Welcome to StudyMats. This comprehensive educational guide for class 10 Pair of linear equation in two variables test paper 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 10 Maths Test Paper | Chapter: Pair of Linear Equations in Two Variables
(दो चर वाले रैखिक समीकरणों के युग्म)
Pair of Linear Equations in Two Variables – Test Paper
Time: 40 Minutes Maximum Marks: 20
Section A: Objective / Conceptual Questions
(1 × 4 = 4 marks)
Q1. (1 mark) The pair of equations \(2x + 3y = 11\) and \(4x + 6y = 22\) has:
समीकरणों का युग्म \(2x + 3y = 11\) तथा \(4x + 6y = 22\) है:
(a) कोई हल नहीं
(b) एकमात्र हल
(c) अनंत हल
(d) ठीक दो हल
Q2. (1 mark) For which value of \(k\) will the pair \(x + ky = 3\) and \(2x + 6y = 6\) have infinitely many solutions?
किस \(k\) के मान पर समीकरणों के युग्म \(x + ky = 3\) और \(2x + 6y = 6\) के अनंत हल होंगे?
(a) 1 (b) 2 (c) 3 (d) 6
Q3. (1 mark) The pair of equations \(3x - 2y = 5\) and \(6x - 4y = 7\) is:
समीकरणों का युग्म \(3x - 2y = 5\) तथा \(6x - 4y = 7\) है:
(a) संगत एवं स्वतंत्र
(b) संगत एवं आश्रित
(c) असंगत
(d) समापवर्ती
Q4. (1 mark) Which of the following pairs represents intersecting lines?
निम्न में से कौन-सा युग्म प्रतिच्छेदी रेखाओं को दर्शाता है?
(a) \(x - y = 2,\; 2x - 2y = 4\)
(b) \(x + y = 3,\; x + y = 5\)
(c) \(2x + y = 4,\; x - y = 1\)
(d) \(3x - y = 6,\; 6x - 2y = 12\)
Section B: Short Answer Questions
(2 × 3 = 6 marks)
Q5. (2 marks) Find the value of \(k\) for which the pair of equations \(kx + 2y = 4\) and \(6x + ky = 12\) has no solution.
\(k\) का मान ज्ञात कीजिए जिसके लिए समीकरणों का युग्म \(kx + 2y = 4\) तथा \(6x + ky = 12\) का कोई हल न हो।
Q6. (2 marks) Determine whether the following pair of linear equations is consistent or inconsistent: \(2x + y = 3,\; 4x + 2y = 6\).
जाँच कीजिए कि निम्न समीकरणों का युग्म संगत है या असंगत: \(2x + y = 3,\; 4x + 2y = 6\)।
Q7. (2 marks) Solve the following pair of equations using substitution method: \(x + y = 7,\; x - y = 1\).
प्रतिस्थापन विधि द्वारा निम्न समीकरणों का युग्म हल कीजिए: \(x + y = 7,\; x - y = 1\)।
Section C: Long Answer Questions
(3 × 2 = 6 marks)
Q8. (3 marks) Solve the following pair of linear equations using elimination method: \(2x + 3y = 11,\; 4x - 3y = 5\).
उन्मूलन विधि द्वारा निम्न समीकरणों का युग्म हल कीजिए: \(2x + 3y = 11,\; 4x - 3y = 5\)।
Q9. (3 marks) Solve the following pair of equations graphically: \(x + y = 4,\; 2x - y = 2\). Hence, find the coordinates of the point of intersection.
आलेखीय विधि द्वारा निम्न समीकरणों का युग्म हल कीजिए तथा प्रतिच्छेदन बिंदु के निर्देशांक ज्ञात कीजिए: \(x + y = 4,\; 2x - y = 2\)।
Section D: Word Problem
(4 × 1 = 4 marks)
Q10. (4 marks) The sum of two numbers is 27 and the difference between them is 3. Find the numbers.
दो संख्याओं का योग 27 है तथा उनका अंतर 3 है। संख्याएँ ज्ञात कीजिए।
#Class10Maths #PairOfLinearEquations #CBSEBasicMaths #BoardExamPattern
💡 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.
📚 Related Study Materials on StudyMats
Access more chapter-wise notes and practice papers:
- StudyMats Home — Complete Educational Study Material
- Bilingual Notes Study Notes & Question Papers
- Board Exam Preparation Study Notes & Question Papers
- CBSE Class 10 Study Notes & Question Papers
- Class 10 Maths Study Notes & Question Papers
❓ 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.