1. The problem is to generate a Class 9 CBSE question paper covering various topics with specified marks totaling 80. 2. The topics and marks are: Number System (10), Polynomials (15), Coordinate Geometry (4), Linear Equations in Two Variables (5), Introduction to Euclid Geometry (3), Lines and Angles (5), Triangles (7), Quadrilaterals (12), Heron's Formula (5), Surface Area and Volume (8), Statistics (6), Objective Questions, Case Study (2 marks), Assertion and Reasoning (3 marks). 3. The question paper should include a mix of objective, short answer, and long answer questions as per CBSE standards. 4. Diagrams should be included where necessary, especially for Geometry topics like Triangles, Quadrilaterals, Lines and Angles. 5. The total marks sum to 80, and the paper should be balanced to test conceptual understanding and application. 6. Example question for Number System (10 marks): - Define rational and irrational numbers. - Prove that the square root of 2 is irrational. 7. Example question for Polynomials (15 marks): - Find the zeros of the polynomial $$x^2 - 5x + 6$$ and verify the relationship between zeros and coefficients. 8. Example question for Coordinate Geometry (4 marks): - Find the distance between points $$A(2,3)$$ and $$B(5,7)$$. 9. Example question for Linear Equations in Two Variables (5 marks): - Solve the system: $$2x + 3y = 6$$ and $$x - y = 4$$. 10. Example question for Introduction to Euclid Geometry (3 marks): - State Euclid's fifth postulate. 11. Example question for Lines and Angles (5 marks): - Prove that vertically opposite angles are equal. 12. Example question for Triangles (7 marks): - Prove that the sum of angles in a triangle is $$180^\circ$$. 13. Example question for Quadrilaterals (12 marks): - Prove that the diagonals of a parallelogram bisect each other. 14. Example question for Heron's Formula (5 marks): - Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm using Heron's formula. 15. Example question for Surface Area and Volume (8 marks): - Find the surface area and volume of a cylinder with radius 3 cm and height 7 cm. 16. Example question for Statistics (6 marks): - Calculate the mean and median of the data set: 5, 8, 12, 15, 20. 17. Include objective questions (2 marks), case study questions (3 marks), and assertion-reasoning questions (3 marks) as per CBSE pattern. This structure ensures coverage of all topics with appropriate marks and question types.