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![[Post New]](/templates/default/images/icon_minipost_new.gif) 6 Apr 2007 13:09:41 IST
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hi plz help all of u Q) 7103 is divided by 25 , the remainder is??? Q) (32)32 the last no. is??????????
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6 Apr 2007 13:30:43 IST
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7103=7.7102=7.(49)51=7(50-1)51
expand binomially
7(51C05051 + 51C15050(-1)1+...........+ 51C51(-1)51)
all those terms which have 50n ,for n>0 will be divisible by 25
now in this expansion only one term is there which doesnot have 50
and that is last term i.e -1
multiplying by 7 it will be -7 7 from outside bracket
so remailder will be 25-7=18
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here's a shortcut
in every qs which has single term raise to the power tripple term ....................
remainder = divisor - single term
= 25 - 7 = 18
fr 2nd qs it has another shrtct
ans is 3*2 = 6 so last no. is 6
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I always like to walk in rain as no one can see me crying there :(
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6 Apr 2007 13:38:46 IST
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if u donot understand 1st qs here's another e.
(5)^104 wen divided by 21 leaves remainder = 21 - 5 = 16
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I always like to walk in rain as no one can see me crying there :(
frnds are like diamonds , if u hit them , they don't break but they slip frm ur hands
-----It is better to be hated for what you are than to be loved for what you are not.----
*****wen love and skill work together--expect a masterpiece*****
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6 Apr 2007 13:56:33 IST
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wonderful man !! chimanshu !!!!!!!!!!! dude i must say u got the killing factor in this quest.. gud one !~
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everything's fair in love , war and IIT JEE
   
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6 Apr 2007 13:59:03 IST
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gr8 shorcut himanshu!!!!!!!!!
thanks. ill bookmark this one!!!!!
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6 Apr 2007 14:10:25 IST
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thanx
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I always like to walk in rain as no one can see me crying there :(
frnds are like diamonds , if u hit them , they don't break but they slip frm ur hands
-----It is better to be hated for what you are than to be loved for what you are not.----
*****wen love and skill work together--expect a masterpiece*****
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6 Apr 2007 14:51:31 IST
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Himanshu's method is great! Here's another method. 7 2  (-1)(mod25) So (7 2) 51 (-1)(mod25) 7 102 (-1)(mod25) 7 103 (-7)(mod25) (18)(mod25) So the remainder is 18 32 2(mod10) So 32 5 2(mod10) 32 25 2(mod10) 32 25*32 5 4(mod10) So 32 32 16(mod10) 6(mod10) So the last digit is 6
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ADARSH
NITK Surathkal
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6 Apr 2007 15:23:28 IST
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thanku all of u!!!!!!!!!!!!!!!!
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