List of top Questions asked in AP EAPCET

If $ P = \tan 15^\circ + \cot 15^\circ $, $ Q = \tan 22\frac{1}{2}^\circ + \cot 22\frac{1}{2}^\circ $, and $ R = \sin 54^\circ + \sin 18^\circ $, then their ascending order is
When $ x $ is so small that its square and its higher powers may be neglected, then the value of $ \frac{(1 + \frac{3}{4}x)^{-4} \sqrt{(3 + x)}}{\sqrt{(3 - x)^3}} $ is approximately equal to
If $ 3 + i $ and $ 2 - \sqrt{3} $ are the roots of the equation $ f(x) = a_0 + a_1 x + a_2 x^2 + ... + a_n x^n $, where $ a_0, a_1, ..., a_n \in \mathbb{Z} $, then the least value of $ n $ and the value of $ a_0 $ are respectively:
If $ z_1 = 2 + 3i $, $ z_2 = 4 - 5i $, and $ z_3 $ are three points in the Argand plane such that $ 5z_1 + xz_2 + yz_3 = 0 $ (where $ x, y \in \mathbb{R} $) and $ z_3 $ is the midpoint of the line segment joining the points $ z_1 $ and $ z_2 $, then find $ x + y $.
If $ 1, \omega, \omega^2 $ are the cube roots of unity, then the roots of the equation $ 8z^3 - 12z^2 + 6z - 28 = 0 $ are:
The rank of the matrix \[ \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 & 8 \\ \end{pmatrix} \] is

Let $ A = \begin{bmatrix} 2 & 1 & 3 & -1 \\1 & -2 & 2 & -3 \end{bmatrix}, B = \begin{bmatrix} 2 & 1 & 0 & 3 \\1 & -1 & 2 & 3 \end{bmatrix} $, and the equation $ 2A + 3B - 5C = 0 $. Find the matrix $ C $.

The domain of the function $ y = f(x) $, where $ x $ and $ y $ are related by $ 2^x + 2^y = 2 $, is:
The range of the function $ f(x) = \begin{cases} 4x - 1, & x>3 \\ x^2 - 2, & -2 \leq x \leq 3 \\ 3x + 4, & x<-2 \end{cases} $ is:

At $ x = \frac{\pi^2}{4} $, $ \frac{d}{dx} \left( \operatorname{Tan}^{-1}(\cos \sqrt{x}) + \operatorname{Sec}^{-1}(e^x) \right) = $
At $ x = \frac{\pi^2}{4} $, $ \frac{d}{dx} \left( \operatorname{Tan}^{-1}(\cos \sqrt{x}) + \operatorname{Sec}^{-1}(e^x) \right) = $

Which of the following amine cannot be prepared by the Gabriel phthalimide synthesis method?

The preferred reagent for the following conversion is $CH_3CH_2COOH \rightarrow CH_3CH_2COCl$

Which element of group 14 decomposes steam to form dioxide and dihydrogen gas?
What are the formal charges on terminal oxygens of the ozone molecule?
The standard enthalpy of atomization of ethane according to the equation $ \text{C}_2\text{H}_6(g) \rightarrow 2\text{C}(g) + 6\text{H}(g) $ is $ 622 \, \text{kJ mol}^{-1} $. If standard mean C-H bond dissociation enthalpy is $ 99 \, \text{kJ mol}^{-1} $, the standard mean dissociation enthalpy of C-C bond (in kJ mol$ ^{-1} $) is
The photo current in a photo diode depends on:
A message signal of frequency 14 kHz is used to modulate a carrier of frequency 900 kHz. Then, the frequencies of the sidebands are:
Which of the following sets of quantum numbers is correct for an electron in 4f orbital?
Total number of angular nodes of orbitals associated with third shell $ (n=3) $ of an atom is:
An oxide of chlorine with water gives the strongest acid. The ratio of chlorine and oxygen in its formula is:
Electromagnetic waves of energy flux $ 75 \times 10^4 \, \text{W/m}^2 $ incidents normally on a surface of area $ 40 \, \text{cm}^2 $. If the surface absorbs the flux completely, the total momentum delivered to the surface in one second is: Options:
The minimum excitation energy of an electron revolving in the first orbit of hydrogen is:
The process that mainly takes place in stars to produce energy:

Switch $ S $ is closed. Now the switch is opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. The ratio of total electrostatic energy stored in the capacitors before and after the introduction of the dielectric is:

The resultant resistance between $ A $ and $ B $ in the given figure is: