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![[Post New]](/templates/default/images/icon_minipost_new.gif) 4 Apr 2008 16:24:19 IST
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q1) Find maximum power of 5 in 625! q) Find sum of all factors of 235274 q) 5 american couples and 5 indian couples exchange handshakes. If no woman shakes hands with her own husband and no indian woman shakes hands with a male, find the number of handshakes possible. q) There are n straight intersecting lines , no two of them are parallel or collinear. How many new lines can be made by joining the points of intersections.
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There is no better feeling in this world than being a winner! |
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4 Apr 2008 16:49:16 IST
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1)
625!
=54!
considering all powers of 5
for 51
there are 125 multiples of 5 directly
so 125 times
for 52
625/25=25 multiples
so 25*2=50 times
For 53
5 multiples
5*3=15 times
54
1 multiple
so 4 times
Let these sums be resp P1,P2,P3,P4
now for counting max power we do not consider repetitions
when we count P1,
we count all multiples of 5
when we count P2
we already counted 1-1 power of each
so P1-P2
when we count P3
we consider P1 1-1 time
and P2 5 times
so make similar cases
and eliminate to get answer
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- Bill Gates |
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4 Apr 2008 16:50:18 IST
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are the ans as follws... 1)1+5+52+53+54 2)(1+2+22+23) (1+5+52)(1+7+72+73+74) 3)(4* 10C4)-5
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4 Apr 2008 17:10:51 IST
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1) 2500 2)1302465 3) 10C2 + (15C2 - 5C2 - 5) = 135 4)[n(n-1)/2]C2 = n/2C2C2
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"Imagination is more important than knowledge."
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4 Apr 2008 17:45:35 IST
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For the first question,
[625/5] + [625/52] + [625/53] + [625/54] + .... where [] is GIF
This gives u 156.
2)If N=p1a1p2a2p3a3...................pnan ,then sum of all the divisors is (1+p1+p12+p3+...p1a1)(1+.......+p2a2)..............(1+.....+pnan)
and that equals {(p1(a1+1)-1)/(p1-1)}{............}{(pn(an+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 nc2C2 new 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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Talk less work more!! {To be simplistic and 2 gain respect}
Eat less work more!!! {To "build" ur body}
Work less Do more!!! {2 make ur life big}
don't get scared !!!
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4 Apr 2008 18:28:50 IST
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The right answers are 1) 156 2) (15)(31)(2801) = 1302465 3) 135 4) nC2C2 - n(n-1C2) i need more replies plz!
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4 Apr 2008 18:31:01 IST
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uday_zingtudor is right for the first one except his calc is wrong the answer shd be 156
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4 Apr 2008 18:33:21 IST
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edit
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Impossible To be Impossible is Impossible |
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4 Apr 2008 18:33:47 IST
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Aa yeah that was a calculation mistake!!
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4 Apr 2008 18:40:29 IST
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What about that lines answer??? I couldn't get it!!
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4 Apr 2008 19:07:01 IST
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"new" lines are asked...if you do (nc2)c2 you will get some old lines too, now how many of them , that i need to know!!
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4 Apr 2008 19:19:09 IST
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Okay, got it man!!
As none of the lines were parallel, on each line there are n-1 points of intersection.
those n-1 points correspond to n-1C2 new lines which are nothing but the same line!! There are n such lines.
So, you must subtract n(n-1C2) from nc2C2 .
~Cheerio!!
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Talk less work more!! {To be simplistic and 2 gain respect}
Eat less work more!!! {To "build" ur body}
Work less Do more!!! {2 make ur life big}
don't get scared !!!
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