Welcome to JNVMaths.com, your ultimate destination for mastering the intricacies of polynomials in preparation for the Jawahar Navodaya Vidyalaya Class 9 Entrance Exam. In this extensive blog post, we will leave no stone unturned as we explore the world of polynomials, helping you build a strong foundation and excel in your upcoming entrance exam.
Table of Contents
Understanding Polynomials
What Are Polynomials?
Degree and Leading Coefficient
Types of Polynomials
Addition and Subtraction of Polynomials
Combining Like Terms
Subtraction of Polynomials
Multiplication of Polynomials
The Distributive Property
FOIL Method
Special Products
Division of Polynomials
Long Division
Synthetic Division
Remainder Theorem and Factor Theorem
Factoring Polynomials
Common Factors
Factoring by Grouping
Factoring Quadratics
Special Factoring Techniques
Roots and Zeros of Polynomials
Finding Roots
The Factor Theorem Revisited
Using the Remainder Theorem
Rational and Irrational Roots
Graphing Polynomials
Polynomial Graphs
End Behavior
Transformations of Polynomials
Solving Polynomial Equations
Finding Real Solutions
Complex Solutions
Vieta's Formulas
Applications of Polynomials
Polynomials in Geometry
Polynomials in Algebra
Polynomials in Real Life
Tips and Tricks for Polynomials
Shortcut Techniques
Common Mistakes to Avoid
Practice Problems and Exercises
Worked Examples
Practice Sets
Previous Years' Questions
Exam-Style Questions
Solutions and Explanations
Preparation Strategies
Study Plans
Time Management
Test-Taking Tips
Q1. निम्नलिखित में से कौन सी 4x^3-12x^2+3x+9 की डिग्री है?
A. 1
B. 2
C. 3
D. 4
Ans. D
Q2. x^2 – x किस प्रकार का बहुपद है?
A. द्विघात
B. घन
C. रैखिक
D. उपरोक्त में से कोई नहीं
Ans. A
Q3. x – x^3 किस प्रकार का बहुपद है?
A. द्विघात
B. घन
C. रैखिक
D. उपरोक्त में से कोई नहीं
सही उत्तर है B
Q4. निम्नलिखित में से 7^2 - 5^2 का मान क्या है?
A. 25
B. 24
C. 23
D. 22
सही उत्तर है B
Q5. निम्नलिखित में से कौन सा एक अचर बहुपद है?
A. 4x + 1
B. 3
C. 2x^2
D. 6x + 3
सही उत्तर है B
Q6. निम्नलिखित में से कौन सा एक द्विघात बहुपद है?
A. x + 3x^3 + 1
B. 7x + 3
C. 2x^2+x - 1
D. उपरोक्त में से कोई नहीं
सही उत्तर है C
Q7. 1 + 3x किस प्रकार का बहुपद है?
A. द्विघात
B. घन
C. रैखिक
D. उपरोक्त में से कोई नहीं
सही उत्तर है C
Q8. निम्नलिखित में से कौन सा घात 20 का द्विपद है?
A. x^20 + 1
B. x^2 + 20
C. x/20 + 1
D. 20x + 1
सही उत्तर है A
Q9. जब x = -1, तो निम्न में से f(x) = 5x−4x^2+3 का मान क्या है?
A. 3
B-6
C.-12
D. 6
सही उत्तर है B
Q10. जब t = 0, तो निम्नलिखित में से p(t) = 2+t+2t^2−t^3 का मान क्या है?
A. 4
B1
C. 2
D. 0
सही उत्तर है C
प्रश्न11. बहुपद f(x) = 2x + 7 के लिए निम्नलिखित में से कौन सा शून्य है?
A.-2/7
B. 7/2
C. 2/7
D.-7/2
सही उत्तर है D.
प्रश्न12. बहुपद p(x) = cx + d के लिए निम्नलिखित में से कौन सा शून्य है?
A.-d/c
B. d/c
C.-c
D.-d
सही उत्तर है A.
Q13. बहुपद p(x) = -5x + 5 के लिए निम्नलिखित में से कौन सा शून्य है?
A. -5
B. 0
C. 1
D. -1
सही उत्तर है B.
प्रश्न14. निम्नलिखित में से कौन सा बहुपद 7x^2+6x-2 में x का गुणांक है?
A. -2
B. 6
C. 7
D. 2
सही उत्तर है B
Q1. Which of the following is the degree of 4x^3-12x^2+3x+9?
A. 0
B. 1
C. 2
D. 3
The right answer is d
Q2. What kind of polynomial is x^2 – x?
A. Quadratic
B. Cubic
C. Linear
D. None of the above
The right answer is a
Q3. What kind of polynomial is x – x^3?
A. Quadratic
B. Cubic
C. Linear
D. None of the above
The right answer is b
Q4. Which of the following is the value of 7^2-5^2?
A. 25
B. 24
C. 23
D. 22
The right answer is b
Q5. Amongst the following, which is a constant polynomial?
A. 4x + 1
B. 3
C. 2x^2
D. 6x + 3
The right answer is b
Q6. Which of the following is a quadratic polynomial?
A. x + 3x^3 + 1
B. 7x + 3
C. 2x^2 + x - 1
D. None of the above
The right answer is c
Q7. What kind of polynomial is 1 + 3x?
A. Quadratic
B. Cubic
C. Linear
D. None of the above
The right answer is c
Q8. Which of the following is a binomial of degree 20?
A. x^20 + 1
B. x^2 + 20
C. x/20 + 1
D. 20x + 1
The right answer is a
Q9. When x = -1, which of the following is the value of f(x) = 5x−4x^2+3?
A. 3
B. -6
C. -12
D. 6
The right answer is b
Q10. When t = 0, which of the following is the value of p(t) = 2+t+2t^2−t^3?
A. 4
B. 1
C. 2
D. 0
The right answer is c
Q11. Which of the following is the zero for the polynomial f(x) = 2x + 7?
A. -2/7
B. 7/2
C. 2/7
D. -7/2
The right answer is d.
Q12. Which of the following is the zero for the polynomial p(x) = cx + d?
A. -d/c
B. d/c
C. -c
D. -d
The right answer is a.
Q13. Which of the following is the zero for the polynomial p(x) = -5x + 5?
A. -5
B. 0
C. 1
D. -1
The right answer is b.
Q14. Which of the following is the coefficient of x in the polynomial 7x^2+6x-2?
A. -2
B. 6
C. 7
D. 2
The right answer is b
Conclusion:
By the time you finish reading this comprehensive guide, you will have a deep and thorough understanding of polynomials, equipping you with the knowledge and skills necessary to tackle the mathematics section of the Jawahar Navodaya Vidyalaya Class 9 Entrance Exam with confidence.
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