List of top Mathematics Questions on Combinatorics asked in AP EAPCET

If the coefficients of $x^{10$ and $x^{11}$ in the expansion of $(1 + \alpha x + \beta x^2)(1+x)^{11}$ are 396 and 144 respectively, then $\alpha^2 + \beta^2 =$}

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)

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 the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $(1 + \alpha x + \beta x^2)(1+x)^{11}$ are 396 and 144 respectively, then $\alpha^2 + \beta^2 =$

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)}

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 number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the same number, is

The least value of \( n \) such that \( {}^{n-1}C_6 + {}^{n-1}C_7<{}^nC_8 \) is

A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected is:

A box contains 5 white balls and 7 black balls. In how many ways can 3 balls be drawn from the box such that at least one black ball is included?}

What is the rank of the word ``MOTHER'' when all possible words are formed using all its letters and arranged in dictionary order?

The number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination is:

If \(^{10}P_r = 604800\) and \(^{10}C_r = 120\), then \(r\) is:

A question paper consists of two sections having 3 and 4 questions respectively. One question from each section is compulsory. In how many ways can a candidate select the questions?

In a plane there are \(37\) straight lines of which \(13\) pass through point \(A\) and \(11\) pass through point \(B\). Moreover, no three lines apart from the lines passing through \(A\) and \(B\) pass through the same point and no two are parallel. What is the number of points of intersection of the straight lines?

Let \(P_1,P_2,\ldots,P_{15}\) be \(15\) points on a circle. The number of distinct triangles formed by points \(P_i,P_j,P_k\) such that \(i+j+k\neq 15\), is

If \[ {}^nC_{r-1}=36,\qquad {}^nC_r=84,\qquad {}^nC_{r+1}=126, \] then the value of \(nr^2\) is

The total number of positive integral solutions \((x,y,z)\) of \[ xyz=24 \] is

The number of numbers between \(2000\) and \(5000\) that can be formed with the digits \(0,1,2,3,4\), repetition of digits not allowed, and are multiples of \(3\), is

The number of ways of distributing \(500\) dissimilar boxes equally among \(50\) persons is