List of top Questions asked in AP EAPCET- 2023

The value of the following expression is: \[ \cos \left( \frac{\pi}{2^2} \right) \cdot \cos \left( \frac{\pi}{2^3} \right) \cdot \cos \left( \frac{\pi}{2^4} \right) ... \cdot \cos \left( \frac{\pi}{2^{10}} \right) \]
If the line passing through the points \( (5,1,a) \) and \( (3,b,1) \) crosses the YZ plane at the point \( \left( 0, \frac{17}{2}, \frac{-13}{2} \right) \), then \( a + b = \):
Among the following the correct statements are:
I. Carbon black is obtained by burning hydrocarbons in a limited supply of air
II. Carbon black is obtained by burning hydrocarbons in absence of air
III. Coke is obtained by burning coal at high temperatures in a limited supply of air
IV. Coke is obtained by burning coal at high temperatures in absence of air
The probability that a non-leap year contains 53 Sundays is
If a set \( A \) has \( n \) elements, then the number of functions defined from \( A \) to \( A \) that are not one-one is:
The substitution \( x = vy \) converts which one of the following differential equations to an equation solvable by the variable separable method?
Let \([ \cdot ]\) denote the greatest integer function.
Assertion (A): \(\lim_{x \to \infty} \frac{[x]}{x} = 1\)
Reason (R): \(f(x) = x - 1\), \(g(x) = [x]\), \(h(x) = x\) and \(\lim_{x \to \infty} \frac{f(x)}{x} = \lim_{x \to \infty} \frac{h(x)}{x} = 1\):
If a circle \(S\) passing through the points \(A(1, 2)\) and \(B(2, 1)\) has its centre \(C\) located in the third quadrant at a distance of \(\frac{7}{\sqrt{2}}\) units from \(AB\), then the point \(P(1, -2)\)
If \( f(x) = \begin{vmatrix} 1 & 6 + x & 36 + x^2 \\ 0 & x - 3 & 3x^2 - 27 \\ 0 & 2x - 4 & 8x^2 - 32 \end{vmatrix} \), then \( \lim\limits_{x \to 1} \frac{f(x)}{f(-x)} \) is:
The greatest term in the expansion of $ (1+x)^{15} $, when $ x = \frac{1}{2} $ is

Match the items of List - A with those of the entries of List - B.

The degree of the polynomial \( \left( x + \sqrt{x^4 - 1} \right)^9 + \left( x - \sqrt{x^4 - 1} \right)^9 \) is:
If the standard enthalpy change (\(\Delta H^o\)) for reaction \[ \text{H}_2(g) + \text{Br}_2(l) \rightarrow 2 \text{HBr}(g) \] is \(-72.8 \, \text{kJ}\), the standard enthalpy of formation (\(\Delta H_f^o\)) of \(\text{HBr}(g)\) in \(\text{kJ mol}^{-1}\) is:
Which one of the following is a homogeneous differential equation?
The lengths of the intercepts made by a circle \(S\) on the \(X\) and \(Y\)-axes are \(\frac{2\sqrt{13}}{3}\) and \(\frac{2\sqrt{17}}{3}\) respectively. Then the equation of the circle is:
If \( 1 + \sqrt{1 + a} = (1 + \sqrt{1 - a}) \cot \alpha \) and \( 0<a<1 \), then \( \sin 4\alpha = \)
Which of the following statements regarding the damping force of a damped oscillator is NOT correct? Options:

The de Broglie wavelength of the most energetic photoelectrons emitted from a photosensitive metal of work function \( \phi \), when light of frequency \( \nu \) is incident on it, is \( \lambda \). Then find \( \nu \) in terms of Planck’s constant \( h \), mass of electron \( m \), and other constants.  

The relation between the mean life time \( \tau \) and the half life time \( T_{1/2} \) of a radioactive substance is:
If a straight line \( L \) perpendicular to the line \( 3x - 4y = 6 \) forms a triangle of area 6 square units with coordinate axes, then the minimum perpendicular distance from the point \( (1,1) \) to the line \( L \) is:
If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$
Choose the acidic oxide from the following:
The set \( \{ x \in \mathbb{R} : 16(2^x)>16^{x-1} \} \) is:
The bulk modulus \( B \) and compressibility \( k \) are related by:

Which of the following sets is correct? 

#MoleculeHybridizationGeometryNo. of lone pairs
on central atom
I\(\mathrm{SiH_4}\)\(\mathrm{sp^3}\)tetrahedral0
II\(\mathrm{BeCl_2}\)\(\mathrm{sp^2}\)linear1
III\(\mathrm{SF_4}\)\(\mathrm{dsp^3}\)seesaw1
IV\(\mathrm{SnCl_2}\)\(\mathrm{sp^2}\)bent2
V\(\mathrm{CH_4}\)\(\mathrm{sp^3}\)tetrahedral0