EASY
10th CBSE
IMPORTANT
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The product of two consecutive positive integers is divisible by 2.

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Important Questions on Real Numbers

EASY
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 3
'The product of three consecutive positive integers is divisible by 6'.
HARD
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 4
Write whether the square of any positive integer can be of the form 3m+2, where m is a natural number. Justify your answer.
HARD
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 5
A positive integer is of the form 3q+1, q being a natural number. Can you write its square in any form other than 3m+1, i.e., 3m or 3m+2 for some integer m? Justify your answer.
MEDIUM
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 6
The number 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF525,3000?Justify your answer.
EASY
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 7

Explain why 3×5×7+7 is a composite number.

EASY
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 8
Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
EASY
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 9

Without actually performing the long division, find if 98710500will have terminating or non-terminating (repeating) decimal expansion. Give reason of your answer.

EASY
10th CBSE
IMPORTANT
NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 1 - Real Numbers>Exercise>Q 10
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form pq? Give reasons.