List of top Questions asked in AP EAMCET

Evaluate \( \cosh (\log 4) \):
What is the radius of the second Bohr orbit of \( {He}^+ \) ion?
If \( 0<x<\frac{1}{2} \) and \( \alpha = \sin^{-1} x + \cos^{-1} \left(\frac{x}{2} +\frac{\sqrt{3} - 3x^2}{2} \right) \), then \( \tan \alpha + \cot \alpha = \):
The general solution of \( \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} \) is:
If A, B, C are the angles of a triangle, then \(\frac{\sin A + \sin B + \sin C}{\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} - 1} =\)
Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]
Evaluate the sum: \[ \tan^2 \frac{\pi}{16} + \tan^2 \frac{2\pi}{16} + \tan^2 \frac{3\pi}{16} + \tan^2 \frac{4\pi}{16} + \tan^2 \frac{5\pi}{16} + \tan^2 \frac{6\pi}{16} + \tan^2 \frac{7\pi}{16} \]
Given the partial fraction decomposition: \[ \frac{4x^2 + 5}{(x - 2)^4} = \frac{A}{(x - 2)} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3} + \frac{D}{(x - 2)^4} \] then the value of \[ \sqrt{\frac{A}{C} + \frac{B}{C} + \frac{D}{C}} \] is:
For \(|x|<\frac{1}{\sqrt{2}}\) the coefficient of \(x\) in the expansion of \(\frac{(1-4x)^2(1-2x^2)^{1/2}}{(4-x)^{3/2}}\) is
The independent term in the expansion of \( (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 \) is:
The number of ways of selecting 3 numbers that are in GP from the set \( \{1, 2, 3, \dots, 100\} \) is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + 3x^2 - 10x - 24 = 0. \] If \( \alpha(\beta + \gamma), \beta(\gamma + \alpha) \), and \( \gamma(\alpha + \beta) \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then find the value of \( q \).
The cubic equation whose roots are the squares of the roots of the equation \( 12x^3 - 20x^2 + x + 3 = 0 \) is:
The set of all values of \(k\) for which the inequality \(x^2 - (3k+1)x + 4k^2 + 3k - 3>0\) is true for all real values of \(x\) is
If \( (r, \theta) \) denotes \( r (\cos \theta + i \sin \theta) \). If \[ x = (1, \alpha), \quad y = (1, \beta), \quad z = (1, \gamma) \] and \( x + y + z = 0 \), then \[ \sum \cos (2\alpha - \beta - \gamma) = \]
If \( \omega \) is a complex cube root of unity and if \( Z \) is a complex number satisfying \( |Z - 1| \leq 2 \) and \[ |\omega^2 Z - 1 - \omega| = a, \] then the set of possible values of \( a \) is:
Which of the following is not the correct order regarding the energy of orbitals?
For an amplitude modulated wave, the maximum and minimum amplitudes are respectively 16 V and 4 V. The modulation index is:

Three logic gates are connected as shown in the figure. If the inputs are \(A = 1\), \(B = 0\) and \(C = 0\) then the values of \(y_1\), \(y_2\) and \(y_3\) respectively are: 


 

The voltage gain of a common emitter amplifier is 60. If the output and input resistances are 4 k\(\Omega\) and 2 k\(\Omega\) respectively, the power gain of the amplifier is:
The energy released in the fission of one \(_{92}^{235}{U}\) nucleus is 200 MeV. The energy released in the fission of 235 g of \(_{92}^{235}{U}\) is nearly:
If the angular momentum of an electron in the second orbit of a hydrogen atom is \(J\), then the angular momentum of an electron in the third excited state of hydrogen is:
If the matrix is: 
\(\left| \begin{array}{ccc} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{array} \right|>0, \text{ then } abc>?\)
If \( A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] \), then \(\text{det} (A - A^T) = \): 
The \( n^{th} \) term of the series \[ 1 + (3+5+7) + (9+11+13+15+17) + \dots \] is: