Welcome to StudyMats. This comprehensive educational guide for CBSE Class 10 | Quadratic Equations Important Questions| Chapter 4 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.
NCERT Class 10 Maths – Chapter 4: Quadratic Equations / एनसीईआरटी कक्षा 10 गणित – अध्याय 4: द्विघात समीकरण
20 Bilingual Questions (Paper-based + Practice) / 20 द्विभाषी प्रश्न (पेपर-आधारित + अभ्यास)
Q1. Find the discriminant of \(x^2 - 3x - 2 = 0\)
\(x^2 - 3x - 2 = 0\) का विविक्तांक ज्ञात कीजिए।
Q2. Find the nature of roots of \(x^2 - 5x + 9 = 0\)
\(x^2 - 5x + 9 = 0\) के मूलों की प्रकृति बताइए।
Q3. Find nature of roots of \(2x^2 - 4x + 2 = 0\)
\(2x^2 - 4x + 2 = 0\) के मूलों की प्रकृति बताइए।
Q4. For what value of \(k\) will \(2x^2 + kx + 3 = 0\) have equal roots?
\(2x^2 + kx + 3 = 0\) के लिए k का मान ज्ञात करें (समान मूल)।
Q5. For what value of \(m\) will \(x^2 + mx + 16 = 0\) have equal roots?
\(x^2 + mx + 16 = 0\) के लिए m का मान ज्ञात करें (समान मूल)।
Q6. Convert \(x + \frac{1}{x} = 3\) into quadratic form and find \(a+b+c\)
\(x + \frac{1}{x} = 3\) को द्विघात रूप में बदलकर \(a+b+c\) ज्ञात कीजिए।
Q7. Solve: \(2x^2 - 5x + 1 = 0\)
हल कीजिए: \(2x^2 - 5x + 1 = 0\)
Q8. Solve: \(x^2 - 7x + 10 = 0\)
हल कीजिए: \(x^2 - 7x + 10 = 0\)
Q9. Solve: \(3x^2 - 10x + 3 = 0\)
हल कीजिए: \(3x^2 - 10x + 3 = 0\)
Q10. Solve: \(4x^2 - 12x + 9 = 0\)
हल कीजिए: \(4x^2 - 12x + 9 = 0\)
Q11. Write quadratic equation with roots 3 and 5
जिसके मूल 3 और 5 हों, ऐसा द्विघात समीकरण बनाइए।
Q12. Find quadratic polynomial whose sum of zeroes = 0, product = 9
जिसके मूलों का योग 0 और गुणनफल 9 हो, ऐसा बहुपद बनाइए।
Q13. Form quadratic equation whose roots are 2 and -7
जिसके मूल 2 और -7 हों, ऐसा समीकरण बनाइए।
Q14. If one root of \(x^2 - 7x + k = 0\) is 2, find k and other root
यदि \(x^2 - 7x + k = 0\) का एक मूल 2 है, तो k और दूसरा मूल ज्ञात कीजिए।
Q15. Form quadratic equation whose roots are reciprocals of 4 and 5
जिसके मूल 4 और 5 के व्युत्क्रम हों, ऐसा द्विघात समीकरण बनाइए।
Q16. Difference of squares of two positive numbers = 180, smaller square = 8×larger number. Find numbers
दो धनात्मक संख्याओं के वर्गों का अंतर 180, छोटी संख्या का वर्ग बड़ी का 8 गुना। संख्याएँ ज्ञात करें।
Q17. Product of two consecutive positive integers = 132. Find integers
दो क्रमागत धनात्मक पूर्णांकों का गुणनफल 132। संख्याएँ ज्ञात करें।
Q18. Sum of squares of two numbers = 100, difference = 6. Find numbers
दो संख्याओं के वर्गों का योग 100, अंतर 6। संख्याएँ ज्ञात करें।
Q19. Rectangle: length = breadth + 5m, area = 84m². Find dimensions
आयत: लंबाई = चौड़ाई + 5m, क्षेत्रफल = 84m²। माप ज्ञात करें।
Q20. Train covers 300km at speed s. Speed +5km/h takes 2hrs less. Find original speed
ट्रेन 300km गति s से। गति +5km/h पर 2घंटे कम। मूल गति ज्ञात करें।
💡 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)
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