IIT JEE , AIEEE Forum - Mathematics , Algebra

uday_zingtudor

For the first question,

[625/5] + [625/5²] + [625/5³] + [625/5⁴] + .... where [] is GIF

This gives u 156.

2)If N=p₁^a1p₂^a2p₃^a3...................pn^_an_,then sum of all the divisors is (1+p₁+p₁²+p³+...p₁^a1)(1+.......+p₂^a2)..............(1+.....+p_n^an)
and that equals {(p1^(a₁+1)-1)/(p₁-1)}{............}{(pn^(a_n+1)-1)/(pn-1)}

That gives u (2⁴-1)[(5³-1)/4][(7⁵-1)/6]

4) Well u can have nc2 pts of intersection.

So ^n_c2C₂new lines.

3)Consider american women.They can shake hands with all 10 indians and 4 american men.There are 5 of them .So a total 70.And between themselves they can have 5c2, which implies 10 more.

Now consider American men Each one has 5 indians and there are 5 of them making a total of 25.Now they themselves can have 5c2.

Now the indian men can have 5c2.

The total is 125.
edit: ohh shit!!! i for got to add one thing!! Then indian women can have 5c2.

That gives the total to be 135!!

Gosh!!!! I lost ma hands typing this!!!

~Cheerio!!!

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