Match the following :
Column-I | Column-II |
(i) If S = 1(1!) + 2(2!) + 3(3!) +.....+ n(n!), then (s + 1) is | [A] divisible by n! |
(ii) If n is the number of positive integral solutions of x1x2x3x4 =210 then n is | [B] divisible by n |
(iii) If Im, n = dx then mn+1. Im,n is | [C] divisible by (n+1) |
(iv) If Cr be the binomial coefficient in the expansion of (1+x)n then (2n+1) is | [D] a perfect square |
Text Solution
Verified by Experts(i) [A]; (ii) [B]; (iii) [A]; (iv) [A]
Ans.
(i) [A], [B], [C]
(ii) [B], [D]
(iii) [A], [B]
(iv) [A], [B], [D]
Sol. (i) divisible by n!, divisible by n & divisible by (n+1)
(ii) divisible by n, a perfect square
(iii) divisible by n!, divisible by n
(iv) divisible by n!, divisible by n & a perfect square
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