List of top Questions asked in AP EAPCET

If \( \alpha_1, \alpha_2, \alpha_3 \) are the roots of the equation \( x^3 + 3x + 2 = 0 \), then \( \alpha_1^5 + \alpha_2^5 + \alpha_3^5 \) is:
If \( \alpha \) is the real root and \( \beta \), \( \gamma \) are the other roots of the equation \( x^3 - a^3 = 0 \, (a>0) \), then the number of common points of the curves given by \( |z - \beta| = \frac{\sqrt{3a}}{2} \) and \( |z - \gamma| = \frac{\sqrt{3a}}{2} \) is:
If matrix \( D_1 = \text{diag}(a, b, c) \), matrix \( D_2 = \text{diag}(3, 3, 3) \) and \( A \) is a skew-symmetric matrix of order 3, then
\[ \text{Tr}(D_1 D_2 A + D_2 D_1 + D_1 A + D_2 A) - \text{Tr}(D_1 + D_2) = ? \]
If \( z_1 = 2 + 5i \), \( z_2 = -1 + 4i \) and \( z_3 = i \), then
\[ \frac{|z_1 - z_3|}{|z_3 - z_2|} = ? \]
The modulus of the conjugate of \( z = \frac{-2 + i}{(1 - 2i)^2} \) is:
For \( x \in \mathbb{R} \), the minimum value of \( \frac{x^2 + 2x + 5}{x^2 + 4x + 10} \) is:
The locus of the variable point \( z = x + iy \) whose amplitude is always equal to \( \theta \), is:
If \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \), then \( A^{-1} \) = ?
If \( f(0) = 0, f(1) = 1, f(2) = 2 \) and \( f(x) = f(x-2) + f(x-3) \) for \( x = 3, 4, 5, \dots \), then find \( f(10) \).
If \( f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x} \) for \( x \in \mathbb{R} \), then find \( f(2023) \).
The rank of the matrix \( A = \begin{bmatrix} 1 & 1 & 3 \\ 2 & 2 & 1 \\ 1 & 1 & 1 \end{bmatrix} \) is:
If \( f(x) = \begin{cases} x \left( 1 + \frac{1}{2} \sin(\log x^2) \right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \)
If \( f(x) = \begin{cases} \sqrt{\pi - \cos^{-1} x}, & x = -1 \\ \frac{\sqrt{2(1 + x)}}{\pi + \cos^{-1} x}, & x \neq -1 \end{cases} \) is right continuous at \( x = -1 \), then \( \lambda = \)
If \( f(x) = \begin{cases} x^2, & 0 \le x<1 \\ \sqrt{x}, & 1 \le x \le 2 \end{cases} \), then \( \int_0^2 f(x) dx = \)
What are X and Y respectively in the following reaction? $$ CH_3CH_2CHO + 2Cu^{2+} + 5OH^- \rightarrow X + Y + 3H_2O $$
X and Y (major products) in the following reaction sequence are
X and Y (major products)
Which of the following is the geminal dichloride?
Which of the following is not correct about Grignard reagent?
Catechol and m-cresol respectively are
Hybridization of positively charged and negatively charged carbons of the following respectively are
Hybridization of positively charged
Sulphur containing amino acids of the following are
A. Serine
B. Cysteine
C. Lysine
D. Methionine
X + Y \( \rightarrow \) oleum The sum of oxidation states of central atom in X and Y is
Which one of the following has the highest molar conductivity?
Which of the following bases are present both in DNA and RNA?
bases are present both in DNA and RNA
The formula of tris (ethane -1,2- diamine) cobalt (III) sulphate is: