Match the following :
Column-I | Column-II |
(i) No. of ways in which one can put balls numbered 1, 2, 3 in three boxes a, b, c, such that at most one box is empty (assume any number of balls can go in each box) | [A] 18 |
(ii) No. of solution of = 1 and x + y = 6(y > 0) | [B] 24 |
(iii) If ω is an imaginary fifth root of unity, then log2 | 1 + ω + ω2 + ω3 –| equals | [C] 3 |
(iv) Minimum value of where x, y are positive real nos. is | [D] 1 |
Text Solution
Verified by Experts(i) [B]; (ii) [C]; (iii) [D]; (iv) [A]
Ans.
(i) [B]
(ii) [C]
(iii) [D]
(iv) [A]
Sol. (i) Required ways = No. of ways in which no box is empty + No. of ways by which only one box is empty
= 6 + 3 C 1 (2 3 – 2) = 24
(ii) 
= 1 = y 0 ....(i)
x 2 + 7x + 12 = 0
x = –3, –4
∴ y = 9, 10
Also y = 1 satisfy equation (i)
∴ x = 5
(iii) ω 5 = 1 and 1 + ω + ω 2 + ω 3 + ω 4 = 0
log 2 | 1 + ω + ω 2 + ω 3 – 1/ ω |
= log 2 | – ω 4 – ω 4 |
= log 2 | 2 ω 4 | = log 2 2 + log 2 | ω 4 |
= 1 + log 2 1 {| ω 5 | = 1}
= 1
(iv) use A.M. ≥ G.M.
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