11Yes it's (b) 9
Ques1) Let f(n) = 10 n + 3.4 n+2 + 5 , where n belongs to N. The greatest value of the integer which divides f(n) for all n is
(a) 27 (b) 9 (c)3 (d) none
Ques2) If m and n are any two odd positive integers with n < m , then the largest positive integer which divides all the numbers of the form (m2 - n2) is
(a) 4 (b) 6 (c) 8 (d) 9
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4 Answers
1(9+1)n +3(3+1)n+2 +5
1+9k+3(1+3k2)+5
9(k+k2+1)
but we cant expand with 27 as a factor
expanding 10 in terms of 27 itself we face difficulties
12 > let m=2k+1 ,n=2l+1
so m2 - l2 = 4 ( k2-l2 ) + 4 ( k - l )
as n < m so k -l > 1 , so ans . -- it should be 8 .