100 results found for "equations" in Class 10.
निम्न में से कौन सा समीकरण द्विघात समीकरण है?
Which of the following equations is a quadratic equation?
#quadratic equations
#introduction
#identification
A \(x^2+3x+2=0\)
B (2x+5=0)
C \(x^3+x=0\)
D (7=0)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+2=0\)
Step 1
Concept
A quadratic equation has highest power (2) of (x). In exams first check the degree.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+2=0\). A quadratic equation has highest power (2) of (x). In exams first check the degree.
Step 3
Exam Tip
द्विघात समीकरण में (x) की सबसे बड़ी घात (2) होती है। परीक्षा में सबसे पहले घात देखें।
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समीकरणों (6x+3y=39) और (2x+y=13) के बारे में सही कथन कौन-सा है?
Which statement is correct about the equations (6x+3y=39) and (2x+y=13)?
#linear equations
#equivalent equations
#easy
#class 10
A इनका कोई हल नहीं है / They have no solution
B इनका केवल (x=1,\ y=11) हल है / They have only the solution (x=1,\ y=11)
C इनमें केवल (x) है / They contain only (x)
D पहला समीकरण दूसरे का (3) गुना है / The first equation is (3) times the second
Explanation opens after your attempt
Correct Answer
D. पहला समीकरण दूसरे का (3) गुना है / The first equation is (3) times the second
Step 1
Concept
Multiplying (2x+y=13) by (3) gives (6x+3y=39). Recognizing equivalent equations is also useful in exams.
Step 2
Why this answer is correct
The correct answer is D. पहला समीकरण दूसरे का (3) गुना है / The first equation is (3) times the second. Multiplying (2x+y=13) by (3) gives (6x+3y=39). Recognizing equivalent equations is also useful in exams.
Step 3
Exam Tip
(2x+y=13) को (3) से गुणा करने पर (6x+3y=39) मिलता है। समान समीकरणों को पहचानना भी परीक्षा में उपयोगी है।
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यदि (2x+4y=18) और (x+2y=9), तो इन दोनों समीकरणों के बारे में सही कथन क्या है?
If (2x+4y=18) and (x+2y=9), which statement is correct about these two equations?
#linear equations
#dependent equations
#easy
#class 10
A दोनों अलग-अलग हल देती हैं / They give different solutions
B पहला समीकरण दूसरे का (2) गुना है / The first equation is (2) times the second
C इनमें कोई चर नहीं है / They have no variable
D दोनों में केवल (x) है / They contain only (x)
Explanation opens after your attempt
Correct Answer
B. पहला समीकरण दूसरे का (2) गुना है / The first equation is (2) times the second
Step 1
Concept
The first equation is (2(x+2y)=18), so it is (2) times the second. Recognizing proportional equations is also important.
Step 2
Why this answer is correct
The correct answer is B. पहला समीकरण दूसरे का (2) गुना है / The first equation is (2) times the second. The first equation is (2(x+2y)=18), so it is (2) times the second. Recognizing proportional equations is also important.
Step 3
Exam Tip
पहला समीकरण (2(x+2y)=18) है, इसलिए यह दूसरे का (2) गुना है। समानुपाती समीकरणों को पहचानना भी जरूरी है।
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यदि (D=0), \(D_x=0\) और \(D_y=0\) हैं, तो दो रैखिक समीकरणों के युग्म में क्या होगा?
If (D=0), \(D_x=0\), and \(D_y=0\), what happens in a pair of two linear equations?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अद्वितीय हल / Unique solution
C अनंत हल / Infinitely many solutions
D हमेशा गलत समीकरण / Always false equations
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
When all three determinants are zero, the equations may be dependent. In Class (10), link this with infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. When all three determinants are zero, the equations may be dependent. In Class (10), link this with infinitely many solutions.
Step 3
Exam Tip
तीनों सारणिक शून्य होने पर समीकरण आश्रित हो सकते हैं। कक्षा (10) में इसे अनंत हल की स्थिति से जोड़कर देखें।
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समीकरणों (21x+8y=97) और (42x+16y=194) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (21x+8y=97) and (42x+16y=194)?
#linear equations
#expert
#observation
#same line
A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं और अनंत हल हैं।
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दो वस्तुओं की कीमतों के लिए (10x+3y=470) और (20x+6y=955) समीकरण बने। यह प्रणाली कैसी है?
For prices of two items, the equations (10x+3y=470) and (20x+6y=955) are formed. What type of system is this?
#linear equations
#expert
#word problem
#inconsistent
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (470/955) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (470/955) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (470/955) अलग है। इसलिए प्रणाली असंगत है।
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समीकरणों (7x+19y=86) और (13x+35y=158) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in the equations (7x+19y=86) and (13x+35y=158)?
#linear equations
#expert
#ratio comparison
#unique solution
A (7 / 13=19 / 35), इसलिए कोई हल नहीं / 35), so no solution
B (7 / 13=19 / 35), इसलिए अनंत हल / 35), so infinitely many solutions
C (7 / 13 \ne 19 / 35), इसलिए एक अद्वितीय हल / 35), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (7 / 13 \ne 19 / 35), इसलिए एक अद्वितीय हल / 35), so one unique solution
Step 1
Concept
The first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 13 \ne 19 / 35\), इसलिए एक अद्वितीय हल / 35), so one unique solution. The first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 3
Exam Tip
पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक अद्वितीय हल देती हैं।
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समीकरणों (12x-7y+29=0) और (36x-21y+91=0) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (12x-7y+29=0) and (36x-21y+91=0)?
#linear equations
#expert
#ratio relation
#no solution
A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (12/36=(-7)/(-21)) but (29/91) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (12/36=(-7)/(-21)) but (29/91) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (12/36=(-7)/(-21)) लेकिन (29/91) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (11x+ky=70) और (5x+4y=31) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (11x+ky=70) and (5x+4y=31) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (k=44 / 5)
B (k\ne44 / 5)
C (k=4)
D (k=11)
Explanation opens after your attempt
Correct Answer
B. (k\ne44 / 5)
Step 1
Concept
For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(k\ne44 / 5\). For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(11/5 \ne k/4\) होना चाहिए। इसलिए \(k\ne44/5\) सही शर्त है।
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समीकरणों (px+10y=50) और (14x+35y=122) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+10y=50) and (14x+35y=122) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 2
Why this answer is correct
The correct answer is B. (4). For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/14=10/35) और (50/122) अलग होना चाहिए। इसलिए (p=4)।
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समीकरणों (6x+ay=42) और (18x+33y=126) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (6x+ay=42) and (18x+33y=126) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 2
Why this answer is correct
The correct answer is C. (11). For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 3
Exam Tip
अनंत हल के लिए (6/18=a/33=42/126) होना चाहिए। इसलिए (a=11) सही है।
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समीकरणों (5x+9y=64) और (15x+27y=t) के असंगत होने के लिए (t) के लिए सही शर्त क्या है?
What is the correct condition on (t) for the equations (5x+9y=64) and (15x+27y=t) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
A (t=192)
B \(t\ne192\)
C (t=64)
D (t=128)
Explanation opens after your attempt
Correct Answer
B. \(t\ne192\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne192\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(t\ne192\)।
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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?
#class10
#linear-equations
#solvability
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
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique 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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समीकरणों (29x+12y=101) और (14x+6y=49) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (29x+12y=101) and (14x+6y=49)?
#linear equations
#expert
#unique solution
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(29/14 \ne 12/6\), so the lines will intersect. Hence, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(29/14 \ne 12/6\), so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(29/14 \ne 12/6\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरणों (24x-18y=102) और (4x-3y=18) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing the equations (24x-18y=102) and (4x-3y=18)?
#linear equations
#expert
#no solution
#observation
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Here (24/4=(-18)/(-3)) but (102/18) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Here (24/4=(-18)/(-3)) but (102/18) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (24/4=(-18)/(-3)) लेकिन (102/18) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (18x+13y=89) और (36x+26y=178) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (18x+13y=89) and (36x+26y=178)?
#linear equations
#expert
#observation
#same line
A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं।
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समीकरणों (12x+ky=132) और (3x+10y=33) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (12x+ky=132) and (3x+10y=33) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
A (38)
B (39)
C (40)
D (41)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (4) times the second. Therefore, (k=40).
Step 2
Why this answer is correct
The correct answer is C. (40). The first equation must be (4) times the second. Therefore, (k=40).
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=40) है।
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समीकरणों (10x+9y=38) और (20x+ay=91) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for the equations (10x+9y=38) and (20x+ay=91) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 2
Why this answer is correct
The correct answer is C. (18). For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 3
Exam Tip
कोई हल नहीं के लिए (10/20=9/a) और (38/91) अलग होना चाहिए। इससे (a=18) मिलता है।
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समीकरणों (13x+8y=49) और (26x+16y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (13x+8y=49) and (26x+16y=r) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
A (r=98)
B \(r\ne98\)
C (r=49)
D (r=100)
Explanation opens after your attempt
Correct Answer
B. \(r\ne98\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 2
Why this answer is correct
The correct answer is B. \(r\ne98\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(r\ne98\)।
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समीकरणों (9x+16y=77) और (27x+48y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
#linear equations
#expert
#consistent dependent
#parameter
A (229)
B (230)
C (231)
D (232)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 2
Why this answer is correct
The correct answer is C. (231). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=231)।
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समीकरणों (12x+13y=55) और (24x+25y=107) के लिए कौन-सा कथन सही है?
Which statement is correct for the equations (12x+13y=55) and (24x+25y=107)?
#linear equations
#expert
#ratio comparison
#unique solution
A (12 / 24=13 / 25), इसलिए कोई हल नहीं / 25), so no solution
B (12 / 24 \ne 13 / 25), इसलिए एक अद्वितीय हल / 25), so one unique solution
C तीनों अनुपात बराबर हैं / All three ratios are equal
D रेखाएं संपाती हैं / Lines are coincident
Explanation opens after your attempt
Correct Answer
B. (12 / 24 \ne 13 / 25), इसलिए एक अद्वितीय हल / 25), so one unique solution
Step 1
Concept
Here \(12/24 \ne 13/25\), so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(12 / 24 \ne 13 / 25\), इसलिए एक अद्वितीय हल / 25), so one unique solution. Here \(12/24 \ne 13/25\), so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(12/24 \ne 13/25\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरणों (18x+27y=126) और (2x+3y=16) के लिए कौन-सा संबंध सही है?
Which relation is correct for the equations (18x+27y=126) and (2x+3y=16)?
#linear equations
#expert
#ratio relation
#no solution
A (18 / 2 \ne 27 / 3)
B (18 / 2=27 / 3=126 / 16)
C (18 / 2=27 / 3 \ne 126 / 16)
D (18 / 2=126 / 16 \ne 27 / 3)
Explanation opens after your attempt
Correct Answer
C. (18 / 2=27 / 3 \ne 126 / 16)
Step 1
Concept
The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 2
Why this answer is correct
The correct answer is C. \(18 / 2=27 / 3 \ne 126 / 16\). The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है। इसलिए कोई हल नहीं है।
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समीकरणों (11x+18y=86) और (33x+54y=258) में तीनों अनुपातों का संबंध क्या है?
What is the relation among all three ratios in the equations (11x+18y=86) and (33x+54y=258)?
#linear equations
#expert
#ratio relation
#coincident
A तीनों बराबर हैं / All three are equal
B पहले दो बराबर और तीसरा अलग है / First two are equal and third is different
C पहले दो अलग हैं / First two are different
D केवल स्थिर पद बराबर हैं / Only constants are equal
Explanation opens after your attempt
Correct Answer
A. तीनों बराबर हैं / All three are equal
Step 1
Concept
Here (11/33=18/54=86/258). Therefore, both equations form the same line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बराबर हैं / All three are equal. Here (11/33=18/54=86/258). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (11/33=18/54=86/258)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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दो संख्याओं के लिए (7x+5y=58) और (4x-3y=11) समीकरण बनते हैं, तो हल-स्थिति क्या होगी?
For two numbers, the equations (7x+5y=58) and (4x-3y=11) are formed. What will be the solution status?
#linear equations
#expert
#word problem
#unique solution
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
A. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here (7/4 \ne 5/(-3)), so the lines intersect. Such a pair has one unique solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here (7/4 \ne 5/(-3)), so the lines intersect. Such a pair has one unique solution.
Step 3
Exam Tip
यहां (7/4 \ne 5/(-3)), इसलिए रेखाएं कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है।
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दो टिकटों के दामों के लिए (9x+4y=380) और (18x+8y=775) समीकरण बने। यह प्रणाली कैसी है?
For prices of two tickets, the equations (9x+4y=380) and (18x+8y=775) are formed. What type of system is this?
#linear equations
#expert
#word problem
#inconsistent
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (380/775) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (380/775) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (380/775) अलग है। इसलिए प्रणाली असंगत है।
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एक दुकान में दो वस्तुओं के लिए (6x+11y=420) और (18x+33y=1260) समीकरण बनते हैं। हलों की संख्या क्या होगी?
In a shop, the equations for two items are (6x+11y=420) and (18x+33y=1260). How many solutions will there be?
#linear equations
#expert
#word problem
#infinite solutions
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं।
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समीकरणों (18x+7y=61) और (9x+4y=32) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (18x+7y=61) and (9x+4y=32)?
#linear equations
#expert
#consistent independent
A असंगत / Inconsistent
B संगत और आश्रित / Consistent and dependent
C संगत और स्वतंत्र / Consistent and independent
D समानांतर / Parallel
Explanation opens after your attempt
Correct Answer
C. संगत और स्वतंत्र / Consistent and independent
Step 1
Concept
Here \(18/9 \ne 7/4\), so the lines intersect. Hence, the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. संगत और स्वतंत्र / Consistent and independent. Here \(18/9 \ne 7/4\), so the lines intersect. Hence, the pair is consistent and independent.
Step 3
Exam Tip
यहां \(18/9 \ne 7/4\), इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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समीकरणों (26x+39y=117) और (2x+3y=10) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (26x+39y=117) and (2x+3y=10)?
#linear equations
#expert
#inconsistent
#classification
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D संपाती / Coincident
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
Here (26/2=39/3) but (117/10) is different. Therefore, this is an inconsistent pair.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (26/2=39/3) but (117/10) is different. Therefore, this is an inconsistent pair.
Step 3
Exam Tip
यहां (26/2=39/3) लेकिन (117/10) अलग है। इसलिए यह असंगत युग्म है।
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समीकरणों (30x+45y=210) और (2x+3y=14) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (30x+45y=210) and (2x+3y=14)?
#linear equations
#expert
#dependent pair
#classification
A संगत और आश्रित / Consistent and dependent
B असंगत / Inconsistent
C संगत और स्वतंत्र / Consistent and independent
D असमाधेय / Unsolvable
Explanation opens after your attempt
Correct Answer
A. संगत और आश्रित / Consistent and dependent
Step 1
Concept
The first equation is (15) times the second. Therefore, both are the same line and the pair is dependent.
Step 2
Why this answer is correct
The correct answer is A. संगत और आश्रित / Consistent and dependent. The first equation is (15) times the second. Therefore, both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (15) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरणों (19x+12y=71) और (9x+6y=35) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (19x+12y=71) and (9x+6y=35)?
#linear equations
#expert
#ratio comparison
#unique solution
A (19 / 9=12 / 6), इसलिए अनंत हल / 6), so infinitely many solutions
B (19 / 9=12 / 6), इसलिए कोई हल नहीं / 6), so no solution
C (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
D (19 / 9=71 / 35), इसलिए संपाती / 35), so coincident
Explanation opens after your attempt
Correct Answer
C. (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(19 / 9 \ne 12 / 6\), इसलिए एक अद्वितीय हल / 6), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरणों (24x+32y=96) और (3x+4y=13) को देखकर कौन-सा निष्कर्ष सही है?
Which conclusion is correct by observing the equations (24x+32y=96) and (3x+4y=13)?
#linear equations
#expert
#observation
#no solution
A तीनों अनुपात बराबर हैं / All three ratios are equal
B पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
C पहले दो अनुपात अलग हैं / First two ratios are different
D रेखाएं कटती हैं / Lines intersect
Explanation opens after your attempt
Correct Answer
B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
Step 1
Concept
Here (24/3=32/4) but (96/13) is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different. Here (24/3=32/4) but (96/13) is different. Therefore, there will be no solution.
Step 3
Exam Tip
यहां (24/3=32/4) लेकिन (96/13) अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (8x+15y=73) और (24x+45y=219) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing the equations (8x+15y=73) and (24x+45y=219)?
#linear equations
#expert
#observation
#infinite solutions
A एक अद्वितीय हल है / There is one unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Explanation opens after your attempt
Correct Answer
C. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल हैं / There are infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं।
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समीकरणों (17x+py=51) और (8x+3y=25) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (17x+py=51) and (8x+3y=25) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (p=51 / 8)
B (p\ne51 / 8)
C (p=3)
D (p=17)
Explanation opens after your attempt
Correct Answer
B. (p\ne51 / 8)
Step 1
Concept
For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne51 / 8\). For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(17/8 \ne p/3\) होना चाहिए। इसलिए \(p\ne51/8\) सही शर्त है।
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समीकरणों (7x+dy=63) और (28x+36y=252) के अनंत हल होने के लिए (d) का मान क्या है?
What is the value of (d) for the equations (7x+dy=63) and (28x+36y=252) to have infinitely many solutions?
#linear equations
#expert
#parameter
#dependent pair
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 3
Exam Tip
अनंत हल के लिए (7/28=d/36=63/252) होना चाहिए। इसलिए (d=9)।
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समीकरणों (15x+8y-47=0) और (30x+17y-94=0) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for the equations (15x+8y-47=0) and (30x+17y-94=0)?
#linear equations
#expert
#unique solution
#ratio test
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(15/30 \ne 8/17\), so the lines intersect at one point. In this case, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(15/30 \ne 8/17\), so the lines intersect at one point. In this case, one unique solution is obtained.
Step 3
Exam Tip
यहां \(15/30 \ne 8/17\), इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसी स्थिति में एक अद्वितीय हल मिलता है।
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समीकरणों (16x-9y+55=0) और (32x-18y+113=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for the equations (16x-9y+55=0) and (32x-18y+113=0)?
#linear equations
#expert
#ratio relation
#no solution
A (16 / 32=(-9) / (-18) \ne 55 / 113)
B (16 / 32 \ne (-9) / (-18))
C (16 / 32=(-9) / (-18)=55 / 113)
D (16 / 32=55 / 113 \ne (-9) / (-18))
Explanation opens after your attempt
Correct Answer
A. (16 / 32=(-9) / (-18) \ne 55 / 113)
Step 1
Concept
The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is A. (16 / 32=(-9) / (-18) \ne 55 / 113). The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं और तीसरा अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (10x+13y-71=0) और (30x+39y-213=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for the equations (10x+13y-71=0) and (30x+39y-213=0)?
#linear equations
#expert
#ratio relation
#infinite solutions
A (10 / 30=13 / 39 \ne (-71) / (-213))
B (10 / 30 \ne 13 / 39)
C (10 / 30=13 / 39=(-71) / (-213))
D (10 / 30=(-71) / (-213) \ne 13 / 39)
Explanation opens after your attempt
Correct Answer
C. (10 / 30=13 / 39=(-71) / (-213))
Step 1
Concept
Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (10 / 30=13 / 39=(-71) / (-213)). Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (5x+17y=69) और (12x+41y=166) के ग्राफ का सही वर्णन क्या है?
What is the correct description of the graph of the equations (5x+17y=69) and (12x+41y=166)?
#linear equations
#expert
#graph
#intersecting lines
A संपाती रेखाएं / Coincident lines
B अलग समानांतर रेखाएं / Distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
Step 1
Concept
Here \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(5/12 \ne 17/41\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
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समीकरणों (30x+18y=126) और (5x+3y=21) के ग्राफ में क्या दिखेगा?
What will be shown in the graph of the equations (30x+18y=126) and (5x+3y=21)?
#linear equations
#expert
#graph
#same line
A एक ही रेखा / Same line
B दो अलग समानांतर रेखाएं / Two distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई रेखा नहीं / No line
Explanation opens after your attempt
Correct Answer
A. एक ही रेखा / Same line
Step 1
Concept
The first equation is (6) times the second. Therefore, both equations show the same line.
Step 2
Why this answer is correct
The correct answer is A. एक ही रेखा / Same line. The first equation is (6) times the second. Therefore, both equations show the same line.
Step 3
Exam Tip
पहला समीकरण दूसरे का (6) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं।
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समीकरणों (22x+33y=99) और (2x+3y=12) के ग्राफ के बारे में सही कथन कौन-सा है?
Which statement is correct about the graph of the equations (22x+33y=99) and (2x+3y=12)?
#linear equations
#expert
#graph
#parallel lines
A रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
B रेखाएं संपाती हैं / Lines are coincident
C रेखाएं अलग समानांतर हैं / Lines are distinct parallel
D रेखाएं लंबवत हैं / Lines are perpendicular
Explanation opens after your attempt
Correct Answer
C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Step 1
Concept
Here (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (22/2=33/3) लेकिन (99/12) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
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समीकरणों (bx+16y=64) और (14x+28y=131) का कोई हल न होने के लिए (b) का मान क्या होगा?
What is the value of (b) for the equations (bx+16y=64) and (14x+28y=131) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 2
Why this answer is correct
The correct answer is C. (8). For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 3
Exam Tip
कोई हल नहीं के लिए (b/14=16/28) और (64/131) अलग होना चाहिए। इसलिए (b=8)।
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समीकरणों (8x+ay=72) और (24x+30y=216) के अनंत हल होने के लिए (a) क्या होगा?
What will (a) be for the equations (8x+ay=72) and (24x+30y=216) to have infinitely many solutions?
#linear equations
#expert
#ratio condition
#parameter
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 3
Exam Tip
अनंत हल के लिए (8/24=a/30=72/216) होना चाहिए। इससे (a=10) मिलता है।
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समीकरणों (12x+py=60) और (3x+5y=16) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (12x+py=60) and (3x+5y=16) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (p=20)
B \(p\ne20\)
C (p=5)
D (p=12)
Explanation opens after your attempt
Correct Answer
B. \(p\ne20\)
Step 1
Concept
For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne20\). For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(12/3 \ne p/5\) होना चाहिए। इसलिए \(p\ne20\) सही शर्त है।
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समीकरणों (13x+qy=52) और (26x+18y=104) के अनंत हल होने के लिए (q) का मान क्या है?
What is the value of (q) for the equations (13x+qy=52) and (26x+18y=104) to have infinitely many solutions?
#linear equations
#expert
#dependent pair
#parameter
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 2
Why this answer is correct
The correct answer is C. (9). The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए (q/18=1/2) होना चाहिए। अतः (q=9)।
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समीकरणों (kx+14y=42) और (18x+21y=63) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (kx+14y=42) and (18x+21y=63) to have infinitely many solutions?
#linear equations
#expert
#parameter
#infinite solutions
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 2
Why this answer is correct
The correct answer is C. (12). For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 3
Exam Tip
अनंत हल के लिए (k/18=14/21=42/63) होना चाहिए। इसलिए (k=12) सही है।
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समीकरणों (11x+14y=53) और (17x+22y=83) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (11x+14y=53) and (17x+22y=83)?
#linear equations
#expert
#unique solution
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
B. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(11/17 \ne 14/22\), so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. Here \(11/17 \ne 14/22\), so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 3
Exam Tip
यहां \(11/17 \ne 14/22\), इसलिए रेखाएं एक बिंदु पर कटती हैं। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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समीकरणों (9x+5y=41) और (18x+10y=85) के लिए हलों की संख्या क्या होगी?
How many solutions will the equations (9x+5y=41) and (18x+10y=85) have?
#linear equations
#expert
#parallel lines
#no solution
A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (9/18=5/10) but (41/85) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (9/18=5/10) but (41/85) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (9/18=5/10) लेकिन (41/85) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (7x-4y=29) और (21x-12y=87) के लिए सही निष्कर्ष कौन-सा है?
Which conclusion is correct for the equations (7x-4y=29) and (21x-12y=87)?
#linear equations
#expert
#coincident lines
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D अलग समानांतर रेखाएं / Distinct parallel lines
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (px+9y=45) और (20x+30y=103) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+9y=45) and (20x+30y=103) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 2
Why this answer is correct
The correct answer is B. (6). For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/20=9/30) और (45/103) अलग होना चाहिए। इससे (p=6) मिलता है।
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समीकरणों (4x+ay=32) और (12x+21y=96) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (4x+ay=32) and (12x+21y=96) to have infinitely many solutions?
#linear equations
#expert
#parameter
#infinite solutions
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 2
Why this answer is correct
The correct answer is C. (7). For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 3
Exam Tip
अनंत हल के लिए (4/12=a/21=32/96) होना चाहिए। इसलिए (a=7) सही है।
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समीकरणों (18x+5y=79) और (36x+10y=158) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (18x+5y=79) and (36x+10y=158)?
#linear equations
#hard
#observation
#same line
A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं और अनंत हल हैं।
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दो वस्तुओं की कीमतों के लिए (9x+4y=360) और (27x+12y=1090) समीकरण बने। यह प्रणाली कैसी है?
For prices of two items, the equations (9x+4y=360) and (27x+12y=1090) are formed. What type of system is this?
#linear equations
#hard
#word problem
#inconsistent
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (360/1090) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (360/1090) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (360/1090) अलग है। इसलिए प्रणाली असंगत है।
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समीकरणों (6x+17y=71) और (11x+31y=130) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in the equations (6x+17y=71) and (11x+31y=130)?
#linear equations
#hard
#ratio comparison
#unique solution
A (6 / 11=17 / 31), इसलिए कोई हल नहीं / 31), so no solution
B (6 / 11=17 / 31), इसलिए अनंत हल / 31), so infinitely many solutions
C (6 / 11 \ne 17 / 31), इसलिए एक अद्वितीय हल / 31), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (6 / 11 \ne 17 / 31), इसलिए एक अद्वितीय हल / 31), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 2
Why this answer is correct
The correct answer is C. \(6 / 11 \ne 17 / 31\), इसलिए एक अद्वितीय हल / 31), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक अद्वितीय हल देती हैं।
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समीकरणों (14x-8y+25=0) और (21x-12y+40=0) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (14x-8y+25=0) and (21x-12y+40=0)?
#linear equations
#hard
#ratio relation
#no solution
A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (14/21=(-8)/(-12)) but (25/40) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (14/21=(-8)/(-12)) but (25/40) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (14/21=(-8)/(-12)) लेकिन (25/40) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (13x+py=52) और (6x+5y=24) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (13x+py=52) and (6x+5y=24) to have a unique solution?
#linear equations
#hard
#unique solution
#parameter
A (p \ne 65 / 6)
B (p=65 / 6)
C (p=5)
D (p=13)
Explanation opens after your attempt
Correct Answer
A. (p \ne 65 / 6)
Step 1
Concept
For a unique solution, \(13/6 \ne p/5\) must hold. Therefore, \(p \ne 65/6\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is A. \(p \ne 65 / 6\). For a unique solution, \(13/6 \ne p/5\) must hold. Therefore, \(p \ne 65/6\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(13/6 \ne p/5\) होना चाहिए। इसलिए \(p \ne 65/6\) सही शर्त है।
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समीकरणों (bx+9y=36) और (16x+24y=97) का कोई हल न होने के लिए (b) का मान क्या होगा?
What is the value of (b) for the equations (bx+9y=36) and (16x+24y=97) to have no solution?
#linear equations
#hard
#no solution
#parameter
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
For no solution, (b/16=9/24) and (36/97) must be different. Hence, (b=6).
Step 2
Why this answer is correct
The correct answer is D. (6). For no solution, (b/16=9/24) and (36/97) must be different. Hence, (b=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (b/16=9/24) और (36/97) अलग होना चाहिए। इसलिए (b=6)।
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समीकरणों (5x+ay=45) और (20x+28y=180) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (5x+ay=45) and (20x+28y=180) to have infinitely many solutions?
#linear equations
#hard
#infinite solutions
#parameter
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (5/20=a/28=45/180) must hold. Therefore, (a=7) is correct.
Step 2
Why this answer is correct
The correct answer is C. (7). For infinitely many solutions, (5/20=a/28=45/180) must hold. Therefore, (a=7) is correct.
Step 3
Exam Tip
अनंत हल के लिए (5/20=a/28=45/180) होना चाहिए। इसलिए (a=7) सही है।
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समीकरणों (4x+7y=31) और (12x+21y=t) के असंगत होने के लिए (t) के लिए सही शर्त क्या है?
What is the correct condition on (t) for the equations (4x+7y=31) and (12x+21y=t) to be inconsistent?
#linear equations
#hard
#inconsistent
#parameter
A (t=93)
B \(t \ne 93\)
C (t=31)
D (t=62)
Explanation opens after your attempt
Correct Answer
B. \(t \ne 93\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t \ne 93\).
Step 2
Why this answer is correct
The correct answer is B. \(t \ne 93\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t \ne 93\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(t \ne 93\)।
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समीकरणों (23x+10y=83) और (11x+5y=39) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (23x+10y=83) and (11x+5y=39)?
#linear equations
#hard
#unique solution
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(23/11 \ne 10/5\) so the lines will intersect. Hence, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(23/11 \ne 10/5\) so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(23/11 \ne 10/5\) इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरणों (20x-15y=85) और (4x-3y=18) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing the equations (20x-15y=85) and (4x-3y=18)?
#linear equations
#hard
#no solution
#observation
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Here (20/4=(-15)/(-3)) but (85/18) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Here (20/4=(-15)/(-3)) but (85/18) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (20/4=(-15)/(-3)) लेकिन (85/18) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (16x+11y=73) और (32x+22y=146) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (16x+11y=73) and (32x+22y=146)?
#linear equations
#hard
#observation
#same line
A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं।
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समीकरणों (10x+ky=110) और (2x+9y=22) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (10x+ky=110) and (2x+9y=22) to have infinitely many solutions?
#linear equations
#hard
#infinite solutions
#parameter
A (43)
B (44)
C (45)
D (46)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (5) times the second. Therefore, (k=45).
Step 2
Why this answer is correct
The correct answer is C. (45). The first equation must be (5) times the second. Therefore, (k=45).
Step 3
Exam Tip
पहला समीकरण दूसरे का (5) गुना होना चाहिए। इसलिए (k=45) है।
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समीकरणों (8x+7y=34) और (16x+ay=79) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for the equations (8x+7y=34) and (16x+ay=79) to have no solution?
#linear equations
#hard
#no solution
#parameter
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
For no solution, (8/16=7/a) and (34/79) must be different. This gives (a=14).
Step 2
Why this answer is correct
The correct answer is C. (14). For no solution, (8/16=7/a) and (34/79) must be different. This gives (a=14).
Step 3
Exam Tip
कोई हल नहीं के लिए (8/16=7/a) और (34/79) अलग होना चाहिए। इससे (a=14) मिलता है।
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समीकरणों (11x+6y=37) और (22x+12y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (11x+6y=37) and (22x+12y=r) to be inconsistent?
#linear equations
#hard
#inconsistent
#parameter
A (r=74)
B \(r \ne 74\)
C (r=37)
D (r=76)
Explanation opens after your attempt
Correct Answer
B. \(r \ne 74\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r \ne 74\).
Step 2
Why this answer is correct
The correct answer is B. \(r \ne 74\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r \ne 74\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(r \ne 74\)।
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समीकरणों (7x+13y=67) और (21x+39y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (7x+13y=67) and (21x+39y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (199)
B (200)
C (201)
D (202)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).
Step 2
Why this answer is correct
The correct answer is C. (201). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=201)।
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समीकरणों (10x+11y=43) और (20x+21y=84) के लिए कौन-सा कथन सही है?
Which statement is correct for the equations (10x+11y=43) and (20x+21y=84)?
#linear equations
#hard
#ratio comparison
#unique solution
A (10 / 20=11 / 21) इसलिए कोई हल नहीं / 21) so no solution
B (10 / 20 \ne 11 / 21) इसलिए एक अद्वितीय हल / 21) so one unique solution
C तीनों अनुपात बराबर हैं / All three ratios are equal
D रेखाएं संपाती हैं / Lines are coincident
Explanation opens after your attempt
Correct Answer
B. (10 / 20 \ne 11 / 21) इसलिए एक अद्वितीय हल / 21) so one unique solution
Step 1
Concept
Here \(10/20 \ne 11/21\) so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(10 / 20 \ne 11 / 21\) इसलिए एक अद्वितीय हल / 21) so one unique solution. Here \(10/20 \ne 11/21\) so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(10/20 \ne 11/21\) इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरणों (14x+21y=98) और (2x+3y=17) के लिए कौन-सा संबंध सही है?
Which relation is correct for the equations (14x+21y=98) and (2x+3y=17)?
#linear equations
#hard
#ratio relation
#no solution
A (14 / 2 \ne 21 / 3)
B (14 / 2=21 / 3=98 / 17)
C (14 / 2=21 / 3 \ne 98 / 17)
D (14 / 2=98 / 17 \ne 21 / 3)
Explanation opens after your attempt
Correct Answer
C. (14 / 2=21 / 3 \ne 98 / 17)
Step 1
Concept
The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 2
Why this answer is correct
The correct answer is C. \(14 / 2=21 / 3 \ne 98 / 17\). The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है। इसलिए कोई हल नहीं है।
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समीकरणों (9x+16y=74) और (27x+48y=222) में तीनों अनुपातों का संबंध क्या है?
What is the relation among all three ratios in the equations (9x+16y=74) and (27x+48y=222)?
#linear equations
#hard
#ratio relation
#coincident
A तीनों बराबर हैं / All three are equal
B पहले दो बराबर और तीसरा अलग है / First two are equal and third is different
C पहले दो अलग हैं / First two are different
D केवल स्थिर पद बराबर हैं / Only constants are equal
Explanation opens after your attempt
Correct Answer
A. तीनों बराबर हैं / All three are equal
Step 1
Concept
Here (9/27=16/48=74/222). Therefore, both equations form the same line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बराबर हैं / All three are equal. Here (9/27=16/48=74/222). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (9/27=16/48=74/222)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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दो संख्याओं के लिए (6x+5y=49) और (3x-2y=7) समीकरण बनते हैं, तो हल-स्थिति क्या होगी?
For two numbers, the equations (6x+5y=49) and (3x-2y=7) are formed. What will be the solution status?
#linear equations
#hard
#word problem
#unique solution
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
A. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here (6/3 \ne 5/(-2)) so the lines intersect. Such a pair has one unique solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here (6/3 \ne 5/(-2)) so the lines intersect. Such a pair has one unique solution.
Step 3
Exam Tip
यहां (6/3 \ne 5/(-2)) इसलिए रेखाएं कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है।
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दो टिकटों के दामों के लिए (8x+3y=280) और (16x+6y=575) समीकरण बने। यह प्रणाली कैसी है?
For prices of two tickets, the equations (8x+3y=280) and (16x+6y=575) are formed. What type of system is this?
#linear equations
#hard
#word problem
#inconsistent
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (280/575) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (280/575) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (280/575) अलग है। इसलिए प्रणाली असंगत है।
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एक दुकान में दो वस्तुओं के लिए (5x+9y=300) और (15x+27y=900) समीकरण बनते हैं। हलों की संख्या क्या होगी?
In a shop, the equations for two items are (5x+9y=300) and (15x+27y=900). How many solutions will there be?
#linear equations
#hard
#word problem
#infinite solutions
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं।
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समीकरणों (16x+7y=55) और (8x+4y=29) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (16x+7y=55) and (8x+4y=29)?
#linear equations
#hard
#consistent independent
A असंगत / Inconsistent
B संगत और आश्रित / Consistent and dependent
C संगत और स्वतंत्र / Consistent and independent
D समानांतर / Parallel
Explanation opens after your attempt
Correct Answer
C. संगत और स्वतंत्र / Consistent and independent
Step 1
Concept
Here \(16/8 \ne 7/4\) so the lines intersect. Hence, the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. संगत और स्वतंत्र / Consistent and independent. Here \(16/8 \ne 7/4\) so the lines intersect. Hence, the pair is consistent and independent.
Step 3
Exam Tip
यहां \(16/8 \ne 7/4\) इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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समीकरणों (22x+33y=99) और (2x+3y=11) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (22x+33y=99) and (2x+3y=11)?
#linear equations
#hard
#inconsistent
#classification
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D संपाती / Coincident
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
Here (22/2=33/3) but (99/11) is different. Therefore, this is an inconsistent pair.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (22/2=33/3) but (99/11) is different. Therefore, this is an inconsistent pair.
Step 3
Exam Tip
यहां (22/2=33/3) लेकिन (99/11) अलग है। इसलिए यह असंगत युग्म है।
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समीकरणों (24x+36y=168) और (2x+3y=14) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (24x+36y=168) and (2x+3y=14)?
#linear equations
#hard
#dependent pair
#classification
A संगत और आश्रित / Consistent and dependent
B असंगत / Inconsistent
C संगत और स्वतंत्र / Consistent and independent
D असमाधेय / Unsolvable
Explanation opens after your attempt
Correct Answer
A. संगत और आश्रित / Consistent and dependent
Step 1
Concept
The first equation is (12) times the second. Therefore, both are the same line and the pair is dependent.
Step 2
Why this answer is correct
The correct answer is A. संगत और आश्रित / Consistent and dependent. The first equation is (12) times the second. Therefore, both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (12) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरणों (17x+10y=61) और (8x+5y=29) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (17x+10y=61) and (8x+5y=29)?
#linear equations
#hard
#ratio comparison
#unique solution
A (17 / 8=10 / 5) इसलिए अनंत हल / 5) so infinitely many solutions
B (17 / 8=10 / 5) इसलिए कोई हल नहीं / 5) so no solution
C (17 / 8 \ne 10 / 5) इसलिए एक अद्वितीय हल / 5) so one unique solution
D (17 / 8=61 / 29) इसलिए संपाती / 29) so coincident
Explanation opens after your attempt
Correct Answer
C. (17 / 8 \ne 10 / 5) इसलिए एक अद्वितीय हल / 5) so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(17 / 8 \ne 10 / 5\) इसलिए एक अद्वितीय हल / 5) so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरणों (21x+28y=84) और (3x+4y=15) को देखकर कौन-सा निष्कर्ष सही है?
Which conclusion is correct by observing the equations (21x+28y=84) and (3x+4y=15)?
#linear equations
#hard
#observation
#no solution
A तीनों अनुपात बराबर हैं / All three ratios are equal
B पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
C पहले दो अनुपात अलग हैं / First two ratios are different
D रेखाएं कटती हैं / Lines intersect
Explanation opens after your attempt
Correct Answer
B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
Step 1
Concept
Here (21/3=28/4) but (84/15) is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different. Here (21/3=28/4) but (84/15) is different. Therefore, there will be no solution.
Step 3
Exam Tip
यहां (21/3=28/4) लेकिन (84/15) अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (9x+14y=71) और (27x+42y=213) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing the equations (9x+14y=71) and (27x+42y=213)?
#linear equations
#hard
#observation
#infinite solutions
A एक अद्वितीय हल है / There is one unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Explanation opens after your attempt
Correct Answer
C. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल हैं / There are infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं।
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समीकरणों (15x+py=45) और (7x+2y=24) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (15x+py=45) and (7x+2y=24) to have a unique solution?
#linear equations
#hard
#unique solution
#parameter
A (p=30 / 7)
B (p \ne 30 / 7)
C (p=2)
D (p=15)
Explanation opens after your attempt
Correct Answer
B. (p \ne 30 / 7)
Step 1
Concept
For a unique solution, \(15/7 \ne p/2\) must hold. Therefore, \(p \ne 30/7\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p \ne 30 / 7\). For a unique solution, \(15/7 \ne p/2\) must hold. Therefore, \(p \ne 30/7\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(15/7 \ne p/2\) होना चाहिए। इसलिए \(p \ne 30/7\) सही शर्त है।
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समीकरणों (6x+dy=54) और (18x+30y=162) के अनंत हल होने के लिए (d) का मान क्या है?
What is the value of (d) for the equations (6x+dy=54) and (18x+30y=162) to have infinitely many solutions?
#linear equations
#hard
#parameter
#dependent pair
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (6/18=d/30=54/162) must hold. Therefore, (d=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For infinitely many solutions, (6/18=d/30=54/162) must hold. Therefore, (d=10).
Step 3
Exam Tip
अनंत हल के लिए (6/18=d/30=54/162) होना चाहिए। इसलिए (d=10)।
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समीकरणों (13x+6y-41=0) और (26x+13y-82=0) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for the equations (13x+6y-41=0) and (26x+13y-82=0)?
#linear equations
#hard
#unique solution
#ratio test
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(13/26 \ne 6/13\) so the lines intersect at one point. In this case, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(13/26 \ne 6/13\) so the lines intersect at one point. In this case, one unique solution is obtained.
Step 3
Exam Tip
यहां \(13/26 \ne 6/13\) इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसी स्थिति में एक अद्वितीय हल मिलता है।
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समीकरणों (12x-5y+37=0) और (24x-10y+79=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for the equations (12x-5y+37=0) and (24x-10y+79=0)?
#linear equations
#hard
#ratio relation
#no solution
A (12 / 24=(-5) / (-10) \ne 37 / 79)
B (12 / 24 \ne (-5) / (-10))
C (12 / 24=(-5) / (-10)=37 / 79)
D (12 / 24=37 / 79 \ne (-5) / (-10))
Explanation opens after your attempt
Correct Answer
A. (12 / 24=(-5) / (-10) \ne 37 / 79)
Step 1
Concept
The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is A. (12 / 24=(-5) / (-10) \ne 37 / 79). The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं और तीसरा अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (8x+13y-59=0) और (24x+39y-177=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for the equations (8x+13y-59=0) and (24x+39y-177=0)?
#linear equations
#hard
#ratio relation
#infinite solutions
A (8 / 24=13 / 39 \ne (-59) / (-177))
B (8 / 24 \ne 13 / 39)
C (8 / 24=13 / 39=(-59) / (-177))
D (8 / 24=(-59) / (-177) \ne 13 / 39)
Explanation opens after your attempt
Correct Answer
C. (8 / 24=13 / 39=(-59) / (-177))
Step 1
Concept
Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (8 / 24=13 / 39=(-59) / (-177)). Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (4x+15y=53) और (9x+31y=110) के ग्राफ का सही वर्णन क्या है?
What is the correct description of the graph of the equations (4x+15y=53) and (9x+31y=110)?
#linear equations
#hard
#graph
#intersecting lines
A संपाती रेखाएं / Coincident lines
B अलग समानांतर रेखाएं / Distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
Step 1
Concept
Here \(4/9 \ne 15/31\) so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(4/9 \ne 15/31\) so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(4/9 \ne 15/31\) इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
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समीकरणों (25x+10y=95) और (5x+2y=19) के ग्राफ में क्या दिखेगा?
What will be shown in the graph of the equations (25x+10y=95) and (5x+2y=19)?
#linear equations
#hard
#graph
#same line
A एक ही रेखा / Same line
B दो अलग समानांतर रेखाएं / Two distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई रेखा नहीं / No line
Explanation opens after your attempt
Correct Answer
A. एक ही रेखा / Same line
Step 1
Concept
The first equation is (5) times the second. Therefore, both equations show the same line.
Step 2
Why this answer is correct
The correct answer is A. एक ही रेखा / Same line. The first equation is (5) times the second. Therefore, both equations show the same line.
Step 3
Exam Tip
पहला समीकरण दूसरे का (5) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं।
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समीकरणों (20x+30y=90) और (2x+3y=11) के ग्राफ के बारे में सही कथन कौन-सा है?
Which statement is correct about the graph of the equations (20x+30y=90) and (2x+3y=11)?
#linear equations
#hard
#graph
#parallel lines
A रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
B रेखाएं संपाती हैं / Lines are coincident
C रेखाएं अलग समानांतर हैं / Lines are distinct parallel
D रेखाएं लंबवत हैं / Lines are perpendicular
Explanation opens after your attempt
Correct Answer
C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Step 1
Concept
Here (20/2=30/3) but (90/11) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (20/2=30/3) but (90/11) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (20/2=30/3) लेकिन (90/11) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
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समीकरणों (bx+14y=56) और (12x+28y=115) का कोई हल न होने के लिए (b) का मान क्या होगा?
What is the value of (b) for the equations (bx+14y=56) and (12x+28y=115) to have no solution?
#linear equations
#hard
#no solution
#parameter
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For no solution, (b/12=14/28) and (56/115) must be different. Hence, (b=6).
Step 2
Why this answer is correct
The correct answer is C. (6). For no solution, (b/12=14/28) and (56/115) must be different. Hence, (b=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (b/12=14/28) और (56/115) अलग होना चाहिए। इसलिए (b=6)।
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समीकरणों (9x+ay=63) और (27x+24y=189) के अनंत हल होने के लिए (a) क्या होगा?
What will (a) be for the equations (9x+ay=63) and (27x+24y=189) to have infinitely many solutions?
#linear equations
#hard
#ratio condition
#parameter
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (9/27=a/24=63/189) must hold. This gives (a=8).
Step 2
Why this answer is correct
The correct answer is C. (8). For infinitely many solutions, (9/27=a/24=63/189) must hold. This gives (a=8).
Step 3
Exam Tip
अनंत हल के लिए (9/27=a/24=63/189) होना चाहिए। इससे (a=8) मिलता है।
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समीकरणों (10x+py=50) और (2x+7y=19) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (10x+py=50) and (2x+7y=19) to have a unique solution?
#linear equations
#hard
#unique solution
#parameter
A (p=35)
B \(p \ne 35\)
C (p=7)
D (p=10)
Explanation opens after your attempt
Correct Answer
B. \(p \ne 35\)
Step 1
Concept
For a unique solution, \(10/2 \ne p/7\) must hold. Therefore, \(p \ne 35\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p \ne 35\). For a unique solution, \(10/2 \ne p/7\) must hold. Therefore, \(p \ne 35\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(10/2 \ne p/7\) होना चाहिए। इसलिए \(p \ne 35\) सही शर्त है।
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समीकरणों (11x+qy=44) और (22x+18y=88) के अनंत हल होने के लिए (q) का मान क्या है?
What is the value of (q) for the equations (11x+qy=44) and (22x+18y=88) to have infinitely many solutions?
#linear equations
#hard
#dependent pair
#parameter
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The second equation is (2) times the first so (q/18=1/2) must hold. Hence, (q=9).
Step 2
Why this answer is correct
The correct answer is C. (9). The second equation is (2) times the first so (q/18=1/2) must hold. Hence, (q=9).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है इसलिए (q/18=1/2) होना चाहिए। अतः (q=9)।
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समीकरणों (kx+12y=36) और (15x+20y=60) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (kx+12y=36) and (15x+20y=60) to have infinitely many solutions?
#linear equations
#hard
#parameter
#infinite solutions
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (k/15=12/20=36/60) must hold. Therefore, (k=9) is correct.
Step 2
Why this answer is correct
The correct answer is C. (9). For infinitely many solutions, (k/15=12/20=36/60) must hold. Therefore, (k=9) is correct.
Step 3
Exam Tip
अनंत हल के लिए (k/15=12/20=36/60) होना चाहिए। इसलिए (k=9) सही है।
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समीकरणों (8x+13y=41) और (15x+24y=77) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (8x+13y=41) and (15x+24y=77)?
#linear equations
#hard
#unique solution
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
B. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(8/15 \ne 13/24\) so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. Here \(8/15 \ne 13/24\) so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 3
Exam Tip
यहां \(8/15 \ne 13/24\) इसलिए रेखाएं एक बिंदु पर कटती हैं। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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समीकरणों (6x+11y=29) और (12x+22y=63) के लिए हलों की संख्या क्या होगी?
How many solutions will the equations (6x+11y=29) and (12x+22y=63) have?
#linear equations
#hard
#parallel lines
#no solution
A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (6/12=11/22) but (29/63) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (6/12=11/22) but (29/63) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (6/12=11/22) लेकिन (29/63) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (9x-2y=31) और (27x-6y=93) के लिए सही निष्कर्ष कौन-सा है?
Which conclusion is correct for the equations (9x-2y=31) and (27x-6y=93)?
#linear equations
#hard
#coincident lines
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D अलग समानांतर रेखाएं / Distinct parallel lines
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (px+8y=24) और (10x+20y=61) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+8y=24) and (10x+20y=61) to have no solution?
#linear equations
#hard
#no solution
#parameter
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/10=8/20) and (24/61) must be different. This gives (p=4).
Step 2
Why this answer is correct
The correct answer is C. (4). For no solution, (p/10=8/20) and (24/61) must be different. This gives (p=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/10=8/20) और (24/61) अलग होना चाहिए। इससे (p=4) मिलता है।
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समीकरणों (5x+2y=18) और (15x+ay=54) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (5x+2y=18) and (15x+ay=54) to have infinitely many solutions?
#linear equations
#hard
#parameter
#infinite solutions
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (5/15=2/a=18/54) must hold. Therefore, (a=6) is correct.
Step 2
Why this answer is correct
The correct answer is C. (6). For infinitely many solutions, (5/15=2/a=18/54) must hold. Therefore, (a=6) is correct.
Step 3
Exam Tip
अनंत हल के लिए (5/15=2/a=18/54) होना चाहिए। इसलिए (a=6) सही है।
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समीकरणों (7x+10y=39) और (5x+8y=31) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in the equations (7x+10y=39) and (5x+8y=31)?
#linear equations
#hard
#ratio comparison
#unique solution
A (7 / 5=10 / 8), इसलिए कोई हल नहीं / 8), so no solution
B (7 / 5=10 / 8), इसलिए अनंत हल / 8), so infinitely many solutions
C (7 / 5 \ne 10 / 8), इसलिए एक अद्वितीय हल / 8), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (7 / 5 \ne 10 / 8), इसलिए एक अद्वितीय हल / 8), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 5 \ne 10 / 8\), इसलिए एक अद्वितीय हल / 8), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक अद्वितीय हल देती हैं।
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समीकरणों (11x+6y=25) और (22x+12y=53) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (11x+6y=25) and (22x+12y=53)?
#linear equations
#hard
#no solution
#parallel lines
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Here (11/22=6/12) but (25/53) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Here (11/22=6/12) but (25/53) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (11/22=6/12) लेकिन (25/53) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (10x+3y=44) और (20x+ay=88) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (10x+3y=44) and (20x+ay=88) to have infinitely many solutions?
#linear equations
#hard
#infinite solutions
#parameter
A (4)
B (5)
C (7)
D (6)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (10/20=3/a=44/88) must hold. Therefore, (a=6) is correct.
Step 2
Why this answer is correct
The correct answer is D. (6). For infinitely many solutions, (10/20=3/a=44/88) must hold. Therefore, (a=6) is correct.
Step 3
Exam Tip
अनंत हल के लिए (10/20=3/a=44/88) होना चाहिए। इसलिए (a=6) सही है।
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समीकरणों (19x+8y=67) और (9x+4y=32) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (19x+8y=67) and (9x+4y=32)?
#linear equations
#hard
#unique solution
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(19/9 \ne 8/4\), so the lines will intersect. Hence, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(19/9 \ne 8/4\), so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(19/9 \ne 8/4\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरणों (18x-12y=72) और (3x-2y=13) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing the equations (18x-12y=72) and (3x-2y=13)?
#linear equations
#hard
#no solution
#observation
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Here (18/3=(-12)/(-2)) but (72/13) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Here (18/3=(-12)/(-2)) but (72/13) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (18/3=(-12)/(-2)) लेकिन (72/13) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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