13x and y are chosen from naturall numbers....
1. If 2 no.s x and y are chosen from the set of natural no.s, then probabilty that x^2 +y^2 is divisible by 5 is.....
2. If sum of two positive integers is 2n , then the probabilty that their product is grtr than 3/4th of their maximum product is .....
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9 Answers
11 ,2 ,3 , 4 , 5, 6, 7, 8, 9
1, 4, 9, 16 25,36,49,64,81
so nw u can choose those wer x^2+y^2 wil hav 0 or 5 in d unitz place
(1,2) (1,3)(2,4)(3,9)(4,8).................
they can b like 1 or 2 or say 2 or 1...........
similarly u'll get d asnwer ......
they hav said natural nos wich goes upto infi
bt we can consider a group n then it periodically egts repated so willl b d prob
621) x odd, y even or y odd, x even
Is the set of natural numbers given? :O
Or is it any natural number?
62oh sorry i made a mistake...
I put the numbers in the form 4n+1
:((
you have to take the sets
5n, 5n+1, 5n+2, 5n+3 and 5n+4
squares are
5n, 5n+1, 5n-1, 5n-1 and 5n+1
so now you can do the remaining?
622. If sum of two positive integers is 2n , then the probabilty that their product is grtr than 3/4th of their maximum product is .....
maximum product is n2
we want the product to be less than 3/4 n2
k x (2n-k) < 3/4 n2
now try
13nao i m gettin 5/9 but sir but wat i did was ...
1,4,9,6,5,0 are possible unit digits for a sq ... so 11/36.... where did i go wrong
132nd to ho gaya ...... but 1st one mein im even more confused nao.....
62depanshu,
each of those have a different probability of coming..
13ok ....i m gettin it thats bcz each of them hav cum from diff form of the no.s ....
and wat 1 did usmien i counted the same case twice...... 5n