List of top Mathematics Questions asked in AP EAPCET

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 $a = \ln \left( \frac{1}{z^2} \right)$ 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 \( x^2 - 5x + 6 \) is a factor of \( f(x) = x^4 - 17x^3 + kx^2 - 247x + 210 \), find the other quadratic factor of \( f(x) \).
If \( a \pm bi \) 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 \( ax^2 + bx + e>0 \) 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.
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
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The general solution of the differential equation $\left( x \sin \frac{y}{x} \right) \frac{dy}{dx} = y \sin \frac{y}{x} - x$ is
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The differential equation corresponding to the family of parabolas whose axis is along $x = 1$ is
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$\lim_{n \to \infty} \left[ \frac{n+1}{n^2+1^2} + \frac{n+2}{n^2+2^2} + \frac{n+3}{n^2+3^2} + \dots + \frac{n+2n}{n^2+(2n)^2} \right] =$
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$\int (x^3 y^3) \, dx =$
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$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos x - \sin x}{\sin 2x} \, dx =$
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$\int \frac{\sin 2x}{\sin^2 x + 3 \cos x - 3} \, dx =$
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If $\int \frac{dx}{\sin^3 x + \cos^3 x} = A \log \left| \sqrt{2} + t \right| + B \tan^{-1} (t) + c$, then $\left( \frac{B}{A}, t \right) =$
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$\int_0^\pi \frac{x \sin x}{1 + \cos^2 x} \, dx =$
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$\int_0^{\frac{\pi}{2}} \frac{\sin x}{\cos x + \sin x} \, dx =$
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The value of $c$ of Rolle's theorem for the function $f(x) = 2 \sin x + \sin 2x$ in the interval $[0, \pi]$ is
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If the function $y = g(x)$ represents the slopes of the tangents drawn to the curve $y = 3x^3 - 5x^2 - 12x^2 + 18x - 3$ strictly increasing then the domain of $g(x)$ is
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Consider the following functions
I) $f(x) = \left| \frac{1}{2 - x}, x<\frac{1}{2} \right|$
II) $f(x) = \left| \frac{1}{(2 - x)^2}, x \neq 2 \right|$
III) $f(x) = |x|$
IV) $f(x) = |x|$
Then on $[0, 1]$, Lagrange's mean value theorem is applicable to the functions Identify the correct option from the following:
If $\int \left[ 3t^2 \sin^{-1} \left( \frac{1}{-t \cos t} \right) \right] \, dt = f(t) \left( \sin^{-1} \left( \frac{1}{t} \right) \right) + c$, then $f(2) =$
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