(ABC\) are respectively \(z_1\), \(z_2\) and \(z_3\), and if \(\angle C=90^\circ\), then

If \(\alpha_1,\alpha_2,\ldots,\alpha_{23}\) are the \(23^{rd}\) roots of unity, then \[ \alpha_1^{47}+\alpha_2^{47}+\cdots+\alpha_{23}^{47}= \]

Let \[ A= \begin{bmatrix} 1 & 0 & -1 & -3\\ 0 & 1 & 1 & k-1\\ 0 & 0 & k-1 & 1 \end{bmatrix} \] and \(k\in \mathbb{R}\). Then the value of \(k\), if exists, for which the rank of \(A\) is \(2\), is

If \[ A= \begin{bmatrix} \sin\alpha & -\cos\alpha\\ \cos\alpha & \sin\alpha \end{bmatrix} \] and \(A+A^{-1}=I\), then \(\alpha=\)

If \[ A= \begin{bmatrix} x & 1 & 2\\ 2 & 4 & x\\ -3 & 3 & 2 \end{bmatrix} \] is a singular matrix and the distinct values of \(x\) are \(x_1\) and \(x_2\), then \(x_1+x_2+x_1x_2=\)

If the system of simultaneous linear equations \[ 3x-4y+kz+13=0,\quad x+2y-z-9=0 \] \[ kx-y+3z+7=0 \] has a unique solution \(x=\alpha,\ y=\beta,\ z=\gamma\) for \(k\neq m\) and \(2\beta-\gamma=8\), then \(\alpha+m=\)

The domain of the real valued function \[ f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}} \] is

The domain of the real valued function \[ f(x)=\frac{\log_2(x+3)}{\sqrt{x^2+3x+2}} \] is