Algebra
Aptitude

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Q.

How many subsets of {1, 2, 3, ... , 11} contains at least one even integer?

 A.

1900

 B.

1964

 C.

1984

 D.

2048

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Solution:
Option(C) is correct

Given, set = {1,2,3,........,11}

The total number of subsets $=2^{11}$

The number of subsets which contains no even number = 26

The number of subsets which contains at least one even number

$\Rightarrow  2^{11}–2^{6}=2048−64=1984$


(1) Comment(s)


Pragya
 ()

cases to select odd no. : 2^6

cases to select even no. : 2^5

removing the case when no even is selected: 2^5 - 1

Total ways: 2^6 (( 2^5 ) - 1) = 1984