Class 10 solvability MCQ Questions

Question 61/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि दो रेखाओं की ढाल अलग-अलग हों, तो उनके युग्म के लिए कौन-सा निष्कर्ष सही है?

If two lines have different slopes, which conclusion is correct for their pair?

Explanation opens after your attempt

Correct Answer

C. अद्वितीय हलUnique solution

Step 1

Concept

Lines with different slopes meet at exactly one point. Hence the pair is consistent and independent.

Step 2

Why this answer is correct

The correct answer is C. अद्वितीय हल / Unique solution. Lines with different slopes meet at exactly one point. Hence the pair is consistent and independent.

Step 3

Exam Tip

अलग ढाल वाली रेखाएँ केवल एक बिंदु पर मिलती हैं। इसलिए युग्म संगत और स्वतंत्र होता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
यदि दो रेखाओं की ढाल अलग-अलग हों, तो उनके युग्म के लिए कौन-सा निष्कर्ष सही है?

Question English:
If two lines have different slopes, which conclusion is correct for their pair?

Options:
A. कोई हल नहीं / No solution
B. अनंत हल / Infinitely many solutions
C. अद्वितीय हल / Unique solution
D. समीकरण निर्भर हैं / Equations are dependent

Correct Answer:
C. अद्वितीय हल / Unique solution

Explanation Hindi:
अलग ढाल वाली रेखाएँ केवल एक बिंदु पर मिलती हैं। इसलिए युग्म संगत और स्वतंत्र होता है।

Explanation English:
Lines with different slopes meet at exactly one point. Hence the pair is consistent and independent.

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Question 62/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि दो रेखाओं की ढाल समान और (y)-अवरोध अलग हों, तो उनके समीकरणों के युग्म में कितने हल होंगे?

If two lines have the same slope and different (y)-intercepts, how many solutions will their pair of equations have?

Explanation opens after your attempt

Correct Answer

C. कोई हल नहींNo solution

Step 1

Concept

Same slope and different intercepts mean distinct parallel lines. Therefore, they never intersect.

Step 2

Why this answer is correct

The correct answer is C. कोई हल नहीं / No solution. Same slope and different intercepts mean distinct parallel lines. Therefore, they never intersect.

Step 3

Exam Tip

समान ढाल और अलग अवरोध का अर्थ अलग समांतर रेखाएँ है। इसलिए वे कभी नहीं कटतीं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
यदि दो रेखाओं की ढाल समान और (y)-अवरोध अलग हों, तो उनके समीकरणों के युग्म में कितने हल होंगे?

Question English:
If two lines have the same slope and different (y)-intercepts, how many solutions will their pair of equations have?

Options:
A. अद्वितीय हल / Unique solution
B. अनंत हल / Infinitely many solutions
C. कोई हल नहीं / No solution
D. दो हल / Two solutions

Correct Answer:
C. कोई हल नहीं / No solution

Explanation Hindi:
समान ढाल और अलग अवरोध का अर्थ अलग समांतर रेखाएँ है। इसलिए वे कभी नहीं कटतीं।

Explanation English:
Same slope and different intercepts mean distinct parallel lines. Therefore, they never intersect.

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Question 63/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (D=0) और कम से कम एक सहायक सारणिक शून्य नहीं है, तो युग्म की हल-स्थिति क्या होगी?

If (D=0) and at least one auxiliary determinant is non-zero, what is the solution status of the pair?

Explanation opens after your attempt

Correct Answer

C. कोई हल नहींNo solution

Step 1

Concept

(D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.

Step 2

Why this answer is correct

The correct answer is C. कोई हल नहीं / No solution. (D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.

Step 3

Exam Tip

(D=0) और असंगत सहायक सारणिक समांतर अलग रेखाओं का संकेत देते हैं। इसलिए कोई हल नहीं होता।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
यदि (D=0) और कम से कम एक सहायक सारणिक शून्य नहीं है, तो युग्म की हल-स्थिति क्या होगी?

Question English:
If (D=0) and at least one auxiliary determinant is non-zero, what is the solution status of the pair?

Options:
A. अनंत हल / Infinitely many solutions
B. अद्वितीय हल / Unique solution
C. कोई हल नहीं / No solution
D. सदैव हल / Always solvable

Correct Answer:
C. कोई हल नहीं / No solution

Explanation Hindi:
(D=0) और असंगत सहायक सारणिक समांतर अलग रेखाओं का संकेत देते हैं। इसलिए कोई हल नहीं होता।

Explanation English:
(D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.

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Question 64/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

संपाती रेखाओं के लिए सही बीजीय शर्त कौन-सी है?

Which algebraic condition is correct for coincident lines?

Explanation opens after your attempt

Correct Answer

C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

Step 1

Concept

Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.

Step 3

Exam Tip

संपाती रेखाएँ एक ही रेखा को दर्शाती हैं। इसलिए तीनों अनुपात समान होते हैं और अनंत हल मिलते हैं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
संपाती रेखाओं के लिए सही बीजीय शर्त कौन-सी है?

Question English:
Which algebraic condition is correct for coincident lines?

Options:
A. (\frac{a_1}{a_2}\neq\frac{b_1}{b_2})
B. (\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2})
C. (\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2})
D. (a_1b_2-a_2b_1\neq0)

Correct Answer:
C. (\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2})

Explanation Hindi:
संपाती रेखाएँ एक ही रेखा को दर्शाती हैं। इसलिए तीनों अनुपात समान होते हैं और अनंत हल मिलते हैं।

Explanation English:
Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.

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Question 65/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\) है, तो दो रैखिक समीकरणों के युग्म के लिए क्या निष्कर्ष होगा?

If \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\), what is the conclusion for a pair of two linear equations?

Explanation opens after your attempt

Correct Answer

C. अद्वितीय हलUnique solution

Step 1

Concept

When coefficient ratios are different, the lines intersect at one point. Therefore, a unique solution is obtained.

Step 2

Why this answer is correct

The correct answer is C. अद्वितीय हल / Unique solution. When coefficient ratios are different, the lines intersect at one point. Therefore, a unique solution is obtained.

Step 3

Exam Tip

गुणांक अनुपात अलग होने पर रेखाएँ एक बिंदु पर कटती हैं। इसलिए अद्वितीय हल मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
यदि (\frac{a_1}{a_2}\neq\frac{b_1}{b_2}) है, तो दो रैखिक समीकरणों के युग्म के लिए क्या निष्कर्ष होगा?

Question English:
If (\frac{a_1}{a_2}\neq\frac{b_1}{b_2}), what is the conclusion for a pair of two linear equations?

Options:
A. कोई हल नहीं / No solution
B. अनंत हल / Infinitely many solutions
C. अद्वितीय हल / Unique solution
D. हल निर्भर करता है / Solution depends only on constants

Correct Answer:
C. अद्वितीय हल / Unique solution

Explanation Hindi:
गुणांक अनुपात अलग होने पर रेखाएँ एक बिंदु पर कटती हैं। इसलिए अद्वितीय हल मिलता है।

Explanation English:
When coefficient ratios are different, the lines intersect at one point. Therefore, a unique solution is obtained.

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Question 66/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि किसी युग्म में गुणांक अनुपात समान है और स्थिर पद का अनुपात अलग है, तो हल-स्थिति क्या होगी?

If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?

Explanation opens after your attempt

Correct Answer

C. कोई हल नहींNo solution

Step 1

Concept

This condition forms distinct parallel lines. Therefore, the pair is inconsistent.

Step 2

Why this answer is correct

The correct answer is C. कोई हल नहीं / No solution. This condition forms distinct parallel lines. Therefore, the pair is inconsistent.

Step 3

Exam Tip

यह स्थिति अलग-अलग समांतर रेखाएँ बनाती है। इसलिए युग्म असंगत होता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
यदि किसी युग्म में गुणांक अनुपात समान है और स्थिर पद का अनुपात अलग है, तो हल-स्थिति क्या होगी?

Question English:
If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?

Options:
A. अद्वितीय हल / Unique solution
B. अनंत हल / Infinitely many solutions
C. कोई हल नहीं / No solution
D. सदैव दो हल / Always two solutions

Correct Answer:
C. कोई हल नहीं / No solution

Explanation Hindi:
यह स्थिति अलग-अलग समांतर रेखाएँ बनाती है। इसलिए युग्म असंगत होता है।

Explanation English:
This condition forms distinct parallel lines. Therefore, the pair is inconsistent.

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Question 67/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

सामान्य युग्म \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) में कोई हल न होने की शर्त क्या है?

For the general pair \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), what is the condition for no solution?

Explanation opens after your attempt

Correct Answer

C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)

Step 1

Concept

No solution occurs when lines are parallel and distinct. Its ratio form is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\).

Step 2

Why this answer is correct

The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). No solution occurs when lines are parallel and distinct. Its ratio form is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\).

Step 3

Exam Tip

कोई हल नहीं तब होता है जब रेखाएँ समांतर और अलग हों। इसका अनुपात रूप \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\) है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
सामान्य युग्म (a_1x+b_1y+c_1=0) और (a_2x+b_2y+c_2=0) में कोई हल न होने की शर्त क्या है?

Question English:
For the general pair (a_1x+b_1y+c_1=0) and (a_2x+b_2y+c_2=0), what is the condition for no solution?

Options:
A. (\frac{a_1}{a_2}\neq\frac{b_1}{b_2})
B. (\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2})
C. (\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2})
D. (a_1=a_2=0)

Correct Answer:
C. (\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2})

Explanation Hindi:
कोई हल नहीं तब होता है जब रेखाएँ समांतर और अलग हों। इसका अनुपात रूप (\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}) है।

Explanation English:
No solution occurs when lines are parallel and distinct. Its ratio form is (\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}).

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Question 68/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (4x+5y=1) और (8x+9y=2) के लिए हलों की संख्या क्या है?

How many solutions does (4x+5y=1) and (8x+9y=2) have?

Explanation opens after your attempt

Correct Answer

C. अद्वितीय हलUnique solution

Step 1

Concept

Here \(\frac{4}{8}\neq\frac{5}{9}\). Therefore, the lines intersect at one point.

Step 2

Why this answer is correct

The correct answer is C. अद्वितीय हल / Unique solution. Here \(\frac{4}{8}\neq\frac{5}{9}\). Therefore, the lines intersect at one point.

Step 3

Exam Tip

यहाँ \(\frac{4}{8}\neq\frac{5}{9}\) है। इसलिए रेखाएँ एक बिंदु पर कटती हैं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (4x+5y=1) और (8x+9y=2) के लिए हलों की संख्या क्या है?

Question English:
How many solutions does (4x+5y=1) and (8x+9y=2) have?

Options:
A. कोई हल नहीं / No solution
B. अनंत हल / Infinitely many solutions
C. अद्वितीय हल / Unique solution
D. निर्भर हल / Dependent solutions

Correct Answer:
C. अद्वितीय हल / Unique solution

Explanation Hindi:
यहाँ (\frac{4}{8}\neq\frac{5}{9}) है। इसलिए रेखाएँ एक बिंदु पर कटती हैं।

Explanation English:
Here (\frac{4}{8}\neq\frac{5}{9}). Therefore, the lines intersect at one point.

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Question 69/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (3x-y=4) और (6x-2y=9) के बारे में सही कथन चुनिए।

Choose the correct statement about (3x-y=4) and (6x-2y=9).

Explanation opens after your attempt

Correct Answer

C. कोई हल नहीं हैIt has no solution

Step 1

Concept

The coefficient ratio is equal but the constant ratio is not equal. Hence the lines are parallel and distinct.

Step 2

Why this answer is correct

The correct answer is C. कोई हल नहीं है / It has no solution. The coefficient ratio is equal but the constant ratio is not equal. Hence the lines are parallel and distinct.

Step 3

Exam Tip

गुणांक अनुपात समान है लेकिन स्थिर पद अनुपात समान नहीं है। इसलिए रेखाएँ समांतर और अलग हैं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (3x-y=4) और (6x-2y=9) के बारे में सही कथन चुनिए।

Question English:
Choose the correct statement about (3x-y=4) and (6x-2y=9).

Options:
A. अद्वितीय हल है / It has a unique solution
B. अनंत हल हैं / It has infinitely many solutions
C. कोई हल नहीं है / It has no solution
D. दो हल हैं / It has two solutions

Correct Answer:
C. कोई हल नहीं है / It has no solution

Explanation Hindi:
गुणांक अनुपात समान है लेकिन स्थिर पद अनुपात समान नहीं है। इसलिए रेखाएँ समांतर और अलग हैं।

Explanation English:
The coefficient ratio is equal but the constant ratio is not equal. Hence the lines are parallel and distinct.

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Question 70/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (x+2y=3) और (4x+8y=12) के लिए सही हल-स्थिति कौन-सी है?

Which solution status is correct for (x+2y=3) and (4x+8y=12)?

Explanation opens after your attempt

Correct Answer

A. अनंत हलInfinitely many solutions

Step 1

Concept

The second equation is (4) times the first. Both are the same line, so there are infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is A. अनंत हल / Infinitely many solutions. The second equation is (4) times the first. Both are the same line, so there are infinitely many solutions.

Step 3

Exam Tip

दूसरा समीकरण पहले का (4) गुना है। दोनों समान रेखाएँ हैं, इसलिए अनंत हल हैं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (x+2y=3) और (4x+8y=12) के लिए सही हल-स्थिति कौन-सी है?

Question English:
Which solution status is correct for (x+2y=3) and (4x+8y=12)?

Options:
A. अनंत हल / Infinitely many solutions
B. कोई हल नहीं / No solution
C. अद्वितीय हल / Unique solution
D. एक भी बिंदु नहीं / No point at all

Correct Answer:
A. अनंत हल / Infinitely many solutions

Explanation Hindi:
दूसरा समीकरण पहले का (4) गुना है। दोनों समान रेखाएँ हैं, इसलिए अनंत हल हैं।

Explanation English:
The second equation is (4) times the first. Both are the same line, so there are infinitely many solutions.

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Question 71/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (6x+(h+1)y=12) और (15x+20y=30) के अनंत हलों के लिए (h) क्या है?

For infinitely many solutions of (6x+(h+1)y=12) and (15x+20y=30), what is (h)?

Explanation opens after your attempt

Correct Answer

C. (h=7)

Step 1

Concept

For infinitely many solutions, \(\frac{6}{15}=\frac{h+1}{20}=\frac{12}{30}\) must hold. This gives (h=7).

Step 2

Why this answer is correct

The correct answer is C. (h=7). For infinitely many solutions, \(\frac{6}{15}=\frac{h+1}{20}=\frac{12}{30}\) must hold. This gives (h=7).

Step 3

Exam Tip

अनंत हलों के लिए \(\frac{6}{15}=\frac{h+1}{20}=\frac{12}{30}\) होना चाहिए। इससे (h=7) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (6x+(h+1)y=12) और (15x+20y=30) के अनंत हलों के लिए (h) क्या है?

Question English:
For infinitely many solutions of (6x+(h+1)y=12) and (15x+20y=30), what is (h)?

Options:
A. (h=5)
B. (h=6)
C. (h=7)
D. (h=8)

Correct Answer:
C. (h=7)

Explanation Hindi:
अनंत हलों के लिए (\frac{6}{15}=\frac{h+1}{20}=\frac{12}{30}) होना चाहिए। इससे (h=7) मिलता है।

Explanation English:
For infinitely many solutions, (\frac{6}{15}=\frac{h+1}{20}=\frac{12}{30}) must hold. This gives (h=7).

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Question 72/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (lx+6y=8) और (9x+18y=10) में कोई हल न होने के लिए (l) क्या होगा?

What is (l) for no solution in (lx+6y=8) and (9x+18y=10)?

Explanation opens after your attempt

Correct Answer

B. (l=3)

Step 1

Concept

Equating coefficient ratios, \(\frac{l}{9}=\frac{6}{18}\) gives (l=3). The constant ratio is different.

Step 2

Why this answer is correct

The correct answer is B. (l=3). Equating coefficient ratios, \(\frac{l}{9}=\frac{6}{18}\) gives (l=3). The constant ratio is different.

Step 3

Exam Tip

गुणांक अनुपात समान करने पर \(\frac{l}{9}=\frac{6}{18}\) से (l=3) मिलता है। स्थिर पद अनुपात अलग है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (lx+6y=8) और (9x+18y=10) में कोई हल न होने के लिए (l) क्या होगा?

Question English:
What is (l) for no solution in (lx+6y=8) and (9x+18y=10)?

Options:
A. (l=2)
B. (l=3)
C. (l=6)
D. (l=9)

Correct Answer:
B. (l=3)

Explanation Hindi:
गुणांक अनुपात समान करने पर (\frac{l}{9}=\frac{6}{18}) से (l=3) मिलता है। स्थिर पद अनुपात अलग है।

Explanation English:
Equating coefficient ratios, (\frac{l}{9}=\frac{6}{18}) gives (l=3). The constant ratio is different.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 73/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (ax+by=1) और (2ax+3by=5) के अद्वितीय हल की शर्त क्या है?

What is the condition for a unique solution of (ax+by=1) and (2ax+3by=5)?

Explanation opens after your attempt

Correct Answer

C. \(ab\neq0\)

Step 1

Concept

The determinant is (D=3ab-2ab=ab). For a unique solution, \(ab\neq0\) is needed.

Step 2

Why this answer is correct

The correct answer is C. \(ab\neq0\). The determinant is (D=3ab-2ab=ab). For a unique solution, \(ab\neq0\) is needed.

Step 3

Exam Tip

सारणिक (D=3ab-2ab=ab) है। अद्वितीय हल के लिए \(ab\neq0\) चाहिए।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/what-is-the-condition-for-a-unique-solution-of-ax-by-1-and-2ax-3by-5

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (ax+by=1) और (2ax+3by=5) के अद्वितीय हल की शर्त क्या है?

Question English:
What is the condition for a unique solution of (ax+by=1) and (2ax+3by=5)?

Options:
A. (ab=0)
B. (a+b=0)
C. (ab\neq0)
D. (a=b)

Correct Answer:
C. (ab\neq0)

Explanation Hindi:
सारणिक (D=3ab-2ab=ab) है। अद्वितीय हल के लिए (ab\neq0) चाहिए।

Explanation English:
The determinant is (D=3ab-2ab=ab). For a unique solution, (ab\neq0) is needed.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 74/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (2x+3y=d) और (14x+21y=28) में कोई हल न हो, इसके लिए (d) पर कौन-सी शर्त होगी?

For (2x+3y=d) and (14x+21y=28) to have no solution, what condition is required on (d)?

Explanation opens after your attempt

Correct Answer

B. \(d\neq4\)

Step 1

Concept

The coefficient ratio is \(\frac{1}{7}\). For no solution, \(\frac{d}{28}\neq\frac{1}{7}\), so \(d\neq4\).

Step 2

Why this answer is correct

The correct answer is B. \(d\neq4\). The coefficient ratio is \(\frac{1}{7}\). For no solution, \(\frac{d}{28}\neq\frac{1}{7}\), so \(d\neq4\).

Step 3

Exam Tip

गुणांक अनुपात \(\frac{1}{7}\) है। कोई हल नहीं के लिए \(\frac{d}{28}\neq\frac{1}{7}\), इसलिए \(d\neq4\)।

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Question Page:
https://muftshiksha.com/question/for-2x-3y-d-and-14x-21y-28-to-have-no-solution-what-condition-is-required-on-d

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (2x+3y=d) और (14x+21y=28) में कोई हल न हो, इसके लिए (d) पर कौन-सी शर्त होगी?

Question English:
For (2x+3y=d) and (14x+21y=28) to have no solution, what condition is required on (d)?

Options:
A. (d=4)
B. (d\neq4)
C. (d=7)
D. (d\neq7)

Correct Answer:
B. (d\neq4)

Explanation Hindi:
गुणांक अनुपात (\frac{1}{7}) है। कोई हल नहीं के लिए (\frac{d}{28}\neq\frac{1}{7}), इसलिए (d\neq4)।

Explanation English:
The coefficient ratio is (\frac{1}{7}). For no solution, (\frac{d}{28}\neq\frac{1}{7}), so (d\neq4).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 75/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म ((v+2)x-3y=6) और (10x-5y=10) के अनंत हलों के लिए (v) क्या होगा?

For infinitely many solutions of ((v+2)x-3y=6) and (10x-5y=10), what is (v)?

Explanation opens after your attempt

Correct Answer

C. (v=4)

Step 1

Concept

Here \(\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}\) must hold. This gives (v=4).

Step 2

Why this answer is correct

The correct answer is C. (v=4). Here \(\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}\) must hold. This gives (v=4).

Step 3

Exam Tip

यहाँ \(\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}\) होना चाहिए। इससे (v=4) मिलता है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म ((v+2)x-3y=6) और (10x-5y=10) के अनंत हलों के लिए (v) क्या होगा?

Question English:
For infinitely many solutions of ((v+2)x-3y=6) and (10x-5y=10), what is (v)?

Options:
A. (v=2)
B. (v=3)
C. (v=4)
D. (v=5)

Correct Answer:
C. (v=4)

Explanation Hindi:
यहाँ (\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}) होना चाहिए। इससे (v=4) मिलता है।

Explanation English:
Here (\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}) must hold. This gives (v=4).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 76/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (13x-ty=5) और (26x-10y=14) का अद्वितीय हल कब होगा?

When will (13x-ty=5) and (26x-10y=14) have a unique solution?

Explanation opens after your attempt

Correct Answer

D. \(t\neq5\)

Step 1

Concept

For a unique solution, \(\frac{13}{26}\neq\frac{t}{10}\) must hold. Hence \(t\neq5\) is correct.

Step 2

Why this answer is correct

The correct answer is D. \(t\neq5\). For a unique solution, \(\frac{13}{26}\neq\frac{t}{10}\) must hold. Hence \(t\neq5\) is correct.

Step 3

Exam Tip

अद्वितीय हल के लिए \(\frac{13}{26}\neq\frac{t}{10}\) होना चाहिए। अतः \(t\neq5\) सही है।

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Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

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- Name: Muft Shiksha
- Website: https://muftshiksha.com
- Style: dark navy futuristic learning game UI, neon cyan/blue glow, gold reward highlights, clean Devanagari text, premium educational look.
- Do not add wrong facts. Do not change the question, options or answer.

Question Page:
https://muftshiksha.com/question/when-will-13x-ty-5-and-26x-10y-14-have-a-unique-solution

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (13x-ty=5) और (26x-10y=14) का अद्वितीय हल कब होगा?

Question English:
When will (13x-ty=5) and (26x-10y=14) have a unique solution?

Options:
A. (t=5)
B. (t=10)
C. (t\neq10)
D. (t\neq5)

Correct Answer:
D. (t\neq5)

Explanation Hindi:
अद्वितीय हल के लिए (\frac{13}{26}\neq\frac{t}{10}) होना चाहिए। अतः (t\neq5) सही है।

Explanation English:
For a unique solution, (\frac{13}{26}\neq\frac{t}{10}) must hold. Hence (t\neq5) is correct.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 77/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (ux+9y=7) और (4x+6y=11) में कोई हल न होने के लिए (u) का मान क्या है?

For no solution in (ux+9y=7) and (4x+6y=11), what is the value of (u)?

Explanation opens after your attempt

Correct Answer

C. (u=6)

Step 1

Concept

Equating coefficient ratios, \(\frac{u}{4}=\frac{9}{6}\) gives (u=6). The constant ratio is different, so there is no solution.

Step 2

Why this answer is correct

The correct answer is C. (u=6). Equating coefficient ratios, \(\frac{u}{4}=\frac{9}{6}\) gives (u=6). The constant ratio is different, so there is no solution.

Step 3

Exam Tip

गुणांक अनुपात समान करने पर \(\frac{u}{4}=\frac{9}{6}\) से (u=6) मिलता है। स्थिर पद अनुपात अलग है, इसलिए कोई हल नहीं है।

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Question Page:
https://muftshiksha.com/question/for-no-solution-in-ux-9y-7-and-4x-6y-11-what-is-the-value-of-u

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (ux+9y=7) और (4x+6y=11) में कोई हल न होने के लिए (u) का मान क्या है?

Question English:
For no solution in (ux+9y=7) and (4x+6y=11), what is the value of (u)?

Options:
A. (u=4)
B. (u=5)
C. (u=6)
D. (u=9)

Correct Answer:
C. (u=6)

Explanation Hindi:
गुणांक अनुपात समान करने पर (\frac{u}{4}=\frac{9}{6}) से (u=6) मिलता है। स्थिर पद अनुपात अलग है, इसलिए कोई हल नहीं है।

Explanation English:
Equating coefficient ratios, (\frac{u}{4}=\frac{9}{6}) gives (u=6). The constant ratio is different, so there is no solution.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 78/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (12x+sy=18) और (20x+10y=30) के अनंत हलों के लिए (s) क्या होगा?

What is (s) for infinitely many solutions of (12x+sy=18) and (20x+10y=30)?

Explanation opens after your attempt

Correct Answer

C. (s=6)

Step 1

Concept

For infinitely many solutions, \(\frac{12}{20}=\frac{s}{10}=\frac{18}{30}\) is needed. This gives (s=6).

Step 2

Why this answer is correct

The correct answer is C. (s=6). For infinitely many solutions, \(\frac{12}{20}=\frac{s}{10}=\frac{18}{30}\) is needed. This gives (s=6).

Step 3

Exam Tip

अनंत हलों के लिए \(\frac{12}{20}=\frac{s}{10}=\frac{18}{30}\) चाहिए। इससे (s=6) आता है।

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AI Video Prompt 16:9 + 9:16

Is question ka premium MCQ video banane ke liye ready prompt. Copy karke Sora, Runway, Canva AI, CapCut AI, ChatGPT video workflow ya editor me use karein.

Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

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- Name: Muft Shiksha
- Website: https://muftshiksha.com
- Style: dark navy futuristic learning game UI, neon cyan/blue glow, gold reward highlights, clean Devanagari text, premium educational look.
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Question Page:
https://muftshiksha.com/question/what-is-s-for-infinitely-many-solutions-of-12x-sy-18-and-20x-10y-30

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (12x+sy=18) और (20x+10y=30) के अनंत हलों के लिए (s) क्या होगा?

Question English:
What is (s) for infinitely many solutions of (12x+sy=18) and (20x+10y=30)?

Options:
A. (s=4)
B. (s=5)
C. (s=6)
D. (s=8)

Correct Answer:
C. (s=6)

Explanation Hindi:
अनंत हलों के लिए (\frac{12}{20}=\frac{s}{10}=\frac{18}{30}) चाहिए। इससे (s=6) आता है।

Explanation English:
For infinitely many solutions, (\frac{12}{20}=\frac{s}{10}=\frac{18}{30}) is needed. This gives (s=6).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
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- Text overlays for 16:9 and 9:16.
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- Hashtags: #MuftShiksha #FreeEducation #MCQ #Quiz #Class10 #Study

Open Question

Question 79/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (rx+5y=2) और (8x+10y=4) का अद्वितीय हल कब होगा?

When will (rx+5y=2) and (8x+10y=4) have a unique solution?

Explanation opens after your attempt

Correct Answer

B. \(r\neq4\)

Step 1

Concept

For a unique solution, \(\frac{r}{8}\neq\frac{5}{10}\) must hold. So \(r\neq4\) is correct.

Step 2

Why this answer is correct

The correct answer is B. \(r\neq4\). For a unique solution, \(\frac{r}{8}\neq\frac{5}{10}\) must hold. So \(r\neq4\) is correct.

Step 3

Exam Tip

अद्वितीय हल के लिए \(\frac{r}{8}\neq\frac{5}{10}\) होना चाहिए। इसलिए \(r\neq4\) सही है।

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AI Video Prompt 16:9 + 9:16

Is question ka premium MCQ video banane ke liye ready prompt. Copy karke Sora, Runway, Canva AI, CapCut AI, ChatGPT video workflow ya editor me use karein.

Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

Brand:
- Name: Muft Shiksha
- Website: https://muftshiksha.com
- Style: dark navy futuristic learning game UI, neon cyan/blue glow, gold reward highlights, clean Devanagari text, premium educational look.
- Do not add wrong facts. Do not change the question, options or answer.

Question Page:
https://muftshiksha.com/question/when-will-rx-5y-2-and-8x-10y-4-have-a-unique-solution

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (rx+5y=2) और (8x+10y=4) का अद्वितीय हल कब होगा?

Question English:
When will (rx+5y=2) and (8x+10y=4) have a unique solution?

Options:
A. (r=4)
B. (r\neq4)
C. (r=8)
D. (r\neq8)

Correct Answer:
B. (r\neq4)

Explanation Hindi:
अद्वितीय हल के लिए (\frac{r}{8}\neq\frac{5}{10}) होना चाहिए। इसलिए (r\neq4) सही है।

Explanation English:
For a unique solution, (\frac{r}{8}\neq\frac{5}{10}) must hold. So (r\neq4) is correct.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 80/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (5x-2y=c) और (15x-6y=21) में कोई हल न हो, इसके लिए (c) की शर्त क्या है?

For no solution in (5x-2y=c) and (15x-6y=21), what condition should (c) satisfy?

Explanation opens after your attempt

Correct Answer

C. \(c\neq7\)

Step 1

Concept

The coefficient ratio is \(\frac{1}{3}\). For no solution, \(\frac{c}{21}\neq\frac{1}{3}\), hence \(c\neq7\).

Step 2

Why this answer is correct

The correct answer is C. \(c\neq7\). The coefficient ratio is \(\frac{1}{3}\). For no solution, \(\frac{c}{21}\neq\frac{1}{3}\), hence \(c\neq7\).

Step 3

Exam Tip

गुणांक अनुपात \(\frac{1}{3}\) है। कोई हल नहीं के लिए \(\frac{c}{21}\neq\frac{1}{3}\), अतः \(c\neq7\)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (5x-2y=c) और (15x-6y=21) में कोई हल न हो, इसके लिए (c) की शर्त क्या है?

Question English:
For no solution in (5x-2y=c) and (15x-6y=21), what condition should (c) satisfy?

Options:
A. (c=7)
B. (c=21)
C. (c\neq7)
D. (c\neq21)

Correct Answer:
C. (c\neq7)

Explanation Hindi:
गुणांक अनुपात (\frac{1}{3}) है। कोई हल नहीं के लिए (\frac{c}{21}\neq\frac{1}{3}), अतः (c\neq7)।

Explanation English:
The coefficient ratio is (\frac{1}{3}). For no solution, (\frac{c}{21}\neq\frac{1}{3}), hence (c\neq7).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 81/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (3x+ay=6) और (9x+12y=b) के अनंत हलों के लिए ((a,b)) क्या होगा?

For infinitely many solutions of (3x+ay=6) and (9x+12y=b), what is ((a,b))?

Explanation opens after your attempt

Correct Answer

B. (a=4,\ b=18)

Step 1

Concept

All three ratios must be \(\frac{1}{3}\). So (a=4) and (b=18).

Step 2

Why this answer is correct

The correct answer is B. (a=4,\ b=18). All three ratios must be \(\frac{1}{3}\). So (a=4) and (b=18).

Step 3

Exam Tip

तीनों अनुपात \(\frac{1}{3}\) होने चाहिए। इसलिए (a=4) और (b=18) है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (3x+ay=6) और (9x+12y=b) के अनंत हलों के लिए ((a,b)) क्या होगा?

Question English:
For infinitely many solutions of (3x+ay=6) and (9x+12y=b), what is ((a,b))?

Options:
A. (a=3,\ b=12)
B. (a=4,\ b=18)
C. (a=6,\ b=18)
D. (a=4,\ b=12)

Correct Answer:
B. (a=4,\ b=18)

Explanation Hindi:
तीनों अनुपात (\frac{1}{3}) होने चाहिए। इसलिए (a=4) और (b=18) है।

Explanation English:
All three ratios must be (\frac{1}{3}). So (a=4) and (b=18).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 82/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म ((p-2)x+9y=4) और (5x+15y=12) का अद्वितीय हल कब होगा?

When will ((p-2)x+9y=4) and (5x+15y=12) have a unique solution?

Explanation opens after your attempt

Correct Answer

C. \(p\neq5\)

Step 1

Concept

For a unique solution, \(\frac{p-2}{5}\neq\frac{9}{15}\) is needed. Hence \(p\neq5\) is correct.

Step 2

Why this answer is correct

The correct answer is C. \(p\neq5\). For a unique solution, \(\frac{p-2}{5}\neq\frac{9}{15}\) is needed. Hence \(p\neq5\) is correct.

Step 3

Exam Tip

अद्वितीय हल के लिए \(\frac{p-2}{5}\neq\frac{9}{15}\) चाहिए। इसलिए \(p\neq5\) सही है।

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Question Page:
https://muftshiksha.com/question/when-will-p-2-x-9y-4-and-5x-15y-12-have-a-unique-solution

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म ((p-2)x+9y=4) और (5x+15y=12) का अद्वितीय हल कब होगा?

Question English:
When will ((p-2)x+9y=4) and (5x+15y=12) have a unique solution?

Options:
A. (p=5)
B. (p=2)
C. (p\neq5)
D. (p\neq2)

Correct Answer:
C. (p\neq5)

Explanation Hindi:
अद्वितीय हल के लिए (\frac{p-2}{5}\neq\frac{9}{15}) चाहिए। इसलिए (p\neq5) सही है।

Explanation English:
For a unique solution, (\frac{p-2}{5}\neq\frac{9}{15}) is needed. Hence (p\neq5) is correct.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 83/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (7x+(m^-4)y=13) और (14x+6y=26) के अनंत हलों के लिए (m) का मान बताइए।

Find (m) for infinitely many solutions of (7x+(m^-4)y=13) and (14x+6y=26).

Explanation opens after your attempt

Correct Answer

B. (m=7)

Step 1

Concept

For infinitely many solutions, \(\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}\) must hold. This gives (m=7).

Step 2

Why this answer is correct

The correct answer is B. (m=7). For infinitely many solutions, \(\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}\) must hold. This gives (m=7).

Step 3

Exam Tip

अनंत हलों में \(\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}\) होना चाहिए। इससे (m=7) मिलता है।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (7x+(m-4)y=13) और (14x+6y=26) के अनंत हलों के लिए (m) का मान बताइए।

Question English:
Find (m) for infinitely many solutions of (7x+(m-4)y=13) and (14x+6y=26).

Options:
A. (m=6)
B. (m=7)
C. (m=8)
D. (m=10)

Correct Answer:
B. (m=7)

Explanation Hindi:
अनंत हलों में (\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}) होना चाहिए। इससे (m=7) मिलता है।

Explanation English:
For infinitely many solutions, (\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}) must hold. This gives (m=7).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 84/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म ((k+1)x+4y=9) और (6x+8y=15) में कोई हल न होने के लिए (k) क्या होगा?

For no solution in ((k+1)x+4y=9) and (6x+8y=15), what is (k)?

Explanation opens after your attempt

Correct Answer

B. (k=2)

Step 1

Concept

Making coefficient ratios equal gives (k=2). The constant ratio is different, so there is no solution.

Step 2

Why this answer is correct

The correct answer is B. (k=2). Making coefficient ratios equal gives (k=2). The constant ratio is different, so there is no solution.

Step 3

Exam Tip

गुणांक अनुपात समान करने पर (k=2) आता है। स्थिर अनुपात अलग है, इसलिए कोई हल नहीं होगा।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म ((k+1)x+4y=9) और (6x+8y=15) में कोई हल न होने के लिए (k) क्या होगा?

Question English:
For no solution in ((k+1)x+4y=9) and (6x+8y=15), what is (k)?

Options:
A. (k=1)
B. (k=2)
C. (k=3)
D. (k=5)

Correct Answer:
B. (k=2)

Explanation Hindi:
गुणांक अनुपात समान करने पर (k=2) आता है। स्थिर अनुपात अलग है, इसलिए कोई हल नहीं होगा।

Explanation English:
Making coefficient ratios equal gives (k=2). The constant ratio is different, so there is no solution.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 85/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (5x+2y=6) और (15x+7y=18) के लिए हलों की संख्या क्या है?

How many solutions does the pair (5x+2y=6) and (15x+7y=18) have?

Explanation opens after your attempt

Correct Answer

C. अद्वितीय हलUnique solution

Step 1

Concept

Here \(5\times7-15\times2\neq0\). Therefore, the pair has a unique solution.

Step 2

Why this answer is correct

The correct answer is C. अद्वितीय हल / Unique solution. Here \(5\times7-15\times2\neq0\). Therefore, the pair has a unique solution.

Step 3

Exam Tip

यहाँ \(5\times7-15\times2\neq0\) है। इसलिए युग्म का अद्वितीय हल है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/how-many-solutions-does-the-pair-5x-2y-6-and-15x-7y-18-have

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (5x+2y=6) और (15x+7y=18) के लिए हलों की संख्या क्या है?

Question English:
How many solutions does the pair (5x+2y=6) and (15x+7y=18) have?

Options:
A. कोई हल नहीं / No solution
B. अनंत हल / Infinitely many solutions
C. अद्वितीय हल / Unique solution
D. ठीक (2) हल / Exactly (2) solutions

Correct Answer:
C. अद्वितीय हल / Unique solution

Explanation Hindi:
यहाँ (5\times7-15\times2\neq0) है। इसलिए युग्म का अद्वितीय हल है।

Explanation English:
Here (5\times7-15\times2\neq0). Therefore, the pair has a unique solution.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
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- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

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Question 86/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (9x-4y=11) और (18x-8y=21) की प्रकृति क्या है?

What is the nature of the pair (9x-4y=11) and (18x-8y=21)?

Explanation opens after your attempt

Correct Answer

A. कोई हल नहींNo solution

Step 1

Concept

The coefficient ratio is equal but the constant ratio is not equal. In exams, treat this as distinct parallel lines.

Step 2

Why this answer is correct

The correct answer is A. कोई हल नहीं / No solution. The coefficient ratio is equal but the constant ratio is not equal. In exams, treat this as distinct parallel lines.

Step 3

Exam Tip

गुणांक अनुपात समान है लेकिन स्थिर पद का अनुपात समान नहीं है। परीक्षा में इसे समांतर अलग रेखाओं का संकेत मानें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (9x-4y=11) और (18x-8y=21) की प्रकृति क्या है?

Question English:
What is the nature of the pair (9x-4y=11) and (18x-8y=21)?

Options:
A. कोई हल नहीं / No solution
B. अनंत हल / Infinitely many solutions
C. अद्वितीय हल / Unique solution
D. हर मान हल है / Every value is a solution

Correct Answer:
A. कोई हल नहीं / No solution

Explanation Hindi:
गुणांक अनुपात समान है लेकिन स्थिर पद का अनुपात समान नहीं है। परीक्षा में इसे समांतर अलग रेखाओं का संकेत मानें।

Explanation English:
The coefficient ratio is equal but the constant ratio is not equal. In exams, treat this as distinct parallel lines.

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2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
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Question 87/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (2x+3y=5) और (4x+6y=10) के लिए कौन-सा कथन सही है?

Which statement is correct for (2x+3y=5) and (4x+6y=10)?

Explanation opens after your attempt

Correct Answer

D. अनंत हलInfinitely many solutions

Step 1

Concept

The second equation is (2) times the first. Thus both are the same line and have infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is D. अनंत हल / Infinitely many solutions. The second equation is (2) times the first. Thus both are the same line and have infinitely many solutions.

Step 3

Exam Tip

दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों एक ही रेखा हैं और अनंत हल हैं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (2x+3y=5) और (4x+6y=10) के लिए कौन-सा कथन सही है?

Question English:
Which statement is correct for (2x+3y=5) and (4x+6y=10)?

Options:
A. कोई हल नहीं / No solution
B. अद्वितीय हल / Unique solution
C. हल केवल (x=0) पर है / Solution only at (x=0)
D. अनंत हल / Infinitely many solutions

Correct Answer:
D. अनंत हल / Infinitely many solutions

Explanation Hindi:
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों एक ही रेखा हैं और अनंत हल हैं।

Explanation English:
The second equation is (2) times the first. Thus both are the same line and have infinitely many solutions.

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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question 88/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

युग्म (4x-7y=5) और (12x-21y=17) की हल-स्थिति क्या है?

What is the solution status of (4x-7y=5) and (12x-21y=17)?

Explanation opens after your attempt

Correct Answer

C. कोई हल नहींNo solution

Step 1

Concept

The coefficient ratio is \(\frac{1}{3}\) but the constant ratio is \(\frac{5}{17}\). Therefore, there is no solution.

Step 2

Why this answer is correct

The correct answer is C. कोई हल नहीं / No solution. The coefficient ratio is \(\frac{1}{3}\) but the constant ratio is \(\frac{5}{17}\). Therefore, there is no solution.

Step 3

Exam Tip

गुणांक अनुपात \(\frac{1}{3}\) है पर स्थिर अनुपात \(\frac{5}{17}\) है। अतः कोई हल नहीं मिलेगा।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
युग्म (4x-7y=5) और (12x-21y=17) की हल-स्थिति क्या है?

Question English:
What is the solution status of (4x-7y=5) and (12x-21y=17)?

Options:
A. अद्वितीय हल / Unique solution
B. अनंत हल / Infinitely many solutions
C. कोई हल नहीं / No solution
D. तीन हल / Three solutions

Correct Answer:
C. कोई हल नहीं / No solution

Explanation Hindi:
गुणांक अनुपात (\frac{1}{3}) है पर स्थिर अनुपात (\frac{5}{17}) है। अतः कोई हल नहीं मिलेगा।

Explanation English:
The coefficient ratio is (\frac{1}{3}) but the constant ratio is (\frac{5}{17}). Therefore, there is no solution.

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1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question 89/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

रेखाएँ (7x+3y=10) और (14x+6y=19) के लिए सही निष्कर्ष क्या है?

What is the correct conclusion for the lines (7x+3y=10) and (14x+6y=19)?

Explanation opens after your attempt

Correct Answer

B. कोई हल नहींNo solution

Step 1

Concept

Coefficient ratios are equal but the constant ratio is different. Hence the lines are parallel and have no solution.

Step 2

Why this answer is correct

The correct answer is B. कोई हल नहीं / No solution. Coefficient ratios are equal but the constant ratio is different. Hence the lines are parallel and have no solution.

Step 3

Exam Tip

गुणांकों के अनुपात समान हैं पर स्थिर पद का अनुपात अलग है। इसलिए रेखाएँ समांतर हैं और कोई हल नहीं है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
रेखाएँ (7x+3y=10) और (14x+6y=19) के लिए सही निष्कर्ष क्या है?

Question English:
What is the correct conclusion for the lines (7x+3y=10) and (14x+6y=19)?

Options:
A. अनंत हल / Infinitely many solutions
B. कोई हल नहीं / No solution
C. अद्वितीय हल / Unique solution
D. निर्धारित नहीं / Cannot be decided

Correct Answer:
B. कोई हल नहीं / No solution

Explanation Hindi:
गुणांकों के अनुपात समान हैं पर स्थिर पद का अनुपात अलग है। इसलिए रेखाएँ समांतर हैं और कोई हल नहीं है।

Explanation English:
Coefficient ratios are equal but the constant ratio is different. Hence the lines are parallel and have no solution.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question 90/117 Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

रेखाएँ (2x-5y=1) और (6x-15y=3) किस प्रकार का हल देती हैं?

What type of solution is given by the lines (2x-5y=1) and (6x-15y=3)?

Explanation opens after your attempt

Correct Answer

C. अनंत हलInfinitely many solutions

Step 1

Concept

All three ratios are equal, so the lines are coincident. Coincident lines give infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is C. अनंत हल / Infinitely many solutions. All three ratios are equal, so the lines are coincident. Coincident lines give infinitely many solutions.

Step 3

Exam Tip

तीनों अनुपात समान हैं, इसलिए रेखाएँ संपाती हैं। संपाती रेखाएँ अनंत हल देती हैं।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Conditions for solvability
Difficulty: Expert
Level: 59

Question Hindi:
रेखाएँ (2x-5y=1) और (6x-15y=3) किस प्रकार का हल देती हैं?

Question English:
What type of solution is given by the lines (2x-5y=1) and (6x-15y=3)?

Options:
A. कोई हल नहीं / No solution
B. अद्वितीय हल / Unique solution
C. अनंत हल / Infinitely many solutions
D. केवल दो हल / Exactly two solutions

Correct Answer:
C. अनंत हल / Infinitely many solutions

Explanation Hindi:
तीनों अनुपात समान हैं, इसलिए रेखाएँ संपाती हैं। संपाती रेखाएँ अनंत हल देती हैं।

Explanation English:
All three ratios are equal, so the lines are coincident. Coincident lines give infinitely many solutions.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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solvability MCQ Questions for Class 10

Practice Questions

यदि दो रेखाओं की ढाल अलग-अलग हों, तो उनके युग्म के लिए कौन-सा निष्कर्ष सही है?

Concept

Why this answer is correct

Exam Tip

यदि दो रेखाओं की ढाल समान और (y)-अवरोध अलग हों, तो उनके समीकरणों के युग्म में कितने हल होंगे?

Concept

Why this answer is correct

Exam Tip

यदि (D=0) और कम से कम एक सहायक सारणिक शून्य नहीं है, तो युग्म की हल-स्थिति क्या होगी?

Concept

Why this answer is correct

Exam Tip

संपाती रेखाओं के लिए सही बीजीय शर्त कौन-सी है?

Concept

Why this answer is correct

Exam Tip

यदि \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\) है, तो दो रैखिक समीकरणों के युग्म के लिए क्या निष्कर्ष होगा?

Concept

Why this answer is correct

Exam Tip

यदि किसी युग्म में गुणांक अनुपात समान है और स्थिर पद का अनुपात अलग है, तो हल-स्थिति क्या होगी?

Concept

Why this answer is correct

Exam Tip

सामान्य युग्म \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) में कोई हल न होने की शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

युग्म (4x+5y=1) और (8x+9y=2) के लिए हलों की संख्या क्या है?

Concept

Why this answer is correct

Exam Tip

युग्म (3x-y=4) और (6x-2y=9) के बारे में सही कथन चुनिए।

Concept

Why this answer is correct

Exam Tip

युग्म (x+2y=3) और (4x+8y=12) के लिए सही हल-स्थिति कौन-सी है?

Concept

Why this answer is correct

Exam Tip

युग्म (6x+(h+1)y=12) और (15x+20y=30) के अनंत हलों के लिए (h) क्या है?

Concept

Why this answer is correct

Exam Tip

युग्म (lx+6y=8) और (9x+18y=10) में कोई हल न होने के लिए (l) क्या होगा?

Concept

Why this answer is correct

Exam Tip

युग्म (ax+by=1) और (2ax+3by=5) के अद्वितीय हल की शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

युग्म (2x+3y=d) और (14x+21y=28) में कोई हल न हो, इसके लिए (d) पर कौन-सी शर्त होगी?

Concept

Why this answer is correct

Exam Tip

युग्म ((v+2)x-3y=6) और (10x-5y=10) के अनंत हलों के लिए (v) क्या होगा?

Concept

Why this answer is correct

Exam Tip

युग्म (13x-ty=5) और (26x-10y=14) का अद्वितीय हल कब होगा?

Concept

Why this answer is correct

Exam Tip

युग्म (ux+9y=7) और (4x+6y=11) में कोई हल न होने के लिए (u) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

युग्म (12x+sy=18) और (20x+10y=30) के अनंत हलों के लिए (s) क्या होगा?

Concept

Why this answer is correct

Exam Tip

युग्म (rx+5y=2) और (8x+10y=4) का अद्वितीय हल कब होगा?

Concept

Why this answer is correct

Exam Tip

युग्म (5x-2y=c) और (15x-6y=21) में कोई हल न हो, इसके लिए (c) की शर्त क्या है?

Concept

युग्म (7x+(m^-4)y=13) और (14x+6y=26) के अनंत हलों के लिए (m) का मान बताइए।