Re: ISI 2014 MEI

Posted by SINGHAM on Apr 03, 2014; 3:26am
URL: http://discussion-forum.276.s1.nabble.com/ISI-2014-MEI-tp7585912p7586013.html

Neha,

6. Determinant of matrix A is -ab. Now, note that p is prime, so it does not divide any integer less than p itself. But, we have to take p from 0 to p-1 only. So, a & b and for that -ab is divisible by p only if -ab is 0 in itself. So, ab can be zero if either one of a or b is zero. Suppose a is zero, so we have p-1 ways to select b from 1,...,p-1 . Similarly, if b is zero, so we have p-1 ways to select a from 1,...,p-1 . Thus, p-1+p-1 ways. But, if a and b both are 0, then also, -ab=0. So, the final answer is (p-1)+(p-1)+1=2p-1.


7. The first letter can be either A, B, or C. For each of the subsequent ones the only choice is whether it is to be the same or different from the previous one (because in each case there's only one "different" letter allowed).

There's 3 ways to make the first choice and 2 ways to make each of the 6 remaining choices.

Thus, 3*(2^6)=192


8. I am not sure, but I worked with (x-1)^3+(x-2)^3=0, which has only one real root 3/2, so in general, as no other option is there, 1 is the answer.

Please help me with systematic answer of 8.