N = n (n+1) (n+2) (n+3) (n+4); where n is a natural number. Which of the following statements is/are true?
1. Unit digit of N is 0.
2. N is perfectly divisible by 24.
3. N is perfect square.
4. N is odd.

3 Only

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3 and 4 only

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1 only

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1 and 2 only

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Solution

The correct option is D 1 and 2 only
N=n(n+1) (n+2) (n+3) (n+4) is product of 5 consecutive number.
Thus divisible by 5! = 120
So, (i) unit digit is 0 TRUE.
(ii) Perfectly divisible by 24 TRUE.
(iii) N is perfect square not TRUE.
(iv) N is odd X not TRUE.
Thus (d) (i) and (ii) only.

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