Q21GATE 2003MCQ

n couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is

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Q22GATE 2003MCQ

Let $\Sigma$ = (a, b, c, d, e) be an alphabet. We define an encoding scheme as follows : g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11. Let $p_{i}$ denote the i-th prime number ( $p_{i}$ =2). For a non-empty string $s=a_{1}...a_{n}$ , where each $a_{i} \in \Sigma$ , define $f(i)=\prod_{i=1}^{n}{P_{i}}^{g(a_{i})}$ . For a non-empty sequence $< s_{j},...,s_{n} >$ of strings from $\Sigma^{+}$ , define [latex]h( )=\prod_{i=1}^{n}{P_{i}}^{f(s_{i})}[/latex] Which of the following numbers is the encoding, h, of a non-empty sequence of strings?

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Q23GATE 2003MCQ

In a permutation $a_1.....a_n$ of n distinct integers, an inversion is a pair $(a_i, a_j)$ such that $i \lt j$ and $a_i \gt a_j$ . If all permutation are equally likely, what is the expected number of inversions in a randomly chosen permutation of 1.....n?

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Q24GATE 2001MCQ

How many 4-digit even numbers have all 4 digits distinct?

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Q25MCQ

The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is

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Q26MCQ

The number of binary strings of n zeros and k ones in which no two ones are adjacent is

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Q27MCQ

How many sub strings of different lengths (non-zero) can be formed from a character string of length n?

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Q28MCQ

The number of substrings (of all lengths inclusive) that can be formed from a character string of length n is

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Q29MCQ

Choose the correct alternatives (More than one may be correct). The number of ways in which 5 A's, 5 B's and 5 C's can be arranged in a row is:

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