List of top Questions asked in TS EAMCET

If \( n, K \in \mathbb{N} \) such that \( n \neq 3K \), then \( (\sqrt{3}+i)^{2n} + (\sqrt{3}-i)^{2n} = \)

If \( |Z|=2 \), \( Z_1 = \frac{Z}{2}e^{i\alpha} \) and \( \theta \) is the amp(Z), then \( \frac{Z_1^n - Z_1^{-n}}{Z_1^n + Z_1^{-n}} = \)

\( \omega \) is a complex cube root of unity and \( Z \) is a complex number satisfying \( |Z-1| \le 2 \). The possible values of \( r \) such that \( |Z-1| \le 2 \) and \( |\omega Z - 1 - \omega^2| = r \) have no common solution are

A and B are two non-square matrices. If \( P = A + B \), \( Q = A^TB \), \( R = AB^T \), then the matrices whose order is equal to the order of A are

A, C are \( 3 \times 3 \) matrices. B, D are \( 3 \times 1 \) matrices. If \( AX=B \) has a unique solution and \( CX=D \) has an infinite number of solutions, then

If \( A+2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A-B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\0 & 1 & 2 \end{bmatrix} \), then \( \text{tr}(A) - \text{tr}(B) = \)

If \( \left| \begin{matrix} 1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3 \end{matrix} \right| = A\lambda^3 + B\lambda^2 + C\lambda + D \), then \( D+A = \)

The value of the greatest positive integer \( k \), such that \( 49^k + 1 \) is a factor of \( 48(49^{125} + 49^{124} + \dots + 49^2 + 49 + 1) \) is

The inverse of the function \( y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} + 1 \) is \( x = \)

If \( f: \mathbb{R}-\{0\} \to \mathbb{R} \) is defined by \( 3f(x) + 4f\left(\frac{1}{x}\right) = \frac{2-x}{x} \), then \( f(3) = \)

1+(1+3)+(1+3+5)+(1+3+5+7)+... to 10 terms =

In Sr (Z=38), the number of electrons with \(l=0\) is x, number of electrons with \(l=2\) is y. \((x-y)\) is equal to (\(l\) = Azimuthal quantum number)

If \( \frac{2+3i}{i-2} - \frac{4i-3}{3+4i} = x+iy \), then \( 3x+y = \)

The average energy of a neutron produced in the fission of \( ^{235}_{92}U \) is

If $0 \le x \le \frac{3}{4}$, then the number of values of $x$ satisfying the equation $\text{Tan}^{-1}(2x-1) + \text{Tan}^{-1}2x = \text{Tan}^{-1}4x - \text{Tan}^{-1}(2x+1)$ is

If X is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$, $k=0,1,2,\dots,\infty$, then $P(X=3) =$

If \( f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right) \) is a real valued function then the range of \( f \) is

Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

\( (\text{CH}_3)_3\text{CH} \xrightarrow{\text{KMnO}_4} \text{X} \xrightarrow[\text{573K}]{\text{Cu}} \text{Y} \). The number of \( sp^3 \) and \( sp^2 \) carbons in Y are respectively

The range of the real valued function \( f(x)=\sin ^{-1}\left(\sqrt{x^{2}+x+1}\right) \) is

Number of all possible ways of distributing eight identical apples among three persons is

The radius of stationary state (\(n=2\)) of hydrogen atom is \(x\) pm. The radius of stationary state (\(n=3\)) of \( \text{He}^{+} \) ion (in pm) is

Which of the following solution has highest amount of solute?

The sum of bond order of \(O_2\), \(O_2^-\), \(O_2^{2-}\) and \(O_2^+\) is equal to