List of top Questions asked in AP EAPCET- 2022

The smallest integer \( n \) such that \[ \frac{1}{\sin 45^\circ \sin 46^\circ} + \frac{1}{\sin 47^\circ \sin 48^\circ} + \cdots + \frac{1}{\sin 133^\circ \sin 134^\circ} = \frac{1}{\sin(n^\circ)} \]
If \( \frac{4x^3 + 16x + 7}{(x^2 + 4)^2} = \frac{Ax + B}{x^2 + 4} + \frac{Cx + D}{(x^2 + 4)^2} \), then the number of non-zero values among \( A, B, C, D \) is:
Let \( P_1, P_2, \ldots, P_{15} \) be 15 points on a circle. The number of distinct triangles formed by points \( P_i, P_j, P_k \) such that \( i + j + k \ne 15 \), is:
The range of the function \( f(x) = \frac{x^2 + x + 1}{x^2 - x + 1} \) is:
The remainder when the polynomial \( 2x^5 - 3x^4 + 5x^3 - 3x^2 + 7x - 9 \) is divided by \( x^2 - x - 3 \) is:
If \( 1, \omega, \omega^2 \) are the cube roots of unity, then evaluate: \[ (2 - \omega)^2 (2 - \omega^2)^2 (2 - \omega^{10})^2 (2 - \omega^{11})^2 \]
If \( ^nC_{r-1} = 36 \), \( ^nC_r = 84 \), and \( ^nC_{r+1} = 126 \), then the value of \( nr^2 \) is:
Let \( f(x) = x^2 + \frac{1}{x^2} \) and \( g(x) = x - \frac{1}{x} \) for \( x \in \mathbb{R} \setminus \{-1, 0, 1\} \). Then, the local minimum of \( \frac{f(x)}{g(x)} \) is:
Which of the following quadratic equations whose real roots \( x_1, x_2 \) satisfy the conditions \( x_1^2 + x_2^2 = 5 \), \( 3(x_1^5 + x_2^5) = 11(x_1^3 + x_2^3) \)?
Let \(A = \begin{bmatrix}n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n\end{bmatrix}\) and \(B = \begin{bmatrix}0 & 0 & n \\ 0 & n & 0 \\ n & 0 & 0\end{bmatrix}\). Then \(A^2 + B^2 + AB =\)
If the complex numbers \( z_1, z_2, 0 \) are vertices of an equilateral triangle, then \( z_1^2 + z_2^2 = \)
Let \( z = x + iy \) be a complex number with \( x, y \in \mathbb{Z} \). Then the area (in square units) of the rectangle whose vertices are the roots of the equation \( \bar{z} \cdot z^3 + z \cdot \bar{z}^3 = 350 \) is:
The domain of the real-valued function \(f(x) = \frac{\sqrt{\log_{0.5}(x-3)}}{\sqrt{x-1}}\) is:
The maximum value of \( f(x) = \frac{x}{1 + 4x + x^2} \) is
The minimum value of \( f(x) = x + \frac{4}{x + 2} \) is
If \( f(x) = \max \{3 - x, 3 + x, 6\} \) is not differentiable at \( x = a \) and \( x = b \), then \( |a| + |b| = \)
The bond lengths of \( \mathrm{C_2} \), \( \mathrm{N_2} \), and \( \mathrm{B_2} \) molecules are \( X_1 \), \( X_2 \), and \( X_3 \) pm respectively. The correct order of their bond lengths is:
Arrange the following in decreasing order of their pK$_b$ values:
Arrange the following in decreasing order of their pKb values:
Identify the major product formed from the following:
Nai/dry acetone
Arrange the following in increasing order of their reactivity for nucleophilic addition reaction:
Arrange the following in increasing order of their reactivity for nucleophilic addition reaction:
The catalyst used in the manufacture of polyethylene is a mixture of
The diameter range of colloidal particles is approximately:
Which of the following is correct related to the colours of TiCl$_3$ (X) and [Ti(H$_2$O)$_6$]Cl$_3$ (Y)?
Photographic plates are prepared by coating emulsion of which of the following in gelatin?
What are x and y in the following reaction?
$x \text{Pb}_3\text{O}_4 \rightarrow y \text{PbO} + \text{O}_2$