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Let S(n)=sum(k=1)^(n)k denote the sum of...

Let `S_(n)=sum_(k=1)^(n)k` denote the sum of the first n positive integers. The numbers `S_(1),S_(2),S_(3),……S_(99)` are written on 99 cards. The probability of drawing a card with an even number written on it is -

A

`1//2`

B

`49//100`

C

`49//99`

D

`48//99`

Text Solution

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The correct Answer is:
C
1,3,6,10,15,21,28,36,45,55,66,78,91,105 till 98 terms
48 terms are even and 48 terms odd
`99^(th)` term `=(99xx100)/(2)`=even
Total even terms = `48+1=49`
Probability `=(49)/(99)`
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