1. The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer No. According to Euclid’s division lemma, a = 3q + r, where 0 ≤ r < 3 and r is an integer. Therefore, the values of r can be 0, 1 or 2. 2. Can the number 6n, n being a natural number, end with the digit 5? Give reasons. : No, because 6 n = (2 × 3) n = 2 n × 3 n , so the only primes in the factorization of 6 n are 2 and 3, and not 5. Hence, it cannot end with the digit 5. 3. Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer. No, because an integer can be written in the form 4q, 4q+1, 4q+2, 4q+3. 4. “The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons. True, because n (n+1) will always be even, as one out of n or (n+1) must be even 5. “The product of three consecutive positive integers is divisible by 6”. Is this statement true or f
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