100 results found for "6x" in Class 10.
यदि समान्तर श्रेणी में \(a_6=6x-5\), \(a_{13}=13x-33\) और \(a_{20}=20x-61\) हैं, तो \(a_{27}\) क्या होगा?
If in an AP \(a_6=6x-5\), \(a_{13}=13x-33\), and \(a_{20}=20x-61\), what is \(a_{27}\)?
#ap expert algebra pattern
A (27x-83)
B (27x-87)
C (27x-89)
D (27x-93)
Explanation opens after your attempt
Correct Answer
C. (27x-89)
Step 1
Concept
The group difference of equally spaced terms is (7x-28). \(a_{27}=a_{20}+7x-28=27x-89\).
Step 2
Why this answer is correct
The correct answer is C. (27x-89). The group difference of equally spaced terms is (7x-28). \(a_{27}=a_{20}+7x-28=27x-89\).
Step 3
Exam Tip
समान दूरी वाले पदों का समूह अंतर (7x-28) है। \(a_{27}=a_{20}+7x-28=27x-89\)।
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युग्म (mx+7y=13) और (16x+14y=26) का अद्वितीय हल कब होगा?
When will (mx+7y=13) and (16x+14y=26) have a unique solution?
#class10
#linear-equations
#solvability
A (m=8)
B \(m\neq8\)
C (m=16)
D \(m\neq16\)
Explanation opens after your attempt
Correct Answer
B. \(m\neq8\)
Step 1
Concept
For a unique solution, \(\frac{m}{16}\neq\frac{7}{14}\) must hold. Therefore, \(m\neq8\).
Step 2
Why this answer is correct
The correct answer is B. \(m\neq8\). For a unique solution, \(\frac{m}{16}\neq\frac{7}{14}\) must hold. Therefore, \(m\neq8\).
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{m}{16}\neq\frac{7}{14}\) होना चाहिए। इसलिए \(m\neq8\)।
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युग्म (6x+iy=12) और (18x+27y=50) में कोई हल न होने के लिए (i) का मान क्या है?
What is the value of (i) for no solution in (6x+iy=12) and (18x+27y=50)?
#class10
#linear-equations
#solvability
A (i=6)
B (i=7)
C (i=8)
D (i=9)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{6}{18}=\frac{i}{27}\) gives (i=9). The constant ratio is not equal.
Step 2
Why this answer is correct
The correct answer is D. (i=9). Equating coefficient ratios, \(\frac{6}{18}=\frac{i}{27}\) gives (i=9). The constant ratio is not equal.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{6}{18}=\frac{i}{27}\) से (i=9) आता है। स्थिर पद अनुपात समान नहीं है।
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युग्म ((z+2)x+3y=5) और (6x+(z-1)y=7) अद्वितीय न हो, इसके लिए (z) के संभावित मान कौन-से हैं?
For ((z+2)x+3y=5) and (6x+(z-1)y=7) to be non-unique, what are the possible values of (z)?
#class10
#linear-equations
#solvability
A (z=4,-3)
B (z=3,-4)
C (z=2,-5)
D (z=5,-2)
Explanation opens after your attempt
Correct Answer
A. (z=4,-3)
Step 1
Concept
For non-unique solutions, ((z+2)(z-1)-18=0) must hold. This gives (z=4) or (z=-3).
Step 2
Why this answer is correct
The correct answer is A. (z=4,-3). For non-unique solutions, ((z+2)(z-1)-18=0) must hold. This gives (z=4) or (z=-3).
Step 3
Exam Tip
अद्वितीय न होने के लिए ((z+2)(z-1)-18=0) होना चाहिए। इससे (z=4) या (z=-3) मिलता है।
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युग्म (wx-6y=4) और (16x-24y=12) का अद्वितीय हल कब होगा?
When will (wx-6y=4) and (16x-24y=12) have a unique solution?
#class10
#linear-equations
#solvability
A (w=4)
B \(w\neq4\)
C (w=16)
D \(w\neq16\)
Explanation opens after your attempt
Correct Answer
B. \(w\neq4\)
Step 1
Concept
For a unique solution, \(\frac{w}{16}\neq\frac{-6}{-24}\) must hold. Therefore, \(w\neq4\).
Step 2
Why this answer is correct
The correct answer is B. \(w\neq4\). For a unique solution, \(\frac{w}{16}\neq\frac{-6}{-24}\) must hold. Therefore, \(w\neq4\).
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{w}{16}\neq\frac{-6}{-24}\) होना चाहिए। इसलिए \(w\neq4\) होगा।
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युग्म (13x+4y=6) और (26x+8y=12) के लिए सही विकल्प चुनिए।
Choose the correct option for (13x+4y=6) and (26x+8y=12).
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D केवल (x=0) हल / Only (x=0) solution
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
All three ratios are equal. Thus the lines are coincident and the pair has 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. Thus the lines are coincident and the pair has infinitely many solutions.
Step 3
Exam Tip
तीनों अनुपात समान हैं। अतः रेखाएँ संपाती हैं और युग्म के अनंत हल हैं।
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युग्म (6x-ty=18) और (14x-21y=42) के अनंत हलों के लिए (t) का मान क्या होगा?
What is the value of (t) for infinitely many solutions of (6x-ty=18) and (14x-21y=42)?
#class10
#linear-equations
#solvability
A (t=6)
B (t=8)
C (t=9)
D (t=12)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{6}{14}=\frac{-t}{-21}=\frac{18}{42}\) must hold. This gives (t=9).
Step 2
Why this answer is correct
The correct answer is C. (t=9). For infinitely many solutions, \(\frac{6}{14}=\frac{-t}{-21}=\frac{18}{42}\) must hold. This gives (t=9).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{6}{14}=\frac{-t}{-21}=\frac{18}{42}\) होना चाहिए। इससे (t=9) मिलता है।
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युग्म (2x+ny=7) और (6x+15y=19) में कोई हल न होने के लिए (n) का मान क्या है?
What is the value of (n) for no solution in (2x+ny=7) and (6x+15y=19)?
#class10
#linear-equations
#solvability
A (n=3)
B (n=4)
C (n=5)
D (n=6)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{2}{6}=\frac{n}{15}\) gives (n=5). The constant ratio is different, so the pair is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. (n=5). Equating coefficient ratios, \(\frac{2}{6}=\frac{n}{15}\) gives (n=5). The constant ratio is different, so the pair is inconsistent.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{2}{6}=\frac{n}{15}\) से (n=5) मिलता है। स्थिर अनुपात अलग है इसलिए युग्म असंगत है।
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युग्म (kx+5y=10) और (6x+15y=18) का अद्वितीय हल कब होगा?
When will the pair (kx+5y=10) and (6x+15y=18) have a unique solution?
#class10
#linear-equations
#solvability
A (k=2)
B \(k\neq2\)
C (k=6)
D \(k\neq6\)
Explanation opens after your attempt
Correct Answer
B. \(k\neq2\)
Step 1
Concept
For a unique solution, \(\frac{k}{6}\neq\frac{5}{15}\) must hold. Therefore, \(k\neq2\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(k\neq2\). For a unique solution, \(\frac{k}{6}\neq\frac{5}{15}\) must hold. Therefore, \(k\neq2\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{k}{6}\neq\frac{5}{15}\) होना चाहिए। इसलिए \(k\neq2\) सही है।
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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 (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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युग्म (3x+\(\beta-1\)y=10) और (6x+4y=18) में कोई हल न होने के लिए \(\beta\) क्या होगा?
For no solution in (3x+\(\beta-1\)y=10) and (6x+4y=18), what is \(\beta\)?
#class10
#linear-equations
#solvability
A \(\beta=1\)
B \(\beta=2\)
C \(\beta=3\)
D \(\beta=4\)
Explanation opens after your attempt
Correct Answer
C. \(\beta=3\)
Step 1
Concept
Equating coefficient ratios gives \(\beta=3\). The constant ratio \(\frac{5}{9}\) is different, so there is no solution.
Step 2
Why this answer is correct
The correct answer is C. \(\beta=3\). Equating coefficient ratios gives \(\beta=3\). The constant ratio \(\frac{5}{9}\) is different, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\beta=3\) मिलता है। स्थिर अनुपात \(\frac{5}{9}\) अलग है, इसलिए कोई हल नहीं।
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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).
#class10
#linear-equations
#solvability
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
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं है / It 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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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)?
#class10
#linear-equations
#solvability
A (h=5)
B (h=6)
C (h=7)
D (h=8)
Explanation opens after your attempt
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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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?
#class10
#linear-equations
#solvability
A (t=5)
B (t=10)
C \(t\neq10\)
D \(t\neq5\)
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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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)?
#class10
#linear-equations
#solvability
A (k=1)
B (k=2)
C (k=3)
D (k=5)
Explanation opens after your attempt
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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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)?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अद्वितीय हल / Unique solution
C अनंत हल / Infinitely many solutions
D केवल दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely 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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युग्म (6x-8y=16) और (sx-12y=24) के अनंत हलों के लिए (s) का मान क्या होगा?
For infinitely many solutions of (6x-8y=16) and (sx-12y=24), what is (s)?
#class10
#linear-equations
#solvability
A (s=6)
B (s=8)
C (s=9)
D (s=12)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, all ratios must be equal. From \(\frac{6}{s}=\frac{-8}{-12}=\frac{16}{24}\), (s=9).
Step 2
Why this answer is correct
The correct answer is C. (s=9). For infinitely many solutions, all ratios must be equal. From \(\frac{6}{s}=\frac{-8}{-12}=\frac{16}{24}\), (s=9).
Step 3
Exam Tip
अनंत हलों के लिए सभी अनुपात बराबर होने चाहिए। \(\frac{6}{s}=\frac{-8}{-12}=\frac{16}{24}\) से (s=9) है।
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युग्म ((p+2)x+5y=11) और (6x+10y=13) का अद्वितीय हल कब होगा?
When will the pair ((p+2)x+5y=11) and (6x+10y=13) have a unique solution?
#class10
#linear-equations
#solvability
A (p=1)
B (p=3)
C (p=0)
D \(p\neq1\)
Explanation opens after your attempt
Correct Answer
D. \(p\neq1\)
Step 1
Concept
For a unique solution, \(\frac{p+2}{6}\neq\frac{5}{10}\). Hence \(p\neq1\) is correct.
Step 2
Why this answer is correct
The correct answer is D. \(p\neq1\). For a unique solution, \(\frac{p+2}{6}\neq\frac{5}{10}\). Hence \(p\neq1\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{p+2}{6}\neq\frac{5}{10}\) होना चाहिए। इसलिए \(p\neq1\) सही शर्त है।
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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 (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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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 (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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यदि (16x-8y=64) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?
If (16x-8y=64) and (2x-y=t) are inconsistent, what is the correct condition for (t)?
#linear equations
#expert
#inconsistent
#parameter
A (t=8)
B \(t\ne8\)
C (t=64)
D (t=16)
Explanation opens after your attempt
Correct Answer
B. \(t\ne8\)
Step 1
Concept
The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne8\). The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए (64/t) अलग होना चाहिए इसलिए \(t\ne8\)।
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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 (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 (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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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 (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 (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 (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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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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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 (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 (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 (6x+11y=53) और (18x+33y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (6x+11y=53) and (18x+33y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (157)
B (158)
C (159)
D (160)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).
Step 2
Why this answer is correct
The correct answer is C. (159). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=159)।
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समीकरणों (8x+9y=37) और (16x+17y=73) के लिए कौन-सा कथन सही है?
Which statement is correct for the equations (8x+9y=37) and (16x+17y=73)?
#linear equations
#hard
#ratio comparison
#unique solution
A (8 / 16=9 / 17), इसलिए कोई हल नहीं / 17), so no solution
B (8 / 16 \ne 9 / 17), इसलिए एक अद्वितीय हल / 17), 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. (8 / 16 \ne 9 / 17), इसलिए एक अद्वितीय हल / 17), so one unique solution
Step 1
Concept
Here \(8/16 \ne 9/17\), so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(8 / 16 \ne 9 / 17\), इसलिए एक अद्वितीय हल / 17), so one unique solution. Here \(8/16 \ne 9/17\), so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(8/16 \ne 9/17\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरणों (13x+8y=47) और (6x+4y=23) 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 (13x+8y=47) and (6x+4y=23)?
#linear equations
#hard
#ratio comparison
#unique solution
A (13 / 6=8 / 4), इसलिए अनंत हल / 4), so infinitely many solutions
B (13 / 6=8 / 4), इसलिए कोई हल नहीं / 4), so no solution
C (13 / 6 \ne 8 / 4), इसलिए एक अद्वितीय हल / 4), so one unique solution
D (13 / 6=47 / 23), इसलिए संपाती / 23), so coincident
Explanation opens after your attempt
Correct Answer
C. (13 / 6 \ne 8 / 4), इसलिए एक अद्वितीय हल / 4), 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. \(13 / 6 \ne 8 / 4\), इसलिए एक अद्वितीय हल / 4), 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 (13x+py=39) और (6x+3y=20) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (13x+py=39) and (6x+3y=20) to have a unique solution?
#linear equations
#hard
#unique solution
#parameter
A (p=13 / 2)
B (p \ne 13 / 2)
C (p=3)
D (p=13)
Explanation opens after your attempt
Correct Answer
B. (p \ne 13 / 2)
Step 1
Concept
For a unique solution, \(13/6 \ne p/3\) must hold. Therefore, \(p \ne 13/2\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p \ne 13 / 2\). For a unique solution, \(13/6 \ne p/3\) must hold. Therefore, \(p \ne 13/2\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(13/6 \ne p/3\) होना चाहिए। इसलिए \(p \ne 13/2\) सही शर्त है।
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समीकरणों (6x+11y-47=0) और (18x+33y-141=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for the equations (6x+11y-47=0) and (18x+33y-141=0)?
#linear equations
#hard
#ratio relation
#infinite solutions
A (6 / 18=11 / 33 \ne (-47) / (-141))
B (6 / 18 \ne 11 / 33)
C (6 / 18=11 / 33=(-47) / (-141))
D (6 / 18=(-47) / (-141) \ne 11 / 33)
Explanation opens after your attempt
Correct Answer
C. (6 / 18=11 / 33=(-47) / (-141))
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. (6 / 18=11 / 33=(-47) / (-141)). 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 (8x+3y=19) और (16x+6y=45) के लिए हलों की संख्या क्या होगी?
How many solutions will the equations (8x+3y=19) and (16x+6y=45) 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 (8/16=3/6) but (19/45) 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 (8/16=3/6) but (19/45) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (8/16=3/6) लेकिन (19/45) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (6x-5y=17) और (18x-15y=51) के लिए सही निष्कर्ष कौन-सा है?
Which conclusion is correct for the equations (6x-5y=17) and (18x-15y=51)?
#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 रेखाएं अलग समानांतर / 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 (16x-12y=44) और (4x-3y=12) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing the equations (16x-12y=44) and (4x-3y=12)?
#linear equations
#hard
#observation
#no solution
A अनंत हल / Infinitely many solutions
B कोई हल नहीं / No solution
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं / No solution
Step 1
Concept
Here (16/4=(-12)/(-3)) but (44/12) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Here (16/4=(-12)/(-3)) but (44/12) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (16/4=(-12)/(-3)) लेकिन (44/12) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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दो वस्तुओं की कीमतों के लिए (6x+5y=240) और (12x+10y=490) समीकरण बने। यह प्रणाली कैसी है?
For prices of two items, the equations (6x+5y=240) and (12x+10y=490) 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 (240/490) 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 (240/490) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (240/490) अलग है। इसलिए प्रणाली असंगत है।
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समीकरणों (6x-4y+11=0) और (15x-10y+28=0) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (6x-4y+11=0) and (15x-10y+28=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 (6/15=(-4)/(-10)) but (11/28) 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 (6/15=(-4)/(-10)) but (11/28) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (6/15=(-4)/(-10)) लेकिन (11/28) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (6x+7y=31) और (12x+14y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (6x+7y=31) and (12x+14y=r) to be inconsistent?
#linear equations
#hard
#inconsistent
#parameter
A (r=62)
B \(r \ne 62\)
C (r=31)
D (r=64)
Explanation opens after your attempt
Correct Answer
B. \(r \ne 62\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(r \ne 62\).
Step 2
Why this answer is correct
The correct answer is B. \(r \ne 62\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(r \ne 62\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(r \ne 62\)।
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समीकरणों (13x+4y=39) और (6x+2y=17) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (13x+4y=39) and (6x+2y=17)?
#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 \(13/6 \ne 4/2\), 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 \(13/6 \ne 4/2\), so the lines intersect. Hence, the pair is consistent and independent.
Step 3
Exam Tip
यहां \(13/6 \ne 4/2\), इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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समीकरणों (16x+24y=88) और (2x+3y=11) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (16x+24y=88) and (2x+3y=11)?
#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 (8) 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 (8) times the second. Therefore, both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (8) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरणों (6x+7y=41) और (18x+21y=123) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing the equations (6x+7y=41) and (18x+21y=123)?
#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 (8x-3y+22=0) और (16x-6y+47=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for the equations (8x-3y+22=0) and (16x-6y+47=0)?
#linear equations
#hard
#ratio relation
#no solution
A (8 / 16=(-3) / (-6) \ne 22 / 47)
B (8 / 16 \ne (-3) / (-6))
C (8 / 16=(-3) / (-6)=22 / 47)
D (8 / 16=22 / 47 \ne (-3) / (-6))
Explanation opens after your attempt
Correct Answer
A. (8 / 16=(-3) / (-6) \ne 22 / 47)
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. (8 / 16=(-3) / (-6) \ne 22 / 47). 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 (6x+ky=24) और (3x+5y=17) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (6x+ky=24) and (3x+5y=17) to have a unique solution?
#linear equations
#hard
#unique solution
#parameter
A (k=10)
B \(k \ne 10\)
C (k=5)
D (k=6)
Explanation opens after your attempt
Correct Answer
B. \(k \ne 10\)
Step 1
Concept
For a unique solution, \(6/3 \ne k/5\) must hold. Therefore, \(k \ne 10\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(k \ne 10\). For a unique solution, \(6/3 \ne k/5\) must hold. Therefore, \(k \ne 10\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(6/3 \ne k/5\) होना चाहिए। इसलिए \(k \ne 10\) सही शर्त है।
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समीकरणों (ax+4y=10) और (6x+8y=25) का कोई हल न होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (ax+4y=10) and (6x+8y=25) 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, (a/6=4/8) and (10/25) must be different. This gives (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For no solution, (a/6=4/8) and (10/25) must be different. This gives (a=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (a/6=4/8) और (10/25) अलग होना चाहिए। इससे (a=3) मिलता है।
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समीकरण (6x-7y+13=0) और (18x-21y+40=0) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for (6x-7y+13=0) and (18x-21y+40=0)?
#linear equations
#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 (6/18=(-7)/(-21)) but (13/40) 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 (6/18=(-7)/(-21)) but (13/40) is different. Therefore the lines are parallel and distinct.
Step 3
Exam Tip
यहां (6/18=(-7)/(-21)) लेकिन (13/40) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (6x+7y=31) और (12x+14y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (6x+7y=31) and (12x+14y=r) to be inconsistent?
#linear equations
#inconsistent
#parameter
A (r=62)
B \(r \ne 62\)
C (r=31)
D (r=64)
Explanation opens after your attempt
Correct Answer
B. \(r \ne 62\)
Step 1
Concept
The first two ratios are equal so the constant ratio must be different for inconsistency. Hence \(r \ne 62\).
Step 2
Why this answer is correct
The correct answer is B. \(r \ne 62\). The first two ratios are equal so the constant ratio must be different for inconsistency. Hence \(r \ne 62\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(r \ne 62\)।
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समीकरण (13x+4y=39) और (6x+2y=17) का युग्म किस प्रकार का है?
What type of pair is (13x+4y=39) and (6x+2y=17)?
#linear equations
#consistent independent
#classification
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 \(13/6 \ne 4/2\) 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 \(13/6 \ne 4/2\) so the lines intersect. Hence the pair is consistent and independent.
Step 3
Exam Tip
यहां \(13/6 \ne 4/2\) इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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समीकरण (16x+24y=88) और (2x+3y=11) का युग्म किस प्रकार का है?
What type of pair is (16x+24y=88) and (2x+3y=11)?
#linear equations
#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 (8) 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 (8) times the second. Therefore both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (8) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरण (6x+7y=41) और (18x+21y=123) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing (6x+7y=41) and (18x+21y=123)?
#linear equations
#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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समीकरण (8x-3y+22=0) और (16x-6y+47=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for (8x-3y+22=0) and (16x-6y+47=0)?
#linear equations
#ratio relation
#no solution
A (8 / 16=(-3) / (-6) \ne 22 / 47)
B (8 / 16 \ne (-3) / (-6))
C (8 / 16=(-3) / (-6)=22 / 47)
D (8 / 16=22 / 47 \ne (-3) / (-6))
Explanation opens after your attempt
Correct Answer
A. (8 / 16=(-3) / (-6) \ne 22 / 47)
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. (8 / 16=(-3) / (-6) \ne 22 / 47). 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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समीकरण (6x+ky=24) और (3x+5y=17) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (6x+ky=24) and (3x+5y=17) to have a unique solution?
#linear equations
#unique solution
#parameter
A (k=10)
B \(k \ne 10\)
C (k=5)
D (k=6)
Explanation opens after your attempt
Correct Answer
B. \(k \ne 10\)
Step 1
Concept
For a unique solution \(6/3 \ne k/5\) must hold. Therefore \(k \ne 10\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(k \ne 10\). For a unique solution \(6/3 \ne k/5\) must hold. Therefore \(k \ne 10\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(6/3 \ne k/5\) होना चाहिए। इसलिए \(k \ne 10\) सही शर्त है।
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समीकरण (8x+3y=21) और (16x+6y=42) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for (8x+3y=21) and (16x+6y=42)?
#linear equations
#coincident lines
#infinite solutions
A अनंत हल / Infinitely many solutions
B कोई हल नहीं / No solution
C एक अद्वितीय हल / One unique solution
D रेखाएं अलग समानांतर / Lines are distinct parallel
Explanation opens after your attempt
Correct Answer
A. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (2) times the first so both lines are coincident. Coincident lines have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is A. अनंत हल / Infinitely many solutions. The second equation is (2) times the first so both lines are coincident. Coincident lines have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं।
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समीकरण (2x+5y=16) और (6x+15y=k) के अनंत हल होने के लिए (k) का मान क्या होगा?
What is the value of (k) for (2x+5y=16) and (6x+15y=k) to have infinitely many solutions?
#linear equations
#parameter
#infinite solutions
A (42)
B (48)
C (50)
D (54)
Explanation opens after your attempt
Step 1
Concept
The second equation must be (3) times the first so (k=48). For infinitely many solutions all ratios must be equal.
Step 2
Why this answer is correct
The correct answer is B. (48). The second equation must be (3) times the first so (k=48). For infinitely many solutions all ratios must be equal.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना होना चाहिए इसलिए (k=48)। अनंत हल के लिए सभी अनुपात बराबर होने चाहिए।
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समीकरण (6x+ky=42) और (2x+5y=14) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for (6x+ky=42) and (2x+5y=14) to have infinitely many solutions?
#linear equations
#infinite solutions
#parameter
A (12)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (3) times the second. Therefore, (k=15).
Step 2
Why this answer is correct
The correct answer is B. (15). The first equation must be (3) times the second. Therefore, (k=15).
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (k=15) है।
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समीकरण (3x+4y=10) और (6x+ay=25) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for (3x+4y=10) and (6x+ay=25) to have no solution?
#linear equations
#no solution
#parameter
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For no solution, (3/6=4/a) and (10/25) must be different. This gives (a=8).
Step 2
Why this answer is correct
The correct answer is C. (8). For no solution, (3/6=4/a) and (10/25) must be different. This gives (a=8).
Step 3
Exam Tip
कोई हल नहीं के लिए (3/6=4/a) और (10/25) अलग होना चाहिए। इससे (a=8) मिलता है।
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समीकरण (6x+7y=23) और (12x+13y=45) के लिए कौन-सा कथन सही है?
Which statement is correct for (6x+7y=23) and (12x+13y=45)?
#linear equations
#ratio comparison
#unique solution
A (6 / 12=7 / 13), इसलिए कोई हल नहीं / 13), so no solution
B (6 / 12 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), 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. (6 / 12 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), so one unique solution
Step 1
Concept
Here \(6/12 \ne 7/13\), so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(6 / 12 \ne 7 / 13\), इसलिए एक अद्वितीय हल / 13), so one unique solution. Here \(6/12 \ne 7/13\), so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(6/12 \ne 7/13\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरण (3x+4y=22) और (6x+8y=44) में तीनों अनुपातों का संबंध क्या है?
What is the relation among all three ratios in (3x+4y=22) and (6x+8y=44)?
#linear equations
#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 (3/6=4/8=22/44). 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 (3/6=4/8=22/44). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (3/6=4/8=22/44)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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समीकरण (6x+12y=18) और (x+2y=4) को देखकर कौन-सा निष्कर्ष सही है?
Which conclusion is correct by observing (6x+12y=18) and (x+2y=4)?
#linear equations
#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 (6/1=12/2) but (18/4) 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 (6/1=12/2) but (18/4) is different. Therefore, there will be no solution.
Step 3
Exam Tip
यहां (6/1=12/2) लेकिन (18/4) अलग है। इसलिए कोई हल नहीं होगा।
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यदि (6x+5y=31) और (12x+10y=n) के अनंत हल हैं, तो (n) कितना होगा?
If (6x+5y=31) and (12x+10y=n) have infinitely many solutions, what is (n)?
#linear equations
#parameter
#infinite solutions
A (60)
B (61)
C (62)
D (63)
Explanation opens after your attempt
Step 1
Concept
The second equation must be (2) times the first. Therefore, (n=62).
Step 2
Why this answer is correct
The correct answer is C. (62). The second equation must be (2) times the first. Therefore, (n=62).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना होना चाहिए। इसलिए (n=62) होगा।
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समीकरण (6x-7y+9=0) और (12x-14y+25=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for (6x-7y+9=0) and (12x-14y+25=0)?
#linear equations
#ratio relation
#no solution
A (6 / 12=(-7) / (-14) \ne 9 / 25)
B (6 / 12 \ne (-7) / (-14))
C (6 / 12=(-7) / (-14)=9 / 25)
D (6 / 12=9 / 25 \ne (-7) / (-14))
Explanation opens after your attempt
Correct Answer
A. (6 / 12=(-7) / (-14) \ne 9 / 25)
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. (6 / 12=(-7) / (-14) \ne 9 / 25). 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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समीकरण (6x-5y=14) और (12x-10y=31) के लिए हलों की संख्या क्या होगी?
How many solutions will (6x-5y=14) and (12x-10y=31) have?
#linear equations
#parallel lines
#no solution
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं / No solution
Step 1
Concept
Here (6/12=(-5)/(-10)) but (14/31) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Here (6/12=(-5)/(-10)) but (14/31) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (6/12=(-5)/(-10)) लेकिन (14/31) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (13x+2y=31) और (6x+y=14) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for (13x+2y=31) and (6x+y=14)?
#linear equations
#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 \(13/6 \ne 2/1\), 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 \(13/6 \ne 2/1\), so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(13/6 \ne 2/1\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरण (8x+3y=17) और (16x+6y=34) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing (8x+3y=17) and (16x+6y=34)?
#linear equations
#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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यदि (lx+7y=21) और (6x+14y=40) का कोई हल नहीं है, तो (l) का मान क्या होगा?
If (lx+7y=21) and (6x+14y=40) have no solution, what will be the value of (l)?
#linear equations
#parameter
#parallel lines
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
For no solution, (l/6=7/14) and (21/40) must be different. Hence (l=3).
Step 2
Why this answer is correct
The correct answer is C. (3). For no solution, (l/6=7/14) and (21/40) must be different. Hence (l=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (l/6=7/14) और (21/40) अलग होना चाहिए। इसलिए (l=3)।
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समीकरण (3x+5y=14) और (6x+10y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (3x+5y=14) and (6x+10y=r) to be inconsistent?
#linear equations
#inconsistent
#parameter
A (r=28)
B \(r \ne 28\)
C (r=14)
D (r=7)
Explanation opens after your attempt
Correct Answer
B. \(r \ne 28\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must be different. Hence \(r \ne 28\).
Step 2
Why this answer is correct
The correct answer is B. \(r \ne 28\). The first two ratios are equal, so for inconsistency the constant ratio must be different. Hence \(r \ne 28\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(r \ne 28\)।
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समीकरण (6x+9y=30) और (2x+3y=12) के लिए कौन-सा संबंध सही है?
Which relation is correct for (6x+9y=30) and (2x+3y=12)?
#linear equations
#ratio relation
#no solution
A (6 / 2 \ne 9 / 3)
B (6 / 2=9 / 3=30 / 12)
C (6 / 2=9 / 3 \ne 30 / 12)
D (6 / 2=30 / 12 \ne 9 / 3)
Explanation opens after your attempt
Correct Answer
C. (6 / 2=9 / 3 \ne 30 / 12)
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. \(6 / 2=9 / 3 \ne 30 / 12\). 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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दो टिकटों के दामों के लिए (3x+2y=80) और (6x+4y=170) समीकरण बने। यह प्रणाली कैसी है?
For prices of two tickets, the equations (3x+2y=80) and (6x+4y=170) are formed. What type of system is this?
#linear equations
#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 (80/170) 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 (80/170) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (80/170) अलग है। इसलिए प्रणाली असंगत है।
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यदि (6x-2y=18) और (3x-y=t) असंगत हों, तो (t) के लिए सही शर्त क्या है?
If (6x-2y=18) and (3x-y=t) are inconsistent, what is the correct condition for (t)?
#linear equations
#inconsistent
#parameter
A (t=9)
B \(t \ne 9\)
C (t=18)
D (t=6)
Explanation opens after your attempt
Correct Answer
B. \(t \ne 9\)
Step 1
Concept
The first two ratios are equal, so for inconsistency (18/t) must be different. Hence \(t \ne 9\).
Step 2
Why this answer is correct
The correct answer is B. \(t \ne 9\). The first two ratios are equal, so for inconsistency (18/t) must be different. Hence \(t \ne 9\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए (18/t) अलग होना चाहिए। अतः \(t \ne 9\)।
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यदि समीकरण (ax+4y=10) और (6x+8y=25) का कोई हल नहीं है, तो (a) का मान क्या है?
If the equations (ax+4y=10) and (6x+8y=25) have no solution, what is the value of (a)?
#linear equations
#parameter
#no solution
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For no solution, (a/6=4/8) and (10/25) must be different. Hence (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For no solution, (a/6=4/8) and (10/25) must be different. Hence (a=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (a/6=4/8) और (10/25) अलग होना चाहिए। इसलिए (a=3)।
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समीकरण (2x+3y-11=0) और (6x+9y-33=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for (2x+3y-11=0) and (6x+9y-33=0)?
#linear equations
#ratio relation
#infinite solutions
A (2 / 6=3 / 9 \ne (-11) / (-33))
B (2 / 6 \ne 3 / 9)
C (2 / 6=3 / 9=(-11) / (-33))
D (2 / 6=(-11) / (-33) \ne 3 / 9)
Explanation opens after your attempt
Correct Answer
C. (2 / 6=3 / 9=(-11) / (-33))
Step 1
Concept
Here all three ratios are equal to (1/3). Therefore, the equations will have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (2 / 6=3 / 9=(-11) / (-33)). Here all three ratios are equal to (1/3). Therefore, the equations will have infinitely many solutions.
Step 3
Exam Tip
यहां तीनों अनुपात (1/3) के बराबर हैं। इसलिए समीकरणों के अनंत हल होंगे।
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समीकरण (6x+ay=30) और (2x+5y=11) का कोई हल न होने के लिए (a) का मान क्या है?
What is the value of (a) for (6x+ay=30) and (2x+5y=11) to have no solution?
#linear equations
#no solution
#parameter
A (10)
B (12)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
For no solution, (6/2=a/5) and (30/11) must be different. This gives (a=15).
Step 2
Why this answer is correct
The correct answer is D. (15). For no solution, (6/2=a/5) and (30/11) must be different. This gives (a=15).
Step 3
Exam Tip
कोई हल नहीं के लिए (6/2=a/5) और (30/11) अलग होना चाहिए। इससे (a=15) मिलता है।
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समीकरण (3x+4y=13) और (6x+7y=25) के लिए सही विकल्प चुनिए।
Choose the correct option for (3x+4y=13) and (6x+7y=25).
#linear equations
#unique solution
#intersecting lines
A रेखाएं संपाती हैं / Lines are coincident
B कोई हल नहीं / No solution
C रेखाएं समानांतर हैं / Lines are parallel
D एक अद्वितीय हल / One unique solution
Explanation opens after your attempt
Correct Answer
D. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(3/6 \ne 4/7\), so the lines intersect at one point. Different coefficient ratios give one unique solution.
Step 2
Why this answer is correct
The correct answer is D. एक अद्वितीय हल / One unique solution. Here \(3/6 \ne 4/7\), so the lines intersect at one point. Different coefficient ratios give one unique solution.
Step 3
Exam Tip
यहां \(3/6 \ne 4/7\), इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग गुणांक अनुपात एक अद्वितीय हल देता है।
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समीकरण (kx+5y=20) और (6x+10y=45) का कोई हल न होने के लिए (k) क्या होगा?
What should (k) be for (kx+5y=20) and (6x+10y=45) to have no solution?
#linear equations
#no solution
#parameter
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For no solution, (k/6=5/10) and (20/45) must be different. This gives (k=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For no solution, (k/6=5/10) and (20/45) must be different. This gives (k=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (k/6=5/10) और (20/45) अलग होना चाहिए। इससे (k=3) मिलता है।
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समीकरण (3x+ay=12) और (6x+8y=24) के अनंत हल होने के लिए (a) का मान क्या है?
What is the value of (a) for (3x+ay=12) and (6x+8y=24) to have infinitely many solutions?
#linear equations
#infinite solutions
#ratio condition
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (3/6=a/8=12/24), so (a=4). Match the ratios of coefficients and constants first.
Step 2
Why this answer is correct
The correct answer is B. (4). For infinitely many solutions, (3/6=a/8=12/24), so (a=4). Match the ratios of coefficients and constants first.
Step 3
Exam Tip
अनंत हल के लिए (3/6=a/8=12/24), इसलिए (a=4)। पहले गुणांकों और स्थिर पदों के अनुपात मिलाएं।
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समीकरण (6x+11y=7) और (3x+5y=4) के लिए कौन-सा विकल्प सही है?
Which option is correct for (6x+11y=7) and (3x+5y=4)?
#linear equations
#intersecting
#unique solution
A रेखाएं समानांतर हैं / Lines are parallel
B रेखाएं संपाती हैं / Lines are coincident
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
C. रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
Step 1
Concept
Here \(6/3 \ne 11/5\) so the lines are not parallel. They intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point. Here \(6/3 \ne 11/5\) so the lines are not parallel. They intersect at one point.
Step 3
Exam Tip
यहां \(6/3 \ne 11/5\) इसलिए रेखाएं समानांतर नहीं हैं। वे एक बिंदु पर कटती हैं।
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समीकरण (16x-8y=24) और (2x-y=4) के लिए कौन-सा निष्कर्ष सही है?
Which conclusion is correct for (16x-8y=24) and (2x-y=4)?
#linear equations
#no solution
#parallel
A अनंत हल / Infinitely many solutions
B एक अद्वितीय हल / One unique solution
C कोई हल नहीं / No solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (16/2=(-8)/(-1)) but (24/4) 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 (16/2=(-8)/(-1)) but (24/4) is different. Therefore the lines are parallel and distinct.
Step 3
Exam Tip
यहां (16/2=(-8)/(-1)) लेकिन (24/4) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (13x+5y=22) और (26x+10y=45) का युग्म कैसा है?
What kind of pair is (13x+5y=22) and (26x+10y=45)?
#linear equations
#inconsistent
#parallel
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 (13/26=5/10) but (22/45) is different. Therefore the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (13/26=5/10) but (22/45) is different. Therefore the lines are parallel and distinct.
Step 3
Exam Tip
यहां (13/26=5/10) लेकिन (22/45) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (3x+2y=11) और (6x+4y=t) का कोई हल न होने के लिए (t) क्या नहीं होना चाहिए?
What should (t) not be for (3x+2y=11) and (6x+4y=t) to have no solution?
#linear equations
#parameter
#no solution
A (11)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
For no solution \(3/6=2/4 \ne 11/t\) must hold. If (t=22) the pair will have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (22). For no solution \(3/6=2/4 \ne 11/t\) must hold. If (t=22) the pair will have infinitely many solutions.
Step 3
Exam Tip
कोई हल नहीं के लिए \(3/6=2/4 \ne 11/t\) होना चाहिए। यदि (t=22) हो तो अनंत हल हो जाएंगे।
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समीकरण (2x+ay=5) और (6x+9y=15) के अनंत हल होने के लिए (a) का मान क्या है?
What is the value of (a) for (2x+ay=5) and (6x+9y=15) to have infinitely many solutions?
#linear equations
#parameter
#infinite solutions
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions (2/6=a/9=5/15) must hold. Therefore (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For infinitely many solutions (2/6=a/9=5/15) must hold. Therefore (a=3).
Step 3
Exam Tip
अनंत हल के लिए (2/6=a/9=5/15) होना चाहिए। इसलिए (a=3) है।
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समीकरण (6x+2y=8) और (3x+y=5) के लिए सही विकल्प कौन-सा है?
Which option is correct for (6x+2y=8) and (3x+y=5)?
#linear equations
#no solution
#parallel lines
A अनंत हल / Infinitely many solutions
B एक अद्वितीय हल / One unique solution
C कोई हल नहीं / No solution
D समान रेखा / Same line
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (6/3=2/1) but (8/5) 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 (6/3=2/1) but (8/5) is different. Therefore the lines are parallel and distinct.
Step 3
Exam Tip
यहां (6/3=2/1) लेकिन (8/5) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरण (3x+2y=7) और (6x+4y=14) के लिए हलों की संख्या क्या है?
What is the number of solutions for (3x+2y=7) and (6x+4y=14)?
#linear equations
#solvability
#infinite solutions
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (2) times the first so the lines are coincident. Coincident lines 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 (2) times the first so the lines are coincident. Coincident lines have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है इसलिए रेखाएं संपाती हैं। संपाती रेखाओं में अनंत हल होते हैं।
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समीकरण (2x+y=4) और (6x+3y=10) का ग्राफ कैसा होगा?
What will be the graph of (2x+y=4) and (6x+3y=10)?
#linear equations
#graph
#parallel lines
A संपाती रेखाएं / Coincident lines
B कटती रेखाएं / Intersecting lines
C समानांतर अलग रेखाएं / Distinct parallel lines
D लंबवत रेखाएं / Perpendicular lines
Explanation opens after your attempt
Correct Answer
C. समानांतर अलग रेखाएं / Distinct parallel lines
Step 1
Concept
Here (2/6=1/3) but (4/10) is different so the lines are parallel. Such lines never meet.
Step 2
Why this answer is correct
The correct answer is C. समानांतर अलग रेखाएं / Distinct parallel lines. Here (2/6=1/3) but (4/10) is different so the lines are parallel. Such lines never meet.
Step 3
Exam Tip
यहां (2/6=1/3) लेकिन (4/10) अलग है इसलिए रेखाएं समानांतर हैं। ऐसी रेखाएं कभी नहीं मिलतीं।
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समीकरण (ax+2y=5) और (6x+4y=13) का कोई हल न होने के लिए (a) का मान क्या है?
What is the value of (a) for (ax+2y=5) and (6x+4y=13) to have no solution?
#linear equations
#parameter
#parallel lines
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
For no solution (a/6=2/4) and (5/13) must be different. Therefore (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). For no solution (a/6=2/4) and (5/13) must be different. Therefore (a=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (a/6=2/4) और (5/13) अलग होना चाहिए। इसलिए (a=3) है।
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समीकरण (3x+ky=12) और (6x+8y=24) के अनंत हल के लिए (k) क्या होगा?
What will (k) be for infinitely many solutions of (3x+ky=12) and (6x+8y=24)?
#linear equations
#parameter
#infinite solutions
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions (3/6=k/8=12/24) must hold. Therefore (k=4).
Step 2
Why this answer is correct
The correct answer is B. (4). For infinitely many solutions (3/6=k/8=12/24) must hold. Therefore (k=4).
Step 3
Exam Tip
अनंत हल के लिए (3/6=k/8=12/24) होना चाहिए। इसलिए (k=4) है।
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समीकरण (3x+5y=14) और (6x+11y=30) के लिए हल-स्थिति क्या है?
What is the solution status for (3x+5y=14) and (6x+11y=30)?
#linear equations
#unique solution
#ratio test
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 \(3/6 \ne 5/11\) so the lines intersect. Intersecting lines have exactly one common solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here \(3/6 \ne 5/11\) so the lines intersect. Intersecting lines have exactly one common solution.
Step 3
Exam Tip
यहां \(3/6 \ne 5/11\) इसलिए रेखाएं कटती हैं। कटती रेखाओं का केवल एक सामान्य हल होता है।
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समीकरण (6x+3y=12) और (2x+y=4) के लिए सही कथन क्या है?
What is the correct statement for (6x+3y=12) and (2x+y=4)?
#linear equations
#dependent pair
#infinite solutions
A असंगत हैं / They are inconsistent
B एक अद्वितीय हल है / There is one unique solution
C अनंत हल हैं / There are infinitely many solutions
D रेखाएं लंबवत हैं / Lines are perpendicular
Explanation opens after your attempt
Correct Answer
C. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The first equation is (3) times the second so both are the same line. In such questions spotting the common multiplier is the fastest method.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल हैं / There are infinitely many solutions. The first equation is (3) times the second so both are the same line. In such questions spotting the common multiplier is the fastest method.
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना है इसलिए दोनों एक ही रेखा हैं। ऐसे प्रश्नों में समान गुणक पहचानना तेज तरीका है।
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समीकरण (3x+4y=11) और (6x+8y=25) किस प्रकार का युग्म बनाते हैं?
What type of pair is formed by (3x+4y=11) and (6x+8y=25)?
#linear equations
#inconsistent
#parallel lines
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 (3/6=4/8) but (11/25) is different so there is no solution. In exams equal first two ratios and a different third ratio mean inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (3/6=4/8) but (11/25) is different so there is no solution. In exams equal first two ratios and a different third ratio mean inconsistent.
Step 3
Exam Tip
यहां (3/6=4/8) लेकिन (11/25) अलग है इसलिए कोई हल नहीं। परीक्षा में पहले दो अनुपात बराबर और तीसरा अलग हो तो असंगत लिखें।
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समीकरण (6x-2y=4) और (3x-y=2) के हलों की संख्या बताइए।
State the number of solutions of (6x-2y=4) and (3x-y=2).
#linear equations
#infinite solutions
#dependent pair
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The first equation is (2) times the second, so both lines are coincident. Coincident lines have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The first equation is (2) times the second, so both lines are coincident. Coincident lines have infinitely many solutions.
Step 3
Exam Tip
पहला समीकरण दूसरे का (2) गुना है, इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं।
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समीकरण (3x+ky=9) और (6x+8y=20) का कोई हल न होने के लिए (k) का मान क्या है?
What value of (k) makes (3x+ky=9) and (6x+8y=20) have no solution?
#linear equations
#parameter
#parallel lines
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For no solution, (3/6=k/8) and (9/20) must be different. This gives (k=4).
Step 2
Why this answer is correct
The correct answer is C. (4). For no solution, (3/6=k/8) and (9/20) must be different. This gives (k=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (3/6=k/8) और (9/20) अलग होना चाहिए। इससे (k=4) मिलता है।
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