List of top Mathematics Questions asked in AP EAPCET

Evaluate the expression:
\[ \cos^3 \left( \frac{3\pi}{8} \right) \cos \left( \frac{3\pi}{8} \right) + \sin^3 \left( \frac{3\pi}{8} \right) \sin \left( \frac{3\pi}{8} \right) \]
If \(A + B + C = \dfrac{\pi}{4}\), then \(\sin 4A + \sin 4B + \sin 4C =\)
If \( A + B + C = \frac{\pi}{4} \), then evaluate the expression:
\[ \sin 4A + \sin 4B + \sin 4C \]
In a triangle ABC, if \(\sin\frac{A}{2} = \dfrac{1}{4}\sqrt{\dfrac{5}{\sqrt{5}}}, a = 2, c = 5\), and \(b\) is an integer, then the area (in sq. units) of triangle ABC is
In \(\triangle ABC\), if \(a + c = 5b\), then \(\cot\dfrac{A}{2} \cdot \cot\dfrac{C}{2} =\)
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
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 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.
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 \[ \binom{p}{q} = \binom{p}{q} \quad \text{and} \quad \sum_{i=0}^m \binom{10}{i} \binom{20}{m-i} \text{ is maximum, then find } m. \]
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 $a = \ln \left( \frac{1}{z^2} \right)$ and $z$ is any non-zero complex number such that $|z| = 1$, then which of the following is the correct expression for $a$?
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 \( f(x) \).
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 $a - b - c - d$
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 \[ \frac{cd}{fb} + \frac{ln}{em}. \]
The general solution of the differential equation $\frac{dy}{dx} + \frac{y}{x} = \frac{y}{x} e^x$ is
Identify the correct option from the following:
The general solution of the differential equation $\left( x \sin \frac{y}{x} \right) \frac{dy}{dx} = y \sin \frac{y}{x} - x$ is
Identify the correct option from the following:
$\lim_{n \to \infty} \left[ \frac{n+1}{n^2+1^2} + \frac{n+2}{n^2+2^2} + \frac{n+3}{n^2+3^2} + \dots + \frac{n+2n}{n^2+(2n)^2} \right] =$
Identify the correct option from the following:
$\int (x^3 y^3) \, dx =$
Identify the correct option from the following:
$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos x - \sin x}{\sin 2x} \, dx =$
Identify the correct option from the following:
$\int_0^\pi \frac{x \sin x}{1 + \cos^2 x} \, dx =$
Identify the correct option from the following: