for the 22nd qn If two nos x and y are chosen from the set of all natural numbers the probability that x2+y2 is divisible by 5 must be
11Q21)
Sn : {n | n2+1} : Given sequence
In every 5 succesive terms of Sn , 2 terms are divisible by 5
So ,
P = Lt n → ∞ 2 \frac{[\frac{n}{5}]}{n} = \frac{2}{5}
11Q22)
Last digit Last digit
of x2 of y
1 4,9
4 1,6
9 6,1
6 9,4
5 0,5
For any x you choose probability of choosing a y such that x2 + y is divisible by 5 is 2/10 = 1/5 [ last digit of y should be any one of the two mentioned above out of 0 - 9 ]
Hence , P = \frac{1}{5}
