Mark the correct alternative in each of the following:

If a = (−1) × (−1) × (−1) × ... 100 times and b = (−1) × (−1) × (−1) × ... 95 times, then a + b =

(a) −1 (b) −2 (c) 0 (d) 1

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Solution

a = (−1) × (−1) × (−1) × ... 100 times

Here, the number of integers in the product is even.

∴ a = (−1) × (−1) × (−1) × ... 100 times

= 1 × 1 × 1 × ... 100 times

= 1

b = (−1) × (−1) × (−1) × ... 95 times

Here, the number of integers in the product is odd.

∴ b = (−1) × (−1) × (−1) × ... 95 times

= −(1 × 1 × 1 × ... 95 times)

= −1

So,

a + b = 1 + (−1) = 0

Hence, the correct answer is option (c).

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