List of top Questions asked in AP EAPCET

\[ \sum_{r=1}^{15} r^2 \left( \frac{{}^{15}C_r}{{}^{15}C_{r-1}} \right) =\ ? \]
A string of letters is to be formed by using 4 letters from all the letters of the word “MATHEMATICS”. The number of ways this can be done such that two letters are of same kind and the other two are of different kind is
Evaluate the following expression: \[ \frac{1}{81^n} - \binom{2n}{1} . \frac{10}{81^n} + \binom{2n}{2} . \frac{10^2}{81^n} - .s + \frac{10^{2n}}{81^n} = ? \]
If \( x \) is a positive real number and the first negative term in the expansion of \[ (1 + x)^{27/5} \text{ is } t_k, \text{ then } k =\ ? \]
If \[ \frac{x^2}{(x^2 + 2)(x^4 - 1)} = \frac{A}{x^2 - 1} + \frac{B}{x^2 + 1} + \frac{C}{x^2 + 2}, \text{ then } A + B - C =\ ? \]
If \( \omega_1 \) and \( \omega_2 \) are two non-zero complex numbers and \( a, b \) are non-zero real numbers such that \[ |a\omega_1 + b\omega_2| = |a\omega_1 - b\omega_2|, \] then \( \dfrac{\omega_1}{\omega_2} \) is:
If \( \alpha \) is the common root of the quadratic equations \( x^2 - 5x + 4a = 0 \) and \( x^2 - 2ax - 8 = 0 \), where \( a \in \mathbb{R} \), then the value of \( \alpha^4 - \alpha^3 + 68 \) is:
If \( \alpha, \beta \) are the roots of \( x^2 - 5x - 68 = 0 \) and \( \gamma, \delta \) are the roots of \( x^2 - 5\alpha x - 6\beta = 0 \), then \( \alpha + \beta + \gamma + \delta = \) ?
The equation \[ x^{\frac{3}{4}(\log_{x} x)^2 + \log_{x} x^{-\frac{5}{4}}} = \sqrt{2} \] has
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then \[ (\alpha + \beta)(\beta + \gamma)(\gamma + \alpha) =\ ? \]
Benzyl amine can be prepared from which of the following reactions?
If \( f : \mathbb{R} \to A \), defined by \( f(x) = \cos x + \sqrt{3}\sin x - 1 \), is an onto function, then \( A = \)
Let \( g(x) = 1 + x - \lfloor x \rfloor \) and \[ f(x) = \begin{cases} -1, & x<0\\ 0, & x = 0 \\ 1, & x>0 \end{cases} \] where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \). Then for all \( x \), \( f(g(x)) = \)
The remainder obtained when \( (2m + 1)^{2n} \), \( m, n \in \mathbb{N} \) is divided by 8 is
A value of \( \theta \) lying between \( 0 \) and \( \dfrac{\pi}{2} \) and satisfying \[ \begin{vmatrix} 1 + \sin^2 \theta & \cos^2 \theta & 4\sin 4\theta \\ \sin^2 \theta & 1 + \cos^2 \theta & 4\sin 4\theta \\ \sin^2 \theta & \cos^2 \theta & 1 + 4\sin 4\theta \end{vmatrix} = 0 \] is:
If the system of equations \( 2x + py + 6z = 8 \), \( x + 2y + qz = 5 \) and \( x + y + 3z = 4 \) has infinitely many solutions, then \( p = \)?
Which of the following represents nucleoside of RNA?
Which of the following is not an antibiotic?
What are the major products X and Y respectively in the following set of reactions?
Fe (dark)
Which of the following will undergo methylation with CH₃Cl / anhyd. AlCl₃?
What are X and Y respectively in the following set of reactions?
cresol
Match the following:
List-I (Compound)List-II (pKa)
A) p-NitrophenolI) 15.9
B) PhenolII) 7.1
C) EthanolIII) 10.0
D) p-CresolIV) 10.2
The structures of succinic acid (X) and malonic acid (Y), respectively, are:
Which of the following methods is useful for producing semiconductor grade metals of high purity?
Observe the following (Products = .........):
P₄ + SOCl₂ → Products
P₄ + SO₂Cl₂ → Products
In both the reactions, a common product 'X' is obtained. The number of lone pair of electrons on the central atom of 'X' is: