1.CAN ANYBODY SOLVE DIS PROBLEM 4 ME? WAT LL B THE REMAINDER WHEN1+11^11+111^111+1111^1111+..................+1111111111^1111111111 IS DIVIDED BY 100?2.3^36-1=1A009463A296999120 , WHERE A IS A SINGLE DIGIT NATURAL NO.WHAT Z D VALUE OF A?a.5 b.1 c.2 d.8 |
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Answer to Q1.
Reminder of 111111 = (11 +100 )111 = Reminder of 11111
Reminder of 11111111 = (11 +1100 )111 = Reminder of 111111
SO Reminder of 1+11^11+111^111+1111^1111+..................+1111111111^1111111111 IS DIVIDED BY 100
= Reminder of 1+11^11+11^111+11^1111+..................+11^1111111111 IS DIVIDED BY 100
Now
All the terms except 1 'll give a reminder 11 when divided by 100
1111 = (1 +10 )11 = ( 1 + 11 C1 10 + 100 K)
SO Reminder of 1+11^11+11^111+11^1111+..................+11^1111111111 DIVIDED BY 100
= Reminder of 1 + 11 + 11 + 11 +.................. + 11 DIVIDED BY 100
= Reminder of 100 DIVIDED BY 100
= Answer is ZERO (0)
Q 1.
same approach as defined above...no need to do calculations at al...one can do orally also in CAT...basics f binomials is required..
Q:2
how i solved that: i took into account that {sum of no should be divisible(if A is taken into aaccount)-1}..clearly only option b satisfies that.
hi imhimanshu
i don't understand why u opted for option 'b'. As,putting value of A=5,8 also make R.H.S divisible by 3.
then why option 'b' is the answer????????
n/a
Thanks for pointing the mistake..
I was applying some other logic and also there was some mistake in my calculation..
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