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If a pair of linear equations is inconsistent, then their graphs will be:
Step 1: Definition of Inconsistent Equations - Inconsistent equations are linear equations that have NO SOLUTION - Graphically, this means the lines representing these equations NEVER intersect Step 2: Graphical Interpretation Inconsistent equations always result in PARALLEL LINES - These lines haveRead more
Step 1: Definition of Inconsistent Equations
– Inconsistent equations are linear equations that have NO SOLUTION
– Graphically, this means the lines representing these equations NEVER intersect
Step 2: Graphical Interpretation
Inconsistent equations always result in PARALLEL LINES
– These lines have the same slope but different y-intercepts
– They run alongside each other, maintaining a constant distance
– No point exists where these lines cross
Step 3: Algebraic Characteristics
Example of Inconsistent Equations:
– Equation ₁: 2x + y = 4
– Equation ₂: 2x + y = 6
Observe:
– Same coefficient for x (2)
– Same coefficient for y (1)
– Different constant terms (4 and 6)
– This guarantees the lines will be parallel
Step 4: Geometric Visualization
– Imagine two identical lines shifted vertically
– They have the same “direction” but never touch
– No matter how far you extend them, they remain parallel
Conclusion:
For a pair of linear equations to be inconsistent, their graphs MUST be PARALLEL LINES.
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Which of the following statements is not correct about rule of law and respect for rights in a democracy?
Answer: (d) Everyone should not be equal in the eyes of laws. Explanation: In a democracy, the rule of law ensures that everyone is treated equally before the law, regardless of status, wealth, or power. This means: No one is above the law, including government officials. Basic rights and freedoms oRead more
Answer: (d) Everyone should not be equal in the eyes of laws.
Explanation: In a democracy, the rule of law ensures that everyone is treated equally before the law, regardless of status, wealth, or power. This means: No one is above the law, including government officials. Basic rights and freedoms of citizens, such as freedom of speech, association, and political participation, are protected. Legal processes are fair and just, allowing all individuals equal access to justice. Since statement (d) suggests inequality before the law, it contradicts the fundamental principles of democracy and the rule of law, making it incorrect.
This question related to Chapter 1 Social Science Class 9th NCERT. From the Chapter 1 What is Democracy? Why Democracy?. Give answer according to your understanding.
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The pair of equations 2x + 3y = 5** and **4x + 6y = 10 has
Step 1: Equation Analysis Equation ₁: 2x + 3y = 5 Equation ₂: 4x + 6y = 10 Step 2: Proportionality Check - Coefficient of x in Equation ₁: 2 - Coefficient of x in Equation ₂: 4 - Ratio of x coefficients: 4 ÷ 2 = 2 - Coefficient of y in Equation ₁: 3 - Coefficient of y in Equation ₂: 6 - Ratio of y cRead more
Step 1: Equation Analysis
Equation ₁: 2x + 3y = 5
Equation ₂: 4x + 6y = 10
Step 2: Proportionality Check
– Coefficient of x in Equation ₁: 2
– Coefficient of x in Equation ₂: 4
– Ratio of x coefficients: 4 ÷ 2 = 2
– Coefficient of y in Equation ₁: 3
– Coefficient of y in Equation ₂: 6
– Ratio of y coefficients: 6 ÷ 3 = 2
Step 3: Constant Term Verification
– Equation ₁ constant: 5
– Equation ₂ constant: 10
– Ratio of constants: 10 ÷ 5 = 2
Step 4: Algebraic Manipulation
Divide Equation ₂ by 2:
2x + 3y = 5 (Identical to Equation ₁)
Step 5: Interpretation
– The equations represent EXACTLY THE SAME LINE
– This means the system has INFINITELY MANY SOLUTIONS
– Every point on this line satisfies both equations
Mathematical Insight:
When two linear equations represent identical lines,
they have an infinite number of solution points that
perfectly overlap each other.
Conclusion:
The system has INFINITELY MANY SOLUTIONS.
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Which of the following statements is correct about democracy?
Answer: (b) In a democracy, each adult citizen must have one vote and each vote must have one value. Explanation: A democracy is based on the principle of universal adult franchise, which means: Every adult citizen has the right to vote, regardless of gender, caste, religion, or economic status. EacRead more
Answer: (b) In a democracy, each adult citizen must have one vote and each vote must have one value.
Explanation: A democracy is based on the principle of universal adult franchise, which means: Every adult citizen has the right to vote, regardless of gender, caste, religion, or economic status. Each person gets only one vote to ensure fairness in elections. Each vote has equal value, meaning no vote is given more importance than another.
Since option (b) accurately represents these democratic principles, it is the correct answer.
This question related to Chapter 1 Social Science Class 9th NCERT. From the Chapter 1 What is Democracy? Why Democracy?. Give answer according to your understanding.
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India did not face the famine crisis like China because:
Answer: (c) India had an accountable form of government. Explanation: India did not face a famine crisis like China because of its democratic and accountable government. Unlike China, where policies like the Great Leap Forward (1958-1962) led to mass starvation due to poor planning and lack of accouRead more
Answer: (c) India had an accountable form of government.
Explanation: India did not face a famine crisis like China because of its democratic and accountable government. Unlike China, where policies like the Great Leap Forward (1958-1962) led to mass starvation due to poor planning and lack of accountability, India: Had free press and independent institutions, which helped raise awareness and demand government action. Followed a multi-party democratic system, allowing public participation in policymaking. Implemented food security programs, such as the Public Distribution System (PDS) and Green Revolution, to prevent mass starvation.
Thus, India’s accountable government played a crucial role in preventing large-scale famine. This question related to Chapter 1 Social Science Class 9th NCERT. From the Chapter 1 What is Democracy? Why Democracy?. Give answer according to your understanding.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-9/social-science/