List of top Mathematics Questions asked in AP EAPCET

If the function \( f \) defined by \[ f(x) = \begin{cases} \dfrac{1 - \cos 4x}{x^2}, & x<0 \\ a, & x = 0 \\ \dfrac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x>0 \end{cases} \] is continuous at \( x = 0 \), then \( a = \)
If \(\lim\limits_{x \to a^-} f(x) = p\), \(\lim\limits_{x \to a^+} f(x) = m\), and \(f(a) = k\), then which one of the following is true?
If $-\frac{2}{3}<x<\frac{2}{3}$, then the value of the $5^{th}$ term in the expansion of $\frac{1}{\sqrt{2-3x}}$ when $x = \frac{1}{2}$ is
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
The coefficient of \( x^3 \) in the power series expansion of \( \frac{1+4x-3x^2}{(1+3x)^3} \) is
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
If $-\frac{2{3}<x<\frac{2}{3}$, then the value of the $5^{th}$ term in the expansion of $\frac{1}{\sqrt{2-3x}}$ when $x = \frac{1}{2}$ is}
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
For all $n \in \mathbb{N}$, if $n(n^2+3)$ is divisible by $k$, then the maximum value of $k$ is
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done 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 \(x\) is so large that terms containing \(x^{-3}\), \(x^{-4}\), \(x^{-5}\), \ldots can be neglected, then the approximate value of \[ \left(\frac{3x - 5}{4x^2 + 3}\right)^{-4/5} \] is:
The number of all possible positive integral solutions of the equation \(xyz = 30\) is:
The number of divisors of \(7!\) is:
If \( x \) is a positive real number and the first negative term in the expansion of \[ (1 + x)^{27/5} \text{ is } t_k, \text{ then } k =\ ? \]
Find the determinant of the matrix: $$ \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} $$
Evaluate the following expression: \[ \frac{1}{81^n} - \binom{2n}{1} . \frac{10}{81^n} + \binom{2n}{2} . \frac{10^2}{81^n} - .s + \frac{10^{2n}}{81^n} = ? \]
The coefficient of $x^{10}$ in the expansion of $\left(x + \frac{2}{x} - 5 \right)^{12}$ is
The terms containing \( x^r y^s \) (for certain r and s) are present in both the expansions of \( (x+y^2)^{13 \) and \( (x^2+y)^{14} \). If \( \alpha \) is the number of such terms, then the sum \( \sum_{r,s} \alpha (r+s) = \) (Note: The sum is over the common terms)}
The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
If \((1+x)^n = \sum_{r=0}^n \binom{n}{r} x^r\), then the value of \[ C_0 + (C_0 + C_1) + (C_0 + C_1 + C_2) + \cdots + (C_0 + C_1 + \cdots + C_n) \] is:
If a team of 4 persons is to be selected out of 4 married couples to play mixed doubles tennis game, then the number of ways of forming a team in which no married couple appears is
The terms containing \( x^r y^s \) (for certain r and s) are present in both the expansions of \( (x+y^2)^{13} \) and \( (x^2+y)^{14} \). If \( \alpha \) is the number of such terms, then the sum \( \sum_{r,s} \alpha (r+s) = \) (Note: The sum is over the common terms)
Coefficient of $x^2$ in the expansion of $(x^2 + x - 2)^5$ is