X Maths Sample paper for chapter Real number with ...:
1. The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer
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 6n = (2 × 3)n = 2n × 3n, so the only primes in the factorization of 6n 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......................................
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