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Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry?
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Can you generate question paper regarding chapter to real no., polynom...
Question Paper: Mathematics - UPSC Level
Chapter 1: Real Numbers
- Define rational and irrational numbers with examples.
- Prove that the square root of 2 is an irrational number.
Chapter 2: Polynomials
- Explain the types of polynomials based on their degree.
- Solve the polynomial equation: x^3 - 6x^2 + 11x - 6 = 0 and find its roots.
Chapter 3: Pair of Linear Equations
- Solve the following pair of linear equations using the substitution method:
- 2x + 3y = 6
- 4x - y = 5
- Discuss the graphical representation of linear equations and the significance of the intersection point.
Chapter 4: Quadratic Equations
- Derive the quadratic formula from the standard form ax^2 + bx + c = 0.
- Solve the quadratic equation x^2 - 5x + 6 = 0 by factorization.
Chapter 5: Arithmetic Progression
- Define arithmetic progression (AP) and provide the formula for the nth term.
- If the first term of an AP is 5 and the common difference is 3, find the 10th term.
Chapter 6: Triangles
- State and prove Pythagoras' theorem.
- Determine the area of a triangle with vertices at (1, 2), (4, 6), and (7, 2).
Chapter 7: Coordinate Geometry
- Explain the concept of the Cartesian plane and the significance of coordinates.
- Find the distance between the points A(2, 3) and B(5, 7) using the distance formula.
Instructions:
- Each question carries equal marks.
- Show all workings clearly for full credit.
- Ensure clarity and neatness in your responses.
Chapter 1: Real Numbers
- Define rational and irrational numbers with examples.
- Prove that the square root of 2 is an irrational number.
Chapter 2: Polynomials
- Explain the types of polynomials based on their degree.
- Solve the polynomial equation: x^3 - 6x^2 + 11x - 6 = 0 and find its roots.
Chapter 3: Pair of Linear Equations
- Solve the following pair of linear equations using the substitution method:
- 2x + 3y = 6
- 4x - y = 5
- Discuss the graphical representation of linear equations and the significance of the intersection point.
Chapter 4: Quadratic Equations
- Derive the quadratic formula from the standard form ax^2 + bx + c = 0.
- Solve the quadratic equation x^2 - 5x + 6 = 0 by factorization.
Chapter 5: Arithmetic Progression
- Define arithmetic progression (AP) and provide the formula for the nth term.
- If the first term of an AP is 5 and the common difference is 3, find the 10th term.
Chapter 6: Triangles
- State and prove Pythagoras' theorem.
- Determine the area of a triangle with vertices at (1, 2), (4, 6), and (7, 2).
Chapter 7: Coordinate Geometry
- Explain the concept of the Cartesian plane and the significance of coordinates.
- Find the distance between the points A(2, 3) and B(5, 7) using the distance formula.
Instructions:
- Each question carries equal marks.
- Show all workings clearly for full credit.
- Ensure clarity and neatness in your responses.
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Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry?
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Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry?.
Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you generate question paper regarding chapter to real no., polynomial, pair of linear equation, quadratic equation, arithmetic progression, triangle and coordinate geometry?.
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