List of top Questions asked in AP EAPCET

If \(A + B + C = \dfrac{\pi}{4}\), then \(\sin 4A + \sin 4B + \sin 4C =\)
In \(\triangle ABC\), if \(a + c = 5b\), then \(\cot\dfrac{A}{2} \cdot \cot\dfrac{C}{2} =\)
If \[ \binom{p}{q} = \binom{p}{q} \quad \text{and} \quad \sum_{i=0}^m \binom{10}{i} \binom{20}{m-i} \text{ is maximum, then find } m. \]
Coefficient of $x^2$ in the expansion of $(x^2 + x - 2)^5$ is
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
If the polynomial \( f(x) = x^4 + ax^3 + bx^2 + cx + d \) is divided by \( x - 1 \) and \( x + 1 \), the remainders are 5 and 3 respectively. If \( f(x) \) is divided by \( x^2 - 1 \), then the remainder is
If all letters of the word COMBINATION are arranged to form 11-letter words with \( C \) and \( N \) at the ends and no vowel in the middle position, find the number of such words.
The number of ways of distributing 3 dozen fruits (no two fruits are identical) to 9 persons such that each gets the same number of fruits is
The roots $\alpha, \beta$ of the equation \[ x^2 - 6(k-1)x + 4(k-2) = 0 \] are equal in magnitude but opposite in sign. If $\alpha>\beta$, then the product of the roots of the equation \[ 2x^2 - \alpha x + 6\beta (\alpha + 1) = 0 \] is
If \( ax^2 + bx + e>0 \) for all \( x \in \mathbb{R} \) and the expressions \( cx^2 + ax + b \) and \( ax^2 + bx + c \) have their extreme values at the same point \( x \), then for the expression \( cx^2 + ax + b \), find the correct statement regarding its extreme value.
If \( x^2 - 5x + 6 \) is a factor of \( f(x) = x^4 - 17x^3 + kx^2 - 247x + 210 \), find the other quadratic factor of \( f(x) \).
If $a = \ln \left( \frac{1}{z^2} \right)$ and $z$ is any non-zero complex number such that $|z| = 1$, then which of the following is the correct expression for $a$?
If \( a \pm bi \) and \( b \pm ai \) are roots of \( x^4 - 10x^3 + 50x^2 - 130x + 169 = 0 \), then find the value of \( \frac{a}{b} + \frac{b}{a} \).
If \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ l & m & n \end{bmatrix} \] is a matrix such that $|A|>0$ and \[ Adj(A) = \begin{bmatrix} 0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4 \end{bmatrix}, \] then find the value of \[ \frac{cd}{fb} + \frac{ln}{em}. \]
In solving a system of linear equations \(AX = B\) by Cramer's rule, in the usual notation, if \[ \Delta_1 = \begin{vmatrix} -11 & 1 & -7\\ -4 & 1 & -2 \\ 5 & 1 & 1 \end{vmatrix} \quad \text{and} \quad \Delta_3 = \begin{vmatrix} 4 & 1 & -11 \\ 3 & 1 & -4 \\ 4 & 1 & 5 \end{vmatrix}, \quad \text{then } X = ? \]
If $2.5 + 5.9 + 8.13 + 11.17 + \ldots$ to $n$ terms = $an^3 + bn^2 + cn + d$, then find $a - b - c - d$
What are x and y in the following set of reactions?
The improper functioning of 'X' results in Addison's disease. Hormone 'Y' is responsible for the development of secondary female characteristics. 'X' and 'Y' are respectively:
Observe the following reactions:
The order of reactivity of x, y, z towards SN1 reaction
The order of reactivity of x, y, z towards S\textsubscript{N}1 reaction is:
Consider the following sequence of reactions:
isopropyl benzene
The incorrect statement about compound \( z \) is:
What are x and y in the following reaction sequence?
x and y in the following reaction sequence?
When ethyl bromide and \textit{n}-propyl bromide are allowed to react with Na metal in dry ether, the number of different alkanes formed is:
Arrange the products I, II, III from the following reactions in decreasing order of their acid strength.
Arrange the products I, II, III
Which of the following is not an example of an antacid?
The alloy that contains copper and Zn is $x$ and the one that contains copper and Ni is $y$. What are $x$ and $y$ respectively?