List of top Questions asked in AP EAPCET

Which of the following quadratic equations whose real roots \( x_1, x_2 \) satisfy the conditions \( x_1^2 + x_2^2 = 5 \), \( 3(x_1^5 + x_2^5) = 11(x_1^3 + x_2^3) \)?
If \( ^nC_{r-1} = 36 \), \( ^nC_r = 84 \), and \( ^nC_{r+1} = 126 \), then the value of \( nr^2 \) 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:
The total number of positive integral solutions \((x, y, z)\) of \( xyz = 24 \) 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:
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 \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)
If the complex numbers \( z_1, z_2, 0 \) are vertices of an equilateral triangle, then \( z_1^2 + z_2^2 = \)
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 \(A^2 + B^2 + AB =\)
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 \( A^2 + B^2 + AB = \)
Let \( z \) and \( w \) be two complex numbers such that \( \bar{z} + i\bar{w} = 0 \) and \( \text{Arg}(zw) = \pi \). Then \( \text{Arg}(z) = \)
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:
If a function \( f \) satisfies \( f(x+1) + f(x-1) = \sqrt{2}f(x) \), then \( f(x+2) + f(x-2) = \)
The domain of the real-valued function \(f(x) = \frac{\sqrt{\log_{0.5}(x-3)}}{\sqrt{x-1}}\) is:
If the system of equations \(x+y-z=6\), \(3x-y+z=2\), and \(x+ky+z=-8\) has a unique solution \(x=2\), \(y=0\), \(z=-4\), then the value of \(k\) satisfies which quadratic equation?
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 \( |a| + |b| = \)
What are the oxidation states of the three Br atoms in the molecule \( \mathrm{Br_3O_6} \)?
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:
Identify A and B from the following reaction:\ NaNO3(\xrightarrow{\Delta}\) xA + yB
Assertion (A): MgSO4 is readily soluble in water.
Reason (R): The greater hydration enthalpy of Mg2+ ions overcomes its lattice enthalpy.
At T (K), x g of a non-volatile solid (molar mass 78 g mol$^{-1}$) when added to 0.5 kg water, lowered its freezing point by 1.0°C. What is x (in g)? (K$_f$ of water at T(K) = 1.86 K kg mol$^{-1}$)
The rate constant for a zero order reaction A → products is 0.0030 mol L$^{-1}$ s$^{-1}$. How long will it take for the initial concentration of A to fall from 0.10 M to 0.075 M?