Welcome to StudyMats. This comprehensive educational guide for Class 9 Maths Number Systems Test Paper| CBSE 2025–26 is prepared to assist students in preparing effectively for their school, board, and competitive examinations. All questions, exercise solutions, and concept notes strictly adhere to the latest NCERT curriculum and CBSE guidelines.
Class 9 Maths Sample Paper | Chapter: Number Systems
Number Systems – Practice Worksheet
Section A: Very Short Answer (1 Mark Each)
Q1. Is the number −7 a rational number?
क्या संख्या −7 एक परिमेय संख्या है?
Q2. Write one irrational number between 3 and 4.
3 और 4 के बीच एक अपरिमेय संख्या लिखिए।
Q3. Express 0.375 in the form of p/q.
0.375 को p/q के रूप में व्यक्त कीजिए।
Section B: Short Answer (2 Marks Each)
Q4. Represent the following numbers on the number line: √2, √5.
निम्न संख्याओं को संख्या रेखा पर दर्शाइए: √2, √5।
Q5. Find two rational numbers between 2 and 3.
2 और 3 के बीच दो परिमेय संख्याएँ ज्ञात कीजिए।
Q6. Simplify: \[ 16^{-\frac{1}{4}} \times \sqrt[4]{16} \]
सरल कीजिए: \[ 16^{-\frac{1}{4}} \times \sqrt[4]{16} \]
Q7. Find the value of x if \[ 3 + 2^x = 64^{\frac{1}{2}} + 27^{\frac{1}{3}} \]
यदि \[ 3 + 2^x = 64^{\frac{1}{2}} + 27^{\frac{1}{3}} \] हो, तो x का मान ज्ञात कीजिए।
Section C: Long Answer (3 Marks Each)
Q8. Determine rational numbers p and q if \[ \frac{7+\sqrt{5}}{7-\sqrt{5}} - \frac{7-\sqrt{5}}{7+\sqrt{5}} = p - 7\sqrt{5}\,q \]
यदि \[ \frac{7+\sqrt{5}}{7-\sqrt{5}} - \frac{7-\sqrt{5}}{7+\sqrt{5}} = p - 7\sqrt{5}\,q \] हो, तो p तथा q के मान ज्ञात कीजिए।
Q9. Simplify: \[ \frac{6}{2\sqrt{3}-\sqrt{6}} + \frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}} - \frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}} \]
सरल कीजिए: \[ \frac{6}{2\sqrt{3}-\sqrt{6}} + \frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}} - \frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}} \]
Q10. If x = 2 + 3√2, find the value of \[ \left(x + \frac{14}{x}\right) \]
यदि x = 2 + 3√2 हो, तो \[ \left(x + \frac{14}{x}\right) \] का मान ज्ञात कीजिए।
💡 Important Exam & Study Tips
- Master NCERT Fundamentals: Ensure thorough familiarity with standard textbook definitions, formulas, and in-text examples before solving advanced problems.
- Step-by-Step Presentation: In board examinations, neat presentation, correct formula application, and labeled steps earn maximum step-marking.
- Practice Under Timed Conditions: Regular practice with previous years' question papers (PYQs) builds exam speed and accuracy.
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❓ Frequently Asked Questions (FAQs)
Q1: Are these solutions aligned with the latest rationalized syllabus?
Yes, all study notes and practice questions on StudyMats strictly follow the updated NCERT textbook pattern and CBSE assessment guidelines.
Q2: How can I prepare this chapter for highest marks?
Review the theory thoroughly, solve all textbook exercise questions, and repeatedly practice the high-frequency questions provided in this guide.