KVPY SX SB Exam 2012 Question Paper

Question : 15 of 120

Marks: +1, -0

Let

S_n = ∑↖{n}↙{k=1}

denote the sum of the first n positive integers. The numbers

S_1,S_2,S_2,...,S_99

are written on 99 cards. The probability of drawing a card with an even number written on it is

Solution:

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
99th term

={99×100}/2=\even

Total even terms = 48 + 1 = 49
Probability

=49/99

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