CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus
NCERT Exemplar Solutions Class 10 Maths Chapter 1 Real Numbers
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Boards begin February 2027
Pre-boards are in December
Real Numbers is in Number Systems, which carries 6 of the 80 marks in the 2026-27 CBSE Maths paper
9 NCERT Exemplar questions from Chapter 1
Exercise 1.1
Exemplar Ex 1.1 Q61 mark
If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then HCF(a, b) is
Step 1HCF = product of the smallest powers of each common prime factor.
Step-by-step solution
HCF = product of the smallest powers of each common prime factor.
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Step 1We need the smallest length that is a common multiple of 40, 42 and 45 — i.e., LCM.
Step-by-step solution
We need the smallest length that is a common multiple of 40, 42 and 45 — i.e., LCM.
Since a is rational and a ≠ 0, the RHS is rational ⇒ √3 is rational. This contradicts the known fact that √3 is irrational. Hence √3 + √5 is irrational.
Answer:√3 + √5 is irrational (proof by contradiction).
CBSE board pattern: Assertion-Reason and case-based questions
Written in the CBSE board format. These are not numbered NCERT/Exemplar questions; some case studies are built on textbook problems. Neither NCERT book has Assertion-Reason questions: they, and case-based questions, are a CBSE board-paper format, here on this chapter's 2026-27 syllabus, with solutions by LazyTopper.
CBSE board pattern · Case-based4 marks
On a morning walk in a park, three friends Akash, Bhavna and Chirag take steps of length 40 cm, 42 cm and 45 cm respectively. They start together from the same point.
(i) After what minimum common distance will all three be in step together again?
(ii) If Akash takes 1 step per second, how many seconds will he take to cover this minimum distance?
Step 1(i) They will all be in step at distances that are multiples of each of 40, 42 and 45 cm. The minimum such common distance is LCM(40, 42, 45).
Step-by-step solution
(i) They will all be in step at distances that are multiples of each of 40, 42 and 45 cm. The minimum such common distance is LCM(40, 42, 45).
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Questions from the NCERT Class 10 Mathematics Exemplar Problems (the CBSE board-pattern section is in the board format, not numbered book questions); the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.