Short Questions & Answers CBSE Board Class 10 English Medium Mathematics

Important Short Questions with Answers for Class 10 Real Numbers (2 & 3 Marks)

Sep 17, 2026 • Editorial Team • 891 views • 5 min read

Frequently asked 2-mark and 3-mark questions in CBSE Board examinations with complete step-by-step marking scheme answers.

Important Short Questions with Answers for Class 10 Real Numbers (2 & 3 Marks)

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Frequently asked 2-mark and 3-mark questions in CBSE Board examinations with complete step-by-step marking scheme answers.

Questions & Step-by-Step Solutions (2)

Short Answer Question (SAQ • 2-3 Marks)

Q1.

Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

Solution / Detailed Answer:

Let a be any positive odd integer and b = 4.
By Euclid's division algorithm, a = 4q + r, for some integer q >= 0, and r = 0, 1, 2, 3.
Therefore, a can be 4q, 4q + 1, 4q + 2, or 4q + 3.
Since a is odd, a cannot be 4q or 4q + 2 (both are divisible by 2).
Therefore, any positive odd integer is of the form 4q + 1 or 4q + 3.

Short Answer Question (SAQ • 2-3 Marks)

Q2.

Given that HCF(306, 657) = 9, find LCM(306, 657).

Solution / Detailed Answer:

We know that for any two positive integers a and b:
LCM(a, b) * HCF(a, b) = a * b
LCM(306, 657) * 9 = 306 * 657
LCM(306, 657) = (306 * 657) / 9 = 34 * 657 = 22,338.
Hence, LCM(306, 657) = 22,338.

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