PrepBharat

1. Consider all 2ⁿ – 1 non-empty subsets of the set{1, 2, 3, .... n } product of each of its elements. Sum of all these products is
a) (n + 1)!
b) (n + 1)! + 1
c) (n + 1)! – 1
d) n! – 2

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2. Consider all \[2^{n}-1\]  non-empty subsets of the set {1, 2, .... , n} . For every such subset we find the product of reciprocals of each of its elements. Sum of all these products is
a) n
b) n + 1
c) n!
d) n!-1

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3. The number of ways in which we can arrange 4 letters of the word MATHEMATICS is given by
a) 136
b) 2454
c) 1680
d) 192

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4. The number of ways in which we can distribute mn students equally among m sections is given by
a) \[\frac{\left(mn\right)!}{n!}\]
b) \[\frac{\left(mn\right)!}{\left(n!\right)^{m}}\]
c) \[\frac{\left(mn\right)!}{m!n!}\]
d) \[\left(mn\right)^{m}\]

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5. If a polygon has 90 diagonals, the number of its sides is given by
a) 12
b) 11
c) 10
d) 15

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6. Out of 10 white, 8 black and 6 red balls, the number of ways in which one or more balls can be selected is given by
a) 681
b) 691
c) 679
d) 692

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7. A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of choosing P and Q so that \[ P\cap Q \]   contains exactly two elements is
a) \[9\times ^{n}C_{2}\]
b) \[3^{n}- ^{n}C_{2}\]
c) \[2\times ^{n}C_{n}\]
d) \[ ^{n}C_{2}.3^{n-2}\]

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8. Ten different letters of an alphabet are given. Words with five letters are formed from these given letters . The number of words which have at least one of their letters repeated is
a) 69760
b) 30240
c) 99748
d) 60480

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9. The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is
a) 27378
b) 27405
c) 27397
d) 19050

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10. If \[ ^{n}C_{4}\] , \[ ^{n}C_{5}\] and \[ ^{n}C_{6}\] are in A.P., the value of n can be
a) 14
b) 11
c) 9
d) 5

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