Welcome to JNVMaths.com, your trusted destination for comprehensive guidance on Jawahar Navodaya Vidyalaya Class 9 Entrance Exam math preparation. In this extensive blog post, we'll explore the intricacies of linear equations in two variables, a vital topic for your upcoming exam. By the time you finish reading this comprehensive guide, you'll be well-prepared to tackle any linear equation in two variables with confidence and ease.
Chapter 1: Understanding Linear Equations in Two Variables
In this opening section, we'll start by demystifying the basics:
What Are Linear Equations in Two Variables? - We'll provide a clear definition and explain the significance of this concept.
Real-Life Applications - Understanding where these equations show up in the real world can make them more relatable and easier to grasp. We'll present practical examples.
Graphical Interpretation - Dive into the graphical representation of these equations and how they translate to points on a Cartesian plane.
Chapter 2: Solving Linear Equations
Now, let's roll up our sleeves and solve some linear equations in two variables:
Methods of Solving - We'll explore different methods, including substitution, elimination, and the graphical method, with step-by-step examples for each.
Word Problems - Linear equations frequently appear in word problems. We'll provide strategies for translating real-world situations into equations and solving them.
Chapter 3: Graphical Representation
Graphs play a crucial role in understanding linear equations in two variables:
Plotting Linear Equations - Learn how to plot and interpret lines on a graph, and understand the connection between equations and their graphical representations.
Intercepts and Slopes - Discover how to find the intercepts and slopes of a line, and understand their significance.
Chapter 4: Simultaneous Linear Equations
This chapter will focus on the simultaneous linear equations, which involve multiple equations:
Methods of Solving Simultaneous Equations - Explore various methods for solving systems of linear equations, such as the substitution and elimination methods.
Applications in Real Life - See how simultaneous equations are used in practical scenarios, from budget planning to calculating distances.
Chapter 5: Word Problems and Practice Here, we'll provide a collection of word problems and practice exercises to help you reinforce your understanding and problem-solving skills.
Chapter 6: Tips and Tricks for the Exam As you gear up for the Jawahar Navodaya Vidyalaya Class 9 Entrance Exam, we'll share invaluable tips and strategies for tackling linear equations in two variables efficiently.
Chapter 7: Additional Resources We'll conclude with a list of recommended resources, including books, online tutorials, and practice tests, to further enhance your preparation.
प्रश्न: 1 प्रारंभिक गुणांक 6x-12y=0 है
A. अद्वितीय समाधान
B. दो समाधान
C. अनंत समाधान
D. कोई हल नहीं
उत्तर : C. अनंत समाधान
प्रश्न: 2 गुणांक 8x-2y=4 का हल है
A. (0,3)
B. (0,2)
C. (1,2)
D. (2,1)
उत्तर : C. (1,2)
प्रश्न: 3 m का मान ज्ञात किया गया है, यदि x=3, y=6 गुणांक x+2y=m का हल है?
A. 10
B 15
C. 12
D. 14
उत्तर: B. 15
प्रश्न: 4 आर्किटेक्चर गुणांक 6x-2y=8 का ग्राफ़ y-अक्ष को दर्शाता है
A. (0,-4)
B. (0,4)
C. (0,2)
D. (0,-2)
उत्तर : A. (0,-4)
प्रश्न: 5 यदि गुणांक ax+by=c के लिए x और y समाधान नकारात्मक और सकारात्मक हैं, तो रेखा निम्न में स्थित है:
A. प्रथम चतुर्थांश
B. द्वितीय चतुर्थांश
C. तृतीय चतुर्थांश
D. चतुर्थ चतुर्थांश
उत्तर:B. द्वितीय चतुर्थांश
प्रश्न: 6 Y-अक्ष पर कोई बिंदु किस रूप में होता है?
A. (X,Y)
B. (Y,X)
C. (0,y)
D. (y,0)
उत्तर : C
प्रश्न: 7 बिंदु (3,3) पर स्थित है
A. On the line x+y=0
B. on the x-axis
C. On the line x=y
D. On Y-axis
उत्तर : C
प्रश्न: 8 जब गुणांक को दोनों तरफ से एक ही गैर-शून्य संख्या से गुणा या विभाजित किया जाता है, तो गुणांक का हल
A. आदर्श ही रहता है
B. बहुत है
C. गुणा करने पर परिवर्तन ही होता है
D. विभाजन होने पर परिवर्तन ही होता है
उत्तर : A
प्रश्न: 9 प्रारंभिक गुणांक x+3y=9 और 8x+16y=32 की जोड़ी के समाधान की संख्या ज्ञात है।
A. 1
B. 2
C. 0
D. अनंत
उत्तर: D. अनंत
प्रश्न: 10 यदि समाधान x=2 और y=3 है तो प्रारंभिक गुणांक है
A. 2x+6y=14
B. x+5y=17
C. 2x+5y=17
D. x+y=7
उत्तर: B
प्रश्न: 11 दो चर वाले गुणवत्ता गुणांक का मानक रूप है
A. Ax+By=C
B. ay+b=0
C. ax+by+c=0
D. ax+by+xy=0
उत्तर : C. ax+by+c=0
प्रश्न: 12 एक उत्पादकता गुणांक की डिग्री है
A. 1
B. 2
C. 3
D. 0
उत्तर : A
प्रश्न: 13 X और Y अक्षर का अंतर है
A. 0 और अप्रतिभाषित
B. अप्रतिभाषित और 0
C. अनंत
D. 0 और 0
उत्तर : A
प्रश्न: 14 आर्किटेक्चर गुणांक ax+by+c=0 का अंतर है
A. M=a/b
B. M=-a/b
C. M=-b/a
D. M=b/a
उत्तर: B. M=-a/b
प्रश्न: 15 यदि x=4 और y=-2 गुणांक 4px+2y=12 का समाधान है तो p का मान है
A. 1
B. 2
C. 3
D. 4
उत्तर : A. 1
प्रश्न: 16 गुणांक y=4x का बिंदु है
A. (2,4)
B. (1,4)
C.(3,4)
D. कोई नहीं
उत्तर: B. (1,4)
प्रश्न: 17 एक पेन(x) की कीमत पुस्तक(y) की कीमत तीन गुना से दस गुना अधिक है। इसे गुणांक के रूप में जोड़ा जा सकता है
A. x+3y-10=0
B. x-3y-10=0
C. x+3y+10=0
D. x-10(3y)=0
उत्तर: B. x-3y-10=0
प्रश्न: 18 बिंदु (0,0), (-2,2) और (2,-2) से उपयोगकर्ता वाली सीधी रेखा है
A. xy=0
B. y=x
C. x+y=0
D. x+2y=0
उत्तर : C. x+y=0
प्रश्न: 19 एक आर्किटेक्चर गुणांक ax+by+c=0 में a और b के मान हैं
A. A=0 and B=0
B. a≠0 and b≠ 0
C. a ≠ 0 and b=0
D. A=1 and B=0
Answer: B. a≠0 and b≠0
Question:1 The linear equation is 6x-12y=0
A. Unique solution
B. Two solutions
C. infinite solutions
D. No solution
Answer: C. Infinite Solutions
Question:2 The solution to the equation 8x-2y=4 is
A. (0,3)
B. (0,2)
C. (1,2)
D. (2,1)
Answer: C.(1,2)
Question:3 Find the value of m, if x=3, y=6 is the solution of the equation x+2y=m?
A. 10
B. 15
C. 12
D. 14
Answer: B. 15
Question:4 The graph of the linear equation 6x-2y=8 cuts the y-axis.
A. (0,-4)
B. (0,4)
C. (0,2)
D. (0,-2)
Answer: A. (0,-4)
Question:5 If the x and y solutions for the equation ax+by=c are negative and positive, then the line lies in:
A. First Quadrant
B. Second Quadrant
C. Third Quadrant
D. Fourth Quadrant
Answer: B. second quarter
Question:6 What form does a point on the Y-axis take?
A. (X,Y)
B. (Y,X)
C. (0,y)
D. (y,0)
Answer: C
Question:7 is located at the point (3,3)
A. On the line x+y=0
B. on the x-axis
C. On the line x=y
D. On Y-axis
Answer: C
Question:8 When an equation is multiplied or divided by the same non-zero number on both sides, the solution of the equation is
A. remains the same
B. increases
C. Change occurs only when multiplied.
D. Change occurs only when divided
Answer: A
Question:9 Find the number of solutions of the pair of linear equations x+3y=9 and 8x+16y=32.
A. 1
B. 2
C. 0
D. Infinite
Answer: D. Infinite
Question:10 If the solution is x=2 and y=3 then the linear equation is
A. 2x+6y=14
B. x+5y=17
C. 2x+5y=17
D. x+y=7
Answer: B
Question:11 The standard form of a linear equation in two variables is
A. Ax+By=C
B. ay+b=0
C. ax+by+c=0
D. ax+by+xy=0
Answer: C. ax+by+c=0
Question:12 The degree of a linear equation is
A. 1
B. 2
C. 3
D. 0
Answer: A
Question:13 The slope of X and Y axis is
A. 0 and undefined
B. undefined and 0
C. Infinite
D. 0 and 0
Answer: A
Question:14 The slope of the linear equation ax+by+c=0 is
A. M=A/B
B. M=-A/B
C. M=-B/A
D. M=B/A
Answer: B. m=-a/b
Question:15 If x=4 and y=-2 are solutions of the equation 4px+2y=12 then the value of p is
A. 1
B. 2
C. 3
D. 4
Answer: A. 1
Question:16 The point of equation y=4x is
A. (2,4)
B. (1,4)
C. (3,4)
D. Nobody
Answer: B. (1,4)
Question:17 The price of a pen (x) is three times to ten times the price of a book (y). This can be expressed as a linear equation
A. x+3y-10=0
B. x-3y-10=0
C. x+3y+10=0
D. x-10(3y)=0
Answer: B. x-3y-10=0
Question:18 The straight line passing through the points (0,0), (-2,2) and (2,-2) is
A. xy=0
B. y=x
C. x+y=0
D. x+2y=0
Answer: C. x+y=0
Question:19 In a linear equation ax+by+c=0, the values of a and b are
A. A=0 and B=0
B. a≠0 and b≠ 0
C. a ≠ 0 and b=0
D. A=1 and B=0
Answer: B. a≠0 and b≠0
This blog post will be your one-stop resource for mastering linear equations in two variables and acing your JNV Class 9 Entrance Exam. Remember to stay connected with JNVMaths.com for updates, notifications, and more helpful content on your math journey. Get ready to excel in linear equations and beyond!
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