List of top Questions asked in AP EAPCET

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

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

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

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

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

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

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

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

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

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 \[ A= \begin{bmatrix} x & 1 & 2\\ 2 & 4 & x\\ -3 & 3 & 2 \end{bmatrix} \] 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 \[ f(x)=\frac{\log_2(x+3)}{\sqrt{x^2+3x+2}} \] is

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

The reagent \(P\) used for the reaction is

Identify the major product from the following reaction sequence

Arrange the following in increasing order of \(pK_a\) values

In which of the following, Keratin, a fibrous protein is absent?

The reaction of 1-bromohexane with aqueous \(NaOH\) solution follows the order

Identify the major product formed from the sequence of reactions given below

Identify the major product formed from the following reaction sequence

The set with only ambidentate ligands in the following is

The total number of amino acids present in insulin is

The moisture present in ammonia can be removed by using which of the following?

Which of the following ions can reduce dilute acid to give hydrogen gas?