Class 10 Maths Number System Sample Paper

Class 10 Maths Sample Paper | Chapter: Number Systems

Prepare for your exams with this Class 10 Mathematics: Number Systems Solved Worksheet, a premium bilingual (Hindi + English) practice resource strictly based on the latest CBSE & NCERT 2025–26 syllabus. This worksheet focuses on the most scoring unit Real Numbers and includes PYQ-based numericals on decimal expansion, HCF–LCM using prime factorisation, and standard irrational number proofs (√3, √5). Designed for quick revision and exam confidence, this worksheet contains 10 high-yield questions with a hidden answer panel and step-wise solutions.

Number Systems – Solved Worksheet

Section A: Very Short Answer (1 Mark Each)

Q1. Check whether the decimal expansion of 7/250 will terminate or not.

जाँचिए कि 7/250 का दशमलव विस्तार समाप्त होगा या नहीं।

Q2. Without performing division, determine the nature of the decimal expansion of 13/(2³ × 5²).

बिना भाग दिए बताइए कि 13/(2³ × 5²) का दशमलव विस्तार किस प्रकार का होगा।

Q3. Is the number 0.1010010001… rational or irrational?

संख्या 0.1010010001… rational है या irrational?

Q4. Is √81 + √2 a rational number? Give reason.

क्या √81 + √2 एक rational संख्या है? कारण बताइए।

Section B: Short Answer (2 Marks)

Q5. Find the HCF of 180 and 252 using prime factorisation method.

Prime factorisation विधि से 180 और 252 का HCF निकालिए।

Q6. Check whether the decimal expansion of 17/800 will terminate or not.

जाँचिए कि 17/800 का दशमलव विस्तार समाप्त होगा या नहीं।

Q7. Prove that √5 is an irrational number.

सिद्ध कीजिए कि √5 एक irrational संख्या है।

Section C: Numerical & Long Answer (3–4 Marks)

Q8. Two bells ring at intervals of 72 seconds and 120 seconds respectively. If they ring together at a certain time, after how many seconds will they ring together again?

दो घंटियाँ क्रमशः 72 सेकंड और 120 सेकंड के अंतराल पर बजती हैं। यदि वे किसी समय एक साथ बजें, तो कितने सेकंड बाद वे फिर से एक साथ बजेंगी?

Q9. Using prime factorisation method, find the HCF and LCM of 135 and 225. Also verify that HCF × LCM = product of the two numbers.

Prime factorisation विधि से 135 और 225 का HCF तथा LCM निकालिए तथा सत्यापित कीजिए कि HCF × LCM = दोनों संख्याओं का गुणनफल।

Q10. Prove that √3 is an irrational number.

सिद्ध कीजिए कि √3 एक irrational संख्या है।

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Detailed Solutions (विस्तृत समाधान)

Ans 1: Since 250 = 2 × 5³, the decimal expansion of 7/250 is terminating.

Ans 2: Denominator has only powers of 2 and 5, hence the decimal expansion is terminating.

Ans 3: The decimal is non-terminating and non-recurring, hence it is irrational.

Ans 4: √81 = 9 (rational) and √2 is irrational. Their sum is irrational.

Ans 5: HCF of 180 and 252 using prime factorisation is 36.

Ans 6: 800 = 2⁵ × 5², hence the decimal expansion of 17/800 is terminating.

Ans 7: Assuming √5 is rational leads to contradiction. Hence √5 is irrational.

Ans 8: LCM of 72 and 120 = 360 seconds. Bells will ring together after 360 seconds.

Ans 9: HCF = 45, LCM = 675. Verification: 45 × 675 = 135 × 225 ✔

Ans 10: Assuming √3 rational leads to contradiction. Hence √3 is irrational.