Question
The probability of selecting 2 one-rupee coins from a
collection of 'a' one-rupee coins and 4 two-rupee coins is 1/3. Determine the probability of randomly choosing a two-rupee coin from a set consisting of (a + 4) one-rupee coins and 2a two-rupee coins.Solution
ATQ, aC2/(a+ 4)C2 = 1/3 Or, {a(a – 1)}/{(a + 4)(a + 3)} = 1/3 Or, 3a2 – 3a = a2 + 4a + 3a + 12 Or, 2a2 – 10a – 12 = 0 Or, 2a2 – 12a + 2a – 12 = 0 Or, 2a(a – 6) + 2(a – 6) = 0 Or, (a – 6)(2a + 2) = 0 Since, the number of coins cannot be negative, therefore a = 6 Number of one rupees coins = a + 4 = 10 Number of two rupees coins = 2a = 12 Total number of coins = 10 + 12 = 22 Required probability = 12/22 = 6/11
If 6 4 x 5.75 9,
Then, (x²-1) = ?
...3 2 10 ? 17 16
...16, 8, 8, ?, 24, 60
Identify the given logic and complete the series with the correct option. 12, 15, 18, 20,?
?     12     24     44     74     116
...6   16  ?     244  1,245  7,506  52,591
4                14                  130                     512                �...
29    51    95    183    ?     711
1001, 728, 513, 342, 217, ?
6 3.5 2.5 ? 8.5 23.75
...
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