﻿ Engineering Entrance Exam Question and Answers | Permutations and Combinations - Zigya

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# Permutations and Combinations

#### Multiple Choice Questions

61.

If n is an integer with 0  11, then the minimum value of n!(11 - 1)! is attained when a value of n equals to

• 11

• 5

• 7

• 9

62.

The term independent of x in the expansions of

• ${}^{18}\mathrm{C}_{9}{2}^{12}$

• ${}^{18}\mathrm{C}_{9}{2}^{6}$

• ${}^{18}\mathrm{C}_{6}{2}^{8}$

63.

• ${}^{41}\mathrm{C}_{4}$

• ${}^{39}\mathrm{C}_{4}$

• ${}^{42}\mathrm{C}_{4}$

64.

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ...

65.

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ......

#### Multiple Choice Questions

66.

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :

• 36

• 63

• 38

• 54

67.

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

• 3000

• 2250

• 2255

• 1500

68.

• $\frac{1}{8}$

• $\frac{3}{8}$

• $\frac{7}{8}$

• $\frac{5}{8}$

Consider the data on x taking the values 0, 2, 4, 8, ...., 2n with frequencies nC0, nC1, nC2,..., nCn respectively. If the mean of this data is $\frac{728}{{2}^{\mathrm{n}}}$, then n is equal to....