MCQ

Solve the following question and mark the best possible option.

Let A = { 3, 6, 9, 12, ......., 696, 699} & B = {7, 14, 21, .........., 287, 294}

Find no. of ordered pairs of (a, b) such that a ∈ A, b ∈ B, a ≠ b & a + b is odd.

#### Options

4879

4893

2436

2457

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#### Solution

A has `699/3` = 233 elements of which 116 are even & 117 are odd.

B has `294/7= 42` elements out of which 21 are even & 21 are odd.

A∩B = { 21, 42, ........, 273, 294}

∴ n(A ∩ B) = 14

For choice of a & b, 2 cases arise:-**Case- I:** a is even & b is odd.

No. of possible cases = `""^116C_1 xx ""^21C = 116 xx 21`

**Case-II:** a is odd & b is even:-

No. of possible cases = `""^117C_1 xx ""^21C` = 117 x 21

But there are 14 cases where a = b & a, b, x A∩B.

So, required answer = 116 x 21 + 117 x 21 - 14 = **4879.**

Concept: Number System (Entrance Exam)

Is there an error in this question or solution?

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