100 results found for "continuous variables" in Class 10.
पश्चिमी घाट को पूर्वी घाट की तुलना में अधिक निरंतर पर्वत श्रृंखला मानने का सही कारण क्या है?
What is the correct reason for considering the Western Ghats more continuous than the Eastern Ghats?
#indian geography
#western ghats
#eastern ghats
#sahyadri
#continuous range
A पश्चिमी घाट पश्चिमी तट के साथ लंबी और कम कटी हुई श्रृंखला बनाते हैं / Western Ghats form a long and less broken range along the western coast
B पश्चिमी घाट पूरी तरह गंगा मैदान में स्थित हैं / Western Ghats are completely located in the Ganga Plain
C पश्चिमी घाट हिमालय की सबसे बाहरी श्रेणी हैं / Western Ghats are the outermost range of the Himalayas
D पश्चिमी घाट केवल रेतीले टीले हैं / Western Ghats are only sandy dunes
Explanation opens after your attempt
Correct Answer
A. पश्चिमी घाट पश्चिमी तट के साथ लंबी और कम कटी हुई श्रृंखला बनाते हैं / Western Ghats form a long and less broken range along the western coast
Step 1
Concept
The Western Ghats form a relatively continuous mountain wall along the western coast while the Eastern Ghats are cut by many rivers. For exams, link the Western Ghats with Sahyadri and rainfall barrier.
Step 2
Why this answer is correct
The correct answer is A. पश्चिमी घाट पश्चिमी तट के साथ लंबी और कम कटी हुई श्रृंखला बनाते हैं / Western Ghats form a long and less broken range along the western coast. The Western Ghats form a relatively continuous mountain wall along the western coast while the Eastern Ghats are cut by many rivers. For exams, link the Western Ghats with Sahyadri and rainfall barrier.
Step 3
Exam Tip
पश्चिमी घाट पश्चिमी तट के साथ अपेक्षाकृत निरंतर पर्वत दीवार बनाते हैं जबकि पूर्वी घाट कई नदियों से कटे हैं। परीक्षा में पश्चिमी घाट को सह्याद्रि और वर्षा अवरोधक से जोड़ें।
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लगातार रेखा की पहचान क्या है?
What is the identity of a continuous line?
#continuous line
#unbroken
#line
A बीच में बहुत अंतराल / Many gaps in between
B बिना टूटे आगे बढ़ना / Moving without break
C केवल बिंदु होना / Being only dots
D रंगहीन होना / Being colourless
Explanation opens after your attempt
Correct Answer
B. बिना टूटे आगे बढ़ना / Moving without break
Step 1
Concept
A continuous line moves without stopping. Exam tip: understand continuous line as unbroken mark.
Step 2
Why this answer is correct
The correct answer is B. बिना टूटे आगे बढ़ना / Moving without break. A continuous line moves without stopping. Exam tip: understand continuous line as unbroken mark.
Step 3
Exam Tip
लगातार रेखा बिना रुके चलती है। परीक्षा में continuous line को unbroken mark समझें।
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पूर्वी घाट के असतत स्वरूप और पश्चिमी घाट के निरंतर स्वरूप को किससे समझा जा सकता है?
How can the discontinuous nature of Eastern Ghats and continuous nature of Western Ghats be understood?
#indian geography
#eastern ghats
#western ghats
#river cutting
A नदी कटाव और तटीय समानांतरता से / By river cutting and coastal parallelism
B समुद्री प्रवाल निर्माण से / By marine coral formation
C हिमनदी जमाव से / By glacial deposition
D रेगिस्तानी बालू से / By desert sand
Explanation opens after your attempt
Correct Answer
A. नदी कटाव और तटीय समानांतरता से / By river cutting and coastal parallelism
Step 1
Concept
The Eastern Ghats are cut by many rivers while the Western Ghats are more continuous parallel to the coast. For exams, remember their comparison separately.
Step 2
Why this answer is correct
The correct answer is A. नदी कटाव और तटीय समानांतरता से / By river cutting and coastal parallelism. The Eastern Ghats are cut by many rivers while the Western Ghats are more continuous parallel to the coast. For exams, remember their comparison separately.
Step 3
Exam Tip
पूर्वी घाट कई नदियों से कटे हैं जबकि पश्चिमी घाट तट के समानांतर अधिक निरंतर हैं। परीक्षा में दोनों की तुलना अलग-अलग याद रखें।
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पश्चिमी घाट की ऊंचाई सामान्यतः किस घाट की तुलना में अधिक निरंतर है?
The height of the Western Ghats is generally more continuous compared to which Ghats?
#indian geography
#western ghats
#eastern ghats
#rainfall barrier
A हिमालय / Himalayas
B पूर्वी घाट / Eastern Ghats
C अरावली / Aravalli
D शिवालिक / Shiwalik
Explanation opens after your attempt
Correct Answer
B. पूर्वी घाट / Eastern Ghats
Step 1
Concept
The Western Ghats are more continuous and wall-like than the Eastern Ghats. For exams, remember them as a rainfall barrier.
Step 2
Why this answer is correct
The correct answer is B. पूर्वी घाट / Eastern Ghats. The Western Ghats are more continuous and wall-like than the Eastern Ghats. For exams, remember them as a rainfall barrier.
Step 3
Exam Tip
पश्चिमी घाट पूर्वी घाट की तुलना में अधिक निरंतर और स्पष्ट पर्वतीय दीवार जैसे हैं। परीक्षा में पश्चिमी घाट को वर्षा अवरोधक के रूप में याद रखें।
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हिमाद्रि को हिमालय की सबसे ऊंची और सतत श्रेणी कहने का मुख्य कारण क्या है?
What is the main reason for calling Himadri the highest and most continuous Himalayan range?
#himadri
#greater-himalaya
#glaciers
A इसमें उच्च शिखर और व्यापक हिमनद मिलते हैं / It has high peaks and extensive glaciers
B यह समुद्री प्रवालों से बनी है / It is made of marine corals
C यह केवल नई जलोढ़ मिट्टी है / It is only new alluvial soil
D यह थार की पवनों से बनी है / It is formed by winds of Thar
Explanation opens after your attempt
Correct Answer
A. इसमें उच्च शिखर और व्यापक हिमनद मिलते हैं / It has high peaks and extensive glaciers
Step 1
Concept
Himadri is an inner Himalayan range with high peaks and glaciers. For exams remember the Himadri and perennial river source link.
Step 2
Why this answer is correct
The correct answer is A. इसमें उच्च शिखर और व्यापक हिमनद मिलते हैं / It has high peaks and extensive glaciers. Himadri is an inner Himalayan range with high peaks and glaciers. For exams remember the Himadri and perennial river source link.
Step 3
Exam Tip
हिमाद्रि ऊंचे शिखरों और हिमनदों वाली आंतरिक हिमालयी श्रेणी है। परीक्षा में हिमाद्रि और बारहमासी नदी स्रोत संबंध याद रखें।
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पश्चिमी घाट की निरंतर ऊंची दीवार जैसा स्वरूप मानसून को किस प्रकार प्रभावित करता है?
How does the continuous high wall like form of Western Ghats affect the monsoon?
#western-ghats
#monsoon
#rain-shadow
A नम पवनों को ऊपर उठाकर पवनाभिमुख वर्षा और पवनविमुख वर्षाछाया बनाता है / It lifts moist winds causing windward rain and leeward rain shadow
B सभी पवनों को हिमालय की ओर लौटा देता है / It sends all winds back to Himalaya
C पूर्वी तट पर प्रवाल बनाता है / It forms corals on eastern coast
D थार में बर्फ गिराता है / It causes snow in Thar
Explanation opens after your attempt
Correct Answer
A. नम पवनों को ऊपर उठाकर पवनाभिमुख वर्षा और पवनविमुख वर्षाछाया बनाता है / It lifts moist winds causing windward rain and leeward rain shadow
Step 1
Concept
Western Ghats influence both orographic rainfall and rain shadow. For exams remember windward and leeward slopes.
Step 2
Why this answer is correct
The correct answer is A. नम पवनों को ऊपर उठाकर पवनाभिमुख वर्षा और पवनविमुख वर्षाछाया बनाता है / It lifts moist winds causing windward rain and leeward rain shadow. Western Ghats influence both orographic rainfall and rain shadow. For exams remember windward and leeward slopes.
Step 3
Exam Tip
पश्चिमी घाट ओरोग्राफिक वर्षा और वर्षाछाया दोनों को प्रभावित करते हैं। परीक्षा में पवनाभिमुख और पवनविमुख ढाल याद रखें।
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पश्चिमी घाटों की निरंतर और ऊंची स्थिति किस जलवायु प्रक्रिया को अधिक प्रभावी बनाती है?
The continuous and high position of the Western Ghats makes which climatic process more effective?
#western-ghats
#orographic-rainfall
#monsoon
A ओरोग्राफिक वर्षा / Orographic rainfall
B लवणीय दलदल निर्माण / Saline marsh formation
C प्रवाल विरंजन / Coral bleaching
D हिमनदी संचयन / Glacial accumulation
Explanation opens after your attempt
Correct Answer
A. ओरोग्राफिक वर्षा / Orographic rainfall
Step 1
Concept
Western Ghats force moist monsoon winds upward and cause rainfall. For exams remember windward and leeward slopes.
Step 2
Why this answer is correct
The correct answer is A. ओरोग्राफिक वर्षा / Orographic rainfall. Western Ghats force moist monsoon winds upward and cause rainfall. For exams remember windward and leeward slopes.
Step 3
Exam Tip
पश्चिमी घाट नम मानसूनी पवनों को ऊपर उठाकर वर्षा कराते हैं। परीक्षा में पवनाभिमुख और पवनविमुख ढाल याद रखें।
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पश्चिमी घाट और पूर्वी घाट में से कौन अधिक सतत माना जाता है?
Which is considered more continuous Western Ghats or Eastern Ghats?
#western-ghats
#eastern-ghats
#comparison
A पश्चिमी घाट / Western Ghats
B पूर्वी घाट / Eastern Ghats
C दोनों समान रूप से टूटे हुए / Both equally broken
D दोनों समुद्र में हैं / Both are in the sea
Explanation opens after your attempt
Correct Answer
A. पश्चिमी घाट / Western Ghats
Step 1
Concept
Western Ghats are more continuous than Eastern Ghats. For exams remember Eastern Ghats are cut by rivers.
Step 2
Why this answer is correct
The correct answer is A. पश्चिमी घाट / Western Ghats. Western Ghats are more continuous than Eastern Ghats. For exams remember Eastern Ghats are cut by rivers.
Step 3
Exam Tip
पश्चिमी घाट पूर्वी घाट की तुलना में अधिक सतत हैं। परीक्षा में पूर्वी घाट को नदियों से कटा हुआ याद रखें।
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यदि (p(-1)>0) और (p(4)<0), तो निरंतर बहुपद आलेख के लिए कौन सा कथन उचित है?
If (p(-1)>0) and (p(4)<0), which statement is suitable for a continuous polynomial graph?
#sign change zero graph
A (-1) और (4) दोनों शून्यक हैं / Both (-1) and (4) are zeroes
B बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them
C कोई कटान संभव नहीं है / No intersection is possible
D आलेख केवल (y)-अक्ष को काटेगा / The graph will cut only the (y)-axis
Explanation opens after your attempt
Correct Answer
B. बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them
Step 1
Concept
A sign change suggests (p(x)=0) in between. Tip: a polynomial graph does not break.
Step 2
Why this answer is correct
The correct answer is B. बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them. A sign change suggests (p(x)=0) in between. Tip: a polynomial graph does not break.
Step 3
Exam Tip
चिह्न बदलने से बीच में (p(x)=0) होने का संकेत मिलता है। टिप: बहुपद आलेख टूटता नहीं है।
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समीकरणों (3(x-2)+2(y+1)=31) और (5(x-2)-2(y+1)=21) को हल करने पर (x+y) क्या है?
Solving (3(x-2)+2(y+1)=31) and (5(x-2)-2(y+1)=21), what is (x+y)?
#pair-linear-equations-shifted-variables
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let (u=x-2) and (v=y+1). Solving (3u+2v=31), (5u-2v=21) gives values to substitute back for (x+y).
Step 2
Why this answer is correct
The correct answer is D. (13). Let (u=x-2) and (v=y+1). Solving (3u+2v=31), (5u-2v=21) gives values to substitute back for (x+y).
Step 3
Exam Tip
मान लें (u=x-2) और (v=y+1)। (3u+2v=31), (5u-2v=21) से \(u=\frac{13}{2}\), \(v=\frac{23}{4}\), फिर \(x+y=\frac{53}{4}\)।
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समीकरणों (2(x-1)+3(y+2)=25) और (4(x-1)-3(y+2)=5) को हल करने पर (x+y) क्या है?
Solving (2(x-1)+3(y+2)=25) and (4(x-1)-3(y+2)=5), what is (x+y)?
#pair-linear-equations
#shifted-variables
#elimination
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Let (u=x-1) and (v=y+2). From (2u+3v=25), (4u-3v=5), (u=5,v=5), so (x=6,y=3).
Step 2
Why this answer is correct
The correct answer is D. (11). Let (u=x-1) and (v=y+2). From (2u+3v=25), (4u-3v=5), (u=5,v=5), so (x=6,y=3).
Step 3
Exam Tip
मान लें (u=x-1) और (v=y+2)। (2u+3v=25), (4u-3v=5) से (u=5,v=5), इसलिए (x=6,y=3)।
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समीकरण (2x+3y=19) और (x-y=2) का हल क्या है?
What is the solution of (2x+3y=19) and (x-y=2)?
#linear equations
#substitution
#two variables
#medium
#class 10
A ( (4,5) )
B ( (6,2) )
C ( (5,3) )
D ( (3,5) )
Explanation opens after your attempt
Correct Answer
C. ( (5,3) )
Step 1
Concept
From (x-y=2), (x=y+2), so (2(y+2)+3y=19) and (y=3). Then (x=5).
Step 2
Why this answer is correct
The correct answer is C. ( (5,3) ). From (x-y=2), (x=y+2), so (2(y+2)+3y=19) and (y=3). Then (x=5).
Step 3
Exam Tip
(x-y=2) से (x=y+2), इसलिए (2(y+2)+3y=19) और (y=3)। फिर (x=5) मिलेगा।
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युग्म ((y+1)x+2y=3) और (5x+(y-2)y=4) के अद्वितीय हल की सही शर्त कौन-सी है?
Which condition gives a unique solution for ((y+1)x+2y=3) and (5x+(y-2)y=4)?
#class10
#linear-equations
#solvability
A \(y^2-y-12=0\)
B \(y^2-y-12\neq0\)
C \(y^2+y-12=0\)
D \(y^2+y-12\neq0\)
Explanation opens after your attempt
Correct Answer
B. \(y^2-y-12\neq0\)
Step 1
Concept
The determinant is (D=(y+1)(y-2)-10=y-2 -y-12). For a unique solution, \(D\neq0\) is required.
Step 2
Why this answer is correct
The correct answer is B. \(y^2-y-12\neq0\). The determinant is (D=(y+1)(y-2)-10=y-2 -y-12). For a unique solution, \(D\neq0\) is required.
Step 3
Exam Tip
सारणिक (D=(y+1)(y-2)-10=y-2 -y-12) है। अद्वितीय हल के लिए \(D\neq0\) चाहिए।
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युग्म (tx+9y=6) और (20x+15y=10) के अनंत हलों के लिए (t) का मान क्या होगा?
What is the value of (t) for infinitely many solutions of (tx+9y=6) and (20x+15y=10)?
#class10
#linear-equations
#solvability
A (t=10)
B (t=11)
C (t=12)
D (t=13)
Explanation opens after your attempt
Step 1
Concept
All three ratios must be \(\frac{3}{5}\). Therefore, \(\frac{t}{20}=\frac{3}{5}\) gives (t=12).
Step 2
Why this answer is correct
The correct answer is C. (t=12). All three ratios must be \(\frac{3}{5}\). Therefore, \(\frac{t}{20}=\frac{3}{5}\) gives (t=12).
Step 3
Exam Tip
तीनों अनुपात \(\frac{3}{5}\) होने चाहिए। इसलिए \(\frac{t}{20}=\frac{3}{5}\) से (t=12)।
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युग्म (sx+4y=12) और (21x+12y=40) में कोई हल न होने के लिए (s) क्या होगा?
What is (s) for no solution in (sx+4y=12) and (21x+12y=40)?
#class10
#linear-equations
#solvability
A (s=5)
B (s=6)
C (s=7)
D (s=8)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{s}{21}=\frac{4}{12}\) gives (s=7). The constant ratio is not equal.
Step 2
Why this answer is correct
The correct answer is C. (s=7). Equating coefficient ratios, \(\frac{s}{21}=\frac{4}{12}\) gives (s=7). The constant ratio is not equal.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{s}{21}=\frac{4}{12}\) से (s=7) है। स्थिर पद अनुपात समान नहीं है।
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युग्म (rx+2y=5) और (9x+3y=8) का अद्वितीय हल कब होगा?
When will (rx+2y=5) and (9x+3y=8) have a unique solution?
#class10
#linear-equations
#solvability
A (r=6)
B \(r\neq6\)
C (r=9)
D \(r\neq9\)
Explanation opens after your attempt
Correct Answer
B. \(r\neq6\)
Step 1
Concept
For a unique solution, \(\frac{r}{9}\neq\frac{2}{3}\) is required. Hence \(r\neq6\).
Step 2
Why this answer is correct
The correct answer is B. \(r\neq6\). For a unique solution, \(\frac{r}{9}\neq\frac{2}{3}\) is required. Hence \(r\neq6\).
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{r}{9}\neq\frac{2}{3}\) चाहिए। इसलिए \(r\neq6\) होगा।
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युग्म (qx+11y=22) और (18x+33y=66) के अनंत हलों के लिए (q) का मान क्या है?
What is the value of (q) for infinitely many solutions of (qx+11y=22) and (18x+33y=66)?
#class10
#linear-equations
#solvability
A (q=4)
B (q=5)
C (q=6)
D (q=7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{q}{18}=\frac{11}{33}=\frac{22}{66}\). Therefore, (q=6) is correct.
Step 2
Why this answer is correct
The correct answer is C. (q=6). For infinitely many solutions, \(\frac{q}{18}=\frac{11}{33}=\frac{22}{66}\). Therefore, (q=6) is correct.
Step 3
Exam Tip
अनंत हलों में \(\frac{q}{18}=\frac{11}{33}=\frac{22}{66}\) होता है। इसलिए (q=6) सही मान है।
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युग्म (px-5y=7) और (12x-15y=19) में कोई हल न होने के लिए (p) क्या होगा?
What is (p) for no solution in (px-5y=7) and (12x-15y=19)?
#class10
#linear-equations
#solvability
A (p=4)
B (p=5)
C (p=6)
D (p=7)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{p}{12}=\frac{-5}{-15}\) gives (p=4). The constant ratio is different.
Step 2
Why this answer is correct
The correct answer is A. (p=4). Equating coefficient ratios, \(\frac{p}{12}=\frac{-5}{-15}\) gives (p=4). The constant ratio is different.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{p}{12}=\frac{-5}{-15}\) से (p=4) है। स्थिर अनुपात अलग है।
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युग्म (3x+ny=18) और (5x+10y=30) के अनंत हलों के लिए (n) क्या होगा?
For infinitely many solutions of (3x+ny=18) and (5x+10y=30), what is (n)?
#class10
#linear-equations
#solvability
A (n=4)
B (n=5)
C (n=6)
D (n=8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{3}{5}=\frac{n}{10}=\frac{18}{30}\) is needed. This gives (n=6).
Step 2
Why this answer is correct
The correct answer is C. (n=6). For infinitely many solutions, \(\frac{3}{5}=\frac{n}{10}=\frac{18}{30}\) is needed. This gives (n=6).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{3}{5}=\frac{n}{10}=\frac{18}{30}\) चाहिए। इससे (n=6) मिलता है।
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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 (2x+3y=4) और (kx+6y=11) में कोई हल न होने के लिए (k) का मान क्या है?
What is the value of (k) for no solution in (2x+3y=4) and (kx+6y=11)?
#class10
#linear-equations
#solvability
A (k=2)
B (k=3)
C (k=4)
D (k=6)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{2}{k}=\frac{3}{6}\) gives (k=4). The constant ratio is different.
Step 2
Why this answer is correct
The correct answer is C. (k=4). Equating coefficient ratios, \(\frac{2}{k}=\frac{3}{6}\) gives (k=4). The constant ratio is different.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{2}{k}=\frac{3}{6}\) से (k=4) है। स्थिर पद अनुपात अलग है।
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युग्म (jx+5y=10) और (14x+7y=14) के अनंत हलों के लिए (j) क्या होगा?
For infinitely many solutions of (jx+5y=10) and (14x+7y=14), what is (j)?
#class10
#linear-equations
#solvability
A (j=8)
B (j=9)
C (j=10)
D (j=11)
Explanation opens after your attempt
Step 1
Concept
All three ratios must be \(\frac{5}{7}\). Therefore, \(\frac{j}{14}=\frac{5}{7}\) gives (j=10).
Step 2
Why this answer is correct
The correct answer is C. (j=10). All three ratios must be \(\frac{5}{7}\). Therefore, \(\frac{j}{14}=\frac{5}{7}\) gives (j=10).
Step 3
Exam Tip
तीनों अनुपात \(\frac{5}{7}\) होने चाहिए। इसलिए \(\frac{j}{14}=\frac{5}{7}\) से (j=10)।
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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 (hx+12y=6) और (10x+15y=20) का अद्वितीय हल कब होगा?
When will (hx+12y=6) and (10x+15y=20) have a unique solution?
#class10
#linear-equations
#solvability
A (h=8)
B \(h\neq8\)
C (h=10)
D \(h\neq10\)
Explanation opens after your attempt
Correct Answer
B. \(h\neq8\)
Step 1
Concept
For a unique solution, \(\frac{h}{10}\neq\frac{12}{15}\) must hold. Hence \(h\neq8\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(h\neq8\). For a unique solution, \(\frac{h}{10}\neq\frac{12}{15}\) must hold. Hence \(h\neq8\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{h}{10}\neq\frac{12}{15}\) होना चाहिए। इसलिए \(h\neq8\) सही है।
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युग्म ((g-1 )x+10y=15) और (8x+20y=30) के अनंत हलों के लिए (g) क्या होगा?
For infinitely many solutions of ((g-1 )x+10y=15) and (8x+20y=30), what is (g)?
#class10
#linear-equations
#solvability
A (g=4)
B (g=5)
C (g=6)
D (g=7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{g-1}{8}=\frac{10}{20}=\frac{15}{30}\) must hold. This gives (g=5).
Step 2
Why this answer is correct
The correct answer is B. (g=5). For infinitely many solutions, \(\frac{g-1}{8}=\frac{10}{20}=\frac{15}{30}\) must hold. This gives (g=5).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{g-1}{8}=\frac{10}{20}=\frac{15}{30}\) होना चाहिए। इससे (g=5) मिलता है।
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युग्म (7x+fy=2) और (28x+20y=13) में कोई हल न होने के लिए (f) क्या होगा?
What is (f) for no solution in (7x+fy=2) and (28x+20y=13)?
#class10
#linear-equations
#solvability
A (f=4)
B (f=5)
C (f=6)
D (f=7)
Explanation opens after your attempt
Step 1
Concept
To make the coefficient ratio \(\frac{1}{4}\), (f=5) is required. The different constant ratio gives no solution.
Step 2
Why this answer is correct
The correct answer is B. (f=5). To make the coefficient ratio \(\frac{1}{4}\), (f=5) is required. The different constant ratio gives no solution.
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{4}\) बनाने के लिए (f=5) चाहिए। स्थिर पद अनुपात अलग होने से कोई हल नहीं होगा।
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युग्म (ex-4y=9) और (18x-12y=27) का अद्वितीय हल कब होगा?
When will (ex-4y=9) and (18x-12y=27) have a unique solution?
#class10
#linear-equations
#solvability
A (e=6)
B \(e\neq6\)
C (e=18)
D \(e\neq18\)
Explanation opens after your attempt
Correct Answer
B. \(e\neq6\)
Step 1
Concept
For a unique solution, \(\frac{e}{18}\neq\frac{-4}{-12}\) is needed. Hence \(e\neq6\).
Step 2
Why this answer is correct
The correct answer is B. \(e\neq6\). For a unique solution, \(\frac{e}{18}\neq\frac{-4}{-12}\) is needed. Hence \(e\neq6\).
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{e}{18}\neq\frac{-4}{-12}\) चाहिए। अतः \(e\neq6\)।
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युग्म (4x+dy=7) और (12x+15y=21) के अनंत हलों के लिए (d) का मान क्या है?
What is the value of (d) for infinitely many solutions of (4x+dy=7) and (12x+15y=21)?
#class10
#linear-equations
#solvability
A (d=3)
B (d=4)
C (d=5)
D (d=6)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{4}{12}=\frac{d}{15}=\frac{7}{21}\) must hold. So (d=5) is correct.
Step 2
Why this answer is correct
The correct answer is C. (d=5). For infinitely many solutions, \(\frac{4}{12}=\frac{d}{15}=\frac{7}{21}\) must hold. So (d=5) is correct.
Step 3
Exam Tip
अनंत हलों में \(\frac{4}{12}=\frac{d}{15}=\frac{7}{21}\) होना चाहिए। इसलिए (d=5) सही है।
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युग्म (cx+6y=5) और (9x+18y=10) में कोई हल न होने के लिए (c) क्या होगा?
What is (c) for no solution in (cx+6y=5) and (9x+18y=10)?
#class10
#linear-equations
#solvability
A (c=2)
B (c=3)
C (c=4)
D (c=5)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{c}{9}=\frac{6}{18}\) gives (c=3). The constant ratio \(\frac{5}{10}\) is different.
Step 2
Why this answer is correct
The correct answer is B. (c=3). Equating coefficient ratios, \(\frac{c}{9}=\frac{6}{18}\) gives (c=3). The constant ratio \(\frac{5}{10}\) is different.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{c}{9}=\frac{6}{18}\) से (c=3) आता है। स्थिर अनुपात \(\frac{5}{10}\) अलग है।
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युग्म (2x+by=6) और (bx+8y=24) के अनंत हलों के लिए (b) का मान क्या होगा?
What is the value of (b) for infinitely many solutions of (2x+by=6) and (bx+8y=24)?
#class10
#linear-equations
#solvability
A (b=2)
B (b=3)
C (b=4)
D (b=6)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{2}{b}=\frac{b}{8}=\frac{6}{24}\) must hold. This gives (b=4).
Step 2
Why this answer is correct
The correct answer is C. (b=4). For infinitely many solutions, \(\frac{2}{b}=\frac{b}{8}=\frac{6}{24}\) must hold. This gives (b=4).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{2}{b}=\frac{b}{8}=\frac{6}{24}\) होना चाहिए। इससे (b=4) मिलता है।
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युग्म (ax+2y=3) और (4x+ay=9) के अद्वितीय हल की शर्त क्या है?
What is the condition for a unique solution of (ax+2y=3) and (4x+ay=9)?
#class10
#linear-equations
#solvability
A \(a^2=8\)
B \(a^2\neq8\)
C (a=4)
D \(a\neq2\)
Explanation opens after your attempt
Correct Answer
B. \(a^2\neq8\)
Step 1
Concept
The determinant is \(D=a^2-8\). For a unique solution, \(D\neq0\), so \(a^2\neq8\).
Step 2
Why this answer is correct
The correct answer is B. \(a^2\neq8\). The determinant is \(D=a^2-8\). For a unique solution, \(D\neq0\), so \(a^2\neq8\).
Step 3
Exam Tip
सारणिक \(D=a^2-8\) है। अद्वितीय हल के लिए \(D\neq0\) यानी \(a^2\neq8\)।
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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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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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यदि \(a_1b_2-a_2b_1\neq0\) है, तो युग्म के बारे में सही कथन क्या है?
If \(a_1b_2-a_2b_1\neq0\), what is the correct statement about the pair?
#class10
#linear-equations
#solvability
A युग्म असंगत है / The pair is inconsistent
B युग्म के अनंत हल हैं / The pair has infinitely many solutions
C युग्म का अद्वितीय हल है / The pair has a unique solution
D युग्म में कोई रेखा नहीं / The pair has no line
Explanation opens after your attempt
Correct Answer
C. युग्म का अद्वितीय हल है / The pair has a unique solution
Step 1
Concept
When the determinant is non-zero, the lines intersect at one point. Hence there is a unique solution.
Step 2
Why this answer is correct
The correct answer is C. युग्म का अद्वितीय हल है / The pair has a unique solution. When the determinant is non-zero, the lines intersect at one point. Hence there is a unique solution.
Step 3
Exam Tip
सारणिक शून्य नहीं होने पर रेखाएँ एक बिंदु पर कटती हैं। इसलिए अद्वितीय हल होता है।
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यदि दो रेखाएँ अलग-अलग समांतर हैं, तो अनुपातों की सही स्थिति कौन-सी होगी?
If two lines are distinct and parallel, what is the correct ratio condition?
#class10
#linear-equations
#solvability
A \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(a_1b_2-a_2b_1\neq0\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
Step 1
Concept
For distinct parallel lines, coefficient ratios are equal and the constant ratio is different. This is the condition for no solution.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). For distinct parallel lines, coefficient ratios are equal and the constant ratio is different. This is the condition for no solution.
Step 3
Exam Tip
अलग समांतर रेखाओं में गुणांक अनुपात समान और स्थिर पद अनुपात अलग होता है। यही कोई हल नहीं की शर्त है।
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यदि दो रेखाओं की ढाल समान और अवरोध भी समान हो, तो उनके समीकरणों के युग्म में कितने हल होंगे?
If two lines have the same slope and the same intercept, how many solutions will their pair of equations have?
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D सिर्फ मूल बिंदु / Only origin
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
Same slope and same intercept mean the same line. Therefore, such a pair has infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept mean the same line. Therefore, such a pair has infinitely many solutions.
Step 3
Exam Tip
समान ढाल और समान अवरोध का अर्थ एक ही रेखा है। इसलिए ऐसे युग्म में अनंत हल होते हैं।
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यदि \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) है, तो युग्म की हल-स्थिति क्या होगी?
If \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), what is the solution status of the pair?
#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 / Only two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
When all three ratios are equal, the lines are coincident. Therefore, infinitely many solutions occur.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. When all three ratios are equal, the lines are coincident. Therefore, infinitely many solutions occur.
Step 3
Exam Tip
तीनों अनुपात समान होने पर रेखाएँ संपाती होती हैं। इसलिए अनंत हल मिलते हैं।
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सामान्य युग्म \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) में अद्वितीय हल की शर्त क्या है?
For the general pair \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), what is the condition for a unique solution?
#class10
#linear-equations
#solvability
A \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
C \(\frac{a_1}{a_2}=\frac{c_1}{c_2}\)
D \(c_1=c_2=0\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
Step 1
Concept
A unique solution occurs when the lines intersect at one point. Its ratio form is \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). A unique solution occurs when the lines intersect at one point. Its ratio form is \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\).
Step 3
Exam Tip
अद्वितीय हल तब मिलता है जब रेखाएँ एक बिंदु पर कटती हैं। इसका अनुपात रूप \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\) है।
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युग्म \(5x+\gamma y=1\) और (25x+15y=11) में कोई हल न होने के लिए \(\gamma\) का मान क्या होगा?
What is the value of \(\gamma\) for no solution in \(5x+\gamma y=1\) and (25x+15y=11)?
#class10
#linear-equations
#solvability
A \(\gamma=2\)
B \(\gamma=3\)
C \(\gamma=4\)
D \(\gamma=5\)
Explanation opens after your attempt
Correct Answer
B. \(\gamma=3\)
Step 1
Concept
Equating coefficient ratios, \(\frac{5}{25}=\frac{\gamma}{15}\) gives \(\gamma=3\). The constant ratio is different.
Step 2
Why this answer is correct
The correct answer is B. \(\gamma=3\). Equating coefficient ratios, \(\frac{5}{25}=\frac{\gamma}{15}\) gives \(\gamma=3\). The constant ratio is different.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{5}{25}=\frac{\gamma}{15}\) से \(\gamma=3\) मिलता है। स्थिर अनुपात अलग है।
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युग्म (9x+\(\beta+4\)y=15) और (27x+18y=45) के अनंत हलों के लिए \(\beta\) क्या होगा?
For infinitely many solutions of (9x+\(\beta+4\)y=15) and (27x+18y=45), 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
B. \(\beta=2\)
Step 1
Concept
For infinitely many solutions, \(\frac{9}{27}=\frac{\beta+4}{18}=\frac{15}{45}\) must hold. This gives \(\beta=2\).
Step 2
Why this answer is correct
The correct answer is B. \(\beta=2\). For infinitely many solutions, \(\frac{9}{27}=\frac{\beta+4}{18}=\frac{15}{45}\) must hold. This gives \(\beta=2\).
Step 3
Exam Tip
अनंत हलों में \(\frac{9}{27}=\frac{\beta+4}{18}=\frac{15}{45}\) होना चाहिए। इससे \(\beta=2\) मिलता है।
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युग्म (\(\alpha-1\)x+5y=2) और (8x+10y=6) का अद्वितीय हल कब होगा?
When will (\(\alpha-1\)x+5y=2) and (8x+10y=6) have a unique solution?
#class10
#linear-equations
#solvability
A \(\alpha=5\)
B \(\alpha\neq5\)
C \(\alpha=4\)
D \(\alpha\neq4\)
Explanation opens after your attempt
Correct Answer
B. \(\alpha\neq5\)
Step 1
Concept
For a unique solution, \(\frac{\alpha-1}{8}\neq\frac{5}{10}\) is required. Hence \(\alpha\neq5\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(\alpha\neq5\). For a unique solution, \(\frac{\alpha-1}{8}\neq\frac{5}{10}\) is required. Hence \(\alpha\neq5\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{\alpha-1}{8}\neq\frac{5}{10}\) चाहिए। इसलिए \(\alpha\neq5\) सही है।
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युग्म \(14x+\mu y=9\) और (21x+6y=20) में कोई हल न होने के लिए \(\mu\) क्या होगा?
What is \(\mu\) for no solution in \(14x+\mu y=9\) and (21x+6y=20)?
#class10
#linear-equations
#solvability
A \(\mu=3\)
B \(\mu=4\)
C \(\mu=5\)
D \(\mu=6\)
Explanation opens after your attempt
Correct Answer
B. \(\mu=4\)
Step 1
Concept
\(\frac{14}{21}=\frac{2}{3}\). Equating coefficient ratios, \(\frac{\mu}{6}=\frac{2}{3}\) gives \(\mu=4\).
Step 2
Why this answer is correct
The correct answer is B. \(\mu=4\). \(\frac{14}{21}=\frac{2}{3}\). Equating coefficient ratios, \(\frac{\mu}{6}=\frac{2}{3}\) gives \(\mu=4\).
Step 3
Exam Tip
\(\frac{14}{21}=\frac{2}{3}\) है। गुणांक अनुपात समान करने पर \(\frac{\mu}{6}=\frac{2}{3}\) से \(\mu=4\)।
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युग्म \(3x+2y=\lambda\) और (18x+12y=48) के अनंत हलों के लिए \(\lambda\) क्या होगा?
For infinitely many solutions of \(3x+2y=\lambda\) and (18x+12y=48), what is \(\lambda\)?
#class10
#linear-equations
#solvability
A \(\lambda=6\)
B \(\lambda=8\)
C \(\lambda=10\)
D \(\lambda=12\)
Explanation opens after your attempt
Correct Answer
B. \(\lambda=8\)
Step 1
Concept
The coefficient ratio is \(\frac{1}{6}\). For infinitely many solutions, \(\frac{\lambda}{48}=\frac{1}{6}\), so \(\lambda=8\).
Step 2
Why this answer is correct
The correct answer is B. \(\lambda=8\). The coefficient ratio is \(\frac{1}{6}\). For infinitely many solutions, \(\frac{\lambda}{48}=\frac{1}{6}\), so \(\lambda=8\).
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{6}\) है। अनंत हलों के लिए \(\frac{\lambda}{48}=\frac{1}{6}\) इसलिए \(\lambda=8\)।
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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 (5x+(v-2)y=3) और (15x+9y=14) में कोई हल न होने के लिए (v) का मान क्या है?
What is the value of (v) for no solution in (5x+(v-2)y=3) and (15x+9y=14)?
#class10
#linear-equations
#solvability
A (v=3)
B (v=4)
C (v=5)
D (v=6)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios gives (v-2=3). Thus (v=5), and the different constant ratio gives no solution.
Step 2
Why this answer is correct
The correct answer is C. (v=5). Equating coefficient ratios gives (v-2=3). Thus (v=5), and the different constant ratio gives no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर (v-2=3) मिलता है। इसलिए (v=5) और स्थिर अनुपात अलग होने से कोई हल नहीं।
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युग्म ((u+3)x+8y=16) और (10x+20y=40) के अनंत हलों के लिए (u) क्या होगा?
For infinitely many solutions of ((u+3)x+8y=16) and (10x+20y=40), what is (u)?
#class10
#linear-equations
#solvability
A (u=1)
B (u=2)
C (u=3)
D (u=4)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{u+3}{10}=\frac{8}{20}=\frac{16}{40}\) is needed. This gives (u=1).
Step 2
Why this answer is correct
The correct answer is A. (u=1). For infinitely many solutions, \(\frac{u+3}{10}=\frac{8}{20}=\frac{16}{40}\) is needed. This gives (u=1).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{u+3}{10}=\frac{8}{20}=\frac{16}{40}\) चाहिए। इससे (u=1) मिलता है।
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युग्म (12x-7y=5) और (18x-11y=8) की हल-संख्या क्या है?
What is the number of solutions of (12x-7y=5) and (18x-11y=8)?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D शून्य या अनंत / Zero or infinite
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique solution
Step 1
Concept
Since \(\frac{12}{18}\neq\frac{-7}{-11}\), the lines intersect. Hence a unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. अद्वितीय हल / Unique solution. Since \(\frac{12}{18}\neq\frac{-7}{-11}\), the lines intersect. Hence a unique solution is obtained.
Step 3
Exam Tip
\(\frac{12}{18}\neq\frac{-7}{-11}\) होने से रेखाएँ काटती हैं। इसलिए अद्वितीय हल मिलेगा।
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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 (4x+9y=2) और (8x+18y=7) की हल-स्थिति क्या है?
What is the solution status of (4x+9y=2) and (8x+18y=7)?
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D सभी बिंदु हल / All points are solutions
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं / No solution
Step 1
Concept
The coefficient ratio is equal but \(\frac{2}{7}\) is different. Hence both are distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. The coefficient ratio is equal but \(\frac{2}{7}\) is different. Hence both are distinct parallel lines.
Step 3
Exam Tip
गुणांक अनुपात समान है लेकिन \(\frac{2}{7}\) अलग है। इसलिए दोनों अलग समांतर रेखाएँ हैं।
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युग्म (10x+3y=17) और (20x+9y=31) में कितने हल होंगे?
How many solutions will the pair (10x+3y=17) and (20x+9y=31) have?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D निर्धारित नहीं / Cannot be decided
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique solution
Step 1
Concept
Here \(\frac{10}{20}\neq\frac{3}{9}\). Therefore, the lines meet at one point.
Step 2
Why this answer is correct
The correct answer is C. अद्वितीय हल / Unique solution. Here \(\frac{10}{20}\neq\frac{3}{9}\). Therefore, the lines meet at one point.
Step 3
Exam Tip
यहाँ \(\frac{10}{20}\neq\frac{3}{9}\) है। इसलिए रेखाएँ एक बिंदु पर मिलती हैं।
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रेखाएँ (9x-5y=13) और (18x-10y=26) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for the lines (9x-5y=13) and (18x-10y=26)?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अद्वितीय हल / 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 both lines are coincident and give 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 both lines are coincident and give infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएँ संपाती हैं और अनंत हल देती हैं।
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रेखाएँ (7x+2y=9) और (21x+6y=25) किस प्रकार का युग्म बनाती हैं?
What type of pair is formed by the lines (7x+2y=9) and (21x+6y=25)?
#class10
#linear-equations
#solvability
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D सदैव अद्वितीय / Always unique
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
Coefficient ratios are equal but the constant ratio is different. Hence the lines are parallel and the pair is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Coefficient ratios are equal but the constant ratio is different. Hence the lines are parallel and the pair is inconsistent.
Step 3
Exam Tip
गुणांक अनुपात समान है पर स्थिर पद का अनुपात अलग है। इसलिए रेखाएँ समांतर हैं और युग्म असंगत है।
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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 (11x+3y=4) और (22x+sy=10) का अद्वितीय हल कब होगा?
When will (11x+3y=4) and (22x+sy=10) have a unique solution?
#class10
#linear-equations
#solvability
A (s=6)
B \(s\neq6\)
C (s=3)
D \(s\neq3\)
Explanation opens after your attempt
Correct Answer
B. \(s\neq6\)
Step 1
Concept
For a unique solution, \(\frac{11}{22}\neq\frac{3}{s}\) must hold. Hence \(s\neq6\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(s\neq6\). For a unique solution, \(\frac{11}{22}\neq\frac{3}{s}\) must hold. Hence \(s\neq6\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{11}{22}\neq\frac{3}{s}\) होना चाहिए। अतः \(s\neq6\) सही 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 (5x+(r+1)y=11) और (15x+18y=33) के अनंत हलों के लिए (r) क्या होगा?
For infinitely many solutions of (5x+(r+1)y=11) and (15x+18y=33), what is (r)?
#class10
#linear-equations
#solvability
A (r=4)
B (r=5)
C (r=6)
D (r=7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{5}{15}=\frac{r+1}{18}=\frac{11}{33}\) is needed. This gives (r=5).
Step 2
Why this answer is correct
The correct answer is B. (r=5). For infinitely many solutions, \(\frac{5}{15}=\frac{r+1}{18}=\frac{11}{33}\) is needed. This gives (r=5).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{5}{15}=\frac{r+1}{18}=\frac{11}{33}\) चाहिए। इससे (r=5) मिलता है।
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युग्म (qx+4y=9) और (15x+10y=18) का अद्वितीय हल कब होगा?
When will (qx+4y=9) and (15x+10y=18) have a unique solution?
#class10
#linear-equations
#solvability
A \(q\neq6\)
B (q=6)
C \(q\neq15\)
D (q=15)
Explanation opens after your attempt
Correct Answer
A. \(q\neq6\)
Step 1
Concept
For a unique solution, \(\frac{q}{15}\neq\frac{4}{10}\) must hold. Hence \(q\neq6\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(q\neq6\). For a unique solution, \(\frac{q}{15}\neq\frac{4}{10}\) must hold. Hence \(q\neq6\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{q}{15}\neq\frac{4}{10}\) होना चाहिए। इसलिए \(q\neq6\) सही शर्त है।
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युग्म (3x-2y=5) और (12x-8y=c) में कोई हल न हो इसके लिए (c) पर कौन-सी शर्त होगी?
For (3x-2y=5) and (12x-8y=c) to have no solution, what condition is required on (c)?
#class10
#linear-equations
#solvability
A (c=20)
B \(c\neq20\)
C (c=15)
D \(c\neq15\)
Explanation opens after your attempt
Correct Answer
B. \(c\neq20\)
Step 1
Concept
The coefficient ratio is \(\frac{1}{4}\). For no solution, \(\frac{5}{c}\neq\frac{1}{4}\), so \(c\neq20\).
Step 2
Why this answer is correct
The correct answer is B. \(c\neq20\). The coefficient ratio is \(\frac{1}{4}\). For no solution, \(\frac{5}{c}\neq\frac{1}{4}\), so \(c\neq20\).
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{4}\) है। कोई हल नहीं के लिए \(\frac{5}{c}\neq\frac{1}{4}\) इसलिए \(c\neq20\)।
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युग्म (8x+ay=12) और (20x+10y=30) के अनंत हलों के लिए (a) का मान बताइए।
Find the value of (a) for infinitely many solutions of (8x+ay=12) and (20x+10y=30).
#class10
#linear-equations
#solvability
A (a=3)
B (a=4)
C (a=5)
D (a=6)
Explanation opens after your attempt
Step 1
Concept
Here \(\frac{8}{20}=\frac{12}{30}\). Thus \(\frac{a}{10}=\frac{2}{5}\) gives (a=4).
Step 2
Why this answer is correct
The correct answer is B. (a=4). Here \(\frac{8}{20}=\frac{12}{30}\). Thus \(\frac{a}{10}=\frac{2}{5}\) gives (a=4).
Step 3
Exam Tip
यहाँ \(\frac{8}{20}=\frac{12}{30}\) है। अतः \(\frac{a}{10}=\frac{2}{5}\) से (a=4) होगा।
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युग्म ((p-2)x+7y=14) और (9x+21y=42) के अनंत हलों के लिए (p) क्या होगा?
For infinitely many solutions of ((p-2)x+7y=14) and (9x+21y=42), what is (p)?
#class10
#linear-equations
#solvability
A (p=3)
B (p=4)
C (p=5)
D (p=7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, all three ratios must be equal. From \(\frac{p-2}{9}=\frac{7}{21}\), (p=5).
Step 2
Why this answer is correct
The correct answer is C. (p=5). For infinitely many solutions, all three ratios must be equal. From \(\frac{p-2}{9}=\frac{7}{21}\), (p=5).
Step 3
Exam Tip
अनंत हलों के लिए तीनों अनुपात समान होने चाहिए। \(\frac{p-2}{9}=\frac{7}{21}\) से (p=5) मिलता है।
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युग्म (4x+my=8) और (10x+15y=21) में कोई हल न होने के लिए (m) का मान क्या है?
What is the value of (m) for no solution in (4x+my=8) and (10x+15y=21)?
#class10
#linear-equations
#solvability
A (m=4)
B (m=5)
C (m=6)
D (m=8)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios gives (m=6). The constant ratio is different, so there is no solution.
Step 2
Why this answer is correct
The correct answer is C. (m=6). Equating coefficient ratios gives (m=6). The constant ratio is different, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर (m=6) मिलता है। स्थिर पद का अनुपात अलग है इसलिए कोई हल नहीं होगा।
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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 (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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युग्म ((s+2)x+3y=1) और (5x+(s-1 )y=4) के अद्वितीय हल की सही शर्त कौन-सी है?
Which condition gives a unique solution for ((s+2)x+3y=1) and (5x+(s-1 )y=4)?
#class10
#linear-equations
#solvability
A \(s^2+s-17=0\)
B \(s^2+s-17\neq0\)
C \(s^2-s-17=0\)
D \(s^2-s-17\neq0\)
Explanation opens after your attempt
Correct Answer
B. \(s^2+s-17\neq0\)
Step 1
Concept
The determinant is (D=(s+2)(s-1 )-15=s-2 +s-17 ). For a unique solution, \(D\neq0\) is required.
Step 2
Why this answer is correct
The correct answer is B. \(s^2+s-17\neq0\). The determinant is (D=(s+2)(s-1 )-15=s-2 +s-17 ). For a unique solution, \(D\neq0\) is required.
Step 3
Exam Tip
सारणिक (D=(s+2)(s-1 )-15=s-2 +s-17 ) है। अद्वितीय हल के लिए \(D\neq0\) चाहिए।
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युग्म \(5x-2y=\gamma\) और (20x-8y=36) के अनंत हलों के लिए \(\gamma\) का मान क्या है?
What is \(\gamma\) for infinitely many solutions of \(5x-2y=\gamma\) and (20x-8y=36)?
#class10
#linear-equations
#solvability
A \(\gamma=6\)
B \(\gamma=8\)
C \(\gamma=9\)
D \(\gamma=12\)
Explanation opens after your attempt
Correct Answer
C. \(\gamma=9\)
Step 1
Concept
The coefficient ratio is \(\frac{1}{4}\). For infinitely many solutions, \(\frac{\gamma}{36}=\frac{1}{4}\), so \(\gamma=9\).
Step 2
Why this answer is correct
The correct answer is C. \(\gamma=9\). The coefficient ratio is \(\frac{1}{4}\). For infinitely many solutions, \(\frac{\gamma}{36}=\frac{1}{4}\), so \(\gamma=9\).
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{4}\) है। अनंत हलों के लिए \(\frac{\gamma}{36}=\frac{1}{4}\), इसलिए \(\gamma=9\)।
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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 \(\alpha x+4y=7\) और (9x+12y=21) का अद्वितीय हल कब होगा?
When will \(\alpha x+4y=7\) and (9x+12y=21) have a unique solution?
#class10
#linear-equations
#solvability
A \(\alpha=3\)
B \(\alpha\neq3\)
C \(\alpha=9\)
D \(\alpha\neq9\)
Explanation opens after your attempt
Correct Answer
B. \(\alpha\neq3\)
Step 1
Concept
For a unique solution, \(\frac{\alpha}{9}\neq\frac{4}{12}\) must hold. Thus \(\alpha\neq3\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(\alpha\neq3\). For a unique solution, \(\frac{\alpha}{9}\neq\frac{4}{12}\) must hold. Thus \(\alpha\neq3\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{\alpha}{9}\neq\frac{4}{12}\) होना चाहिए। इसलिए \(\alpha\neq3\) सही शर्त है।
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युग्म \(rx+\frac{3}{2}y=6\) और (8x+6y=24) के अनंत हलों के लिए (r) का मान क्या है?
What is (r) for infinitely many solutions of \(rx+\frac{3}{2}y=6\) and (8x+6y=24)?
#class10
#linear-equations
#solvability
A (r=1)
B (r=2)
C (r=3)
D (r=4)
Explanation opens after your attempt
Step 1
Concept
All three ratios must be \(\frac{1}{4}\). Therefore, (r=2) is the correct value.
Step 2
Why this answer is correct
The correct answer is B. (r=2). All three ratios must be \(\frac{1}{4}\). Therefore, (r=2) is the correct value.
Step 3
Exam Tip
तीनों अनुपात \(\frac{1}{4}\) होने चाहिए। इसलिए (r=2) सही मान है।
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युग्म \(\frac{1}{2}x+qy=3\) और (2x+8y=5) के लिए कोई हल न होने पर (q) क्या होगा?
For no solution in \(\frac{1}{2}x+qy=3\) and (2x+8y=5), what is (q)?
#class10
#linear-equations
#solvability
A (q=1)
B (q=2)
C (q=4)
D (q=8)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios gives (q=2). The constant ratio is not equal, so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (q=2). Equating coefficient ratios gives (q=2). The constant ratio is not equal, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर (q=2) मिलता है। स्थिर पद अनुपात समान नहीं है, इसलिए कोई हल नहीं।
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युग्म ((p+4)x-9y=2) और (5x-15y=6) का अद्वितीय हल कब होगा?
When will ((p+4)x-9y=2) and (5x-15y=6) have a unique solution?
#class10
#linear-equations
#solvability
A (p=-1)
B (p=1)
C \(p\neq-1\)
D \(p\neq1\)
Explanation opens after your attempt
Correct Answer
C. \(p\neq-1\)
Step 1
Concept
For a unique solution, \(\frac{p+4}{5}\neq\frac{-9}{-15}\) must hold. Hence \(p\neq-1\).
Step 2
Why this answer is correct
The correct answer is C. \(p\neq-1\). For a unique solution, \(\frac{p+4}{5}\neq\frac{-9}{-15}\) must hold. Hence \(p\neq-1\).
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{p+4}{5}\neq\frac{-9}{-15}\) होना चाहिए। इसलिए \(p\neq-1\)।
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युग्म (4x+(m-5 )y=9) और (12x+6y=27) के अनंत हलों के लिए (m) कितना है?
What is (m) for infinitely many solutions of (4x+(m-5 )y=9) and (12x+6y=27)?
#class10
#linear-equations
#solvability
A (m=5)
B (m=6)
C (m=7)
D (m=9)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{4}{12}=\frac{m-5}{6}=\frac{9}{27}\) is required. This gives (m=7).
Step 2
Why this answer is correct
The correct answer is C. (m=7). For infinitely many solutions, \(\frac{4}{12}=\frac{m-5}{6}=\frac{9}{27}\) is required. This gives (m=7).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{4}{12}=\frac{m-5}{6}=\frac{9}{27}\) चाहिए। इससे (m=7) मिलता है।
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युग्म ((k+1)x+6y=3) और (2x+12y=8) के लिए कोई हल न होने पर (k) का मान क्या होगा?
For no solution in ((k+1)x+6y=3) and (2x+12y=8), what is (k)?
#class10
#linear-equations
#solvability
A (k=-1)
B (k=0)
C (k=1)
D (k=2)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios gives (k=0). The constant ratio \(\frac{3}{8}\) is different, so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (k=0). Equating coefficient ratios gives (k=0). The constant ratio \(\frac{3}{8}\) is different, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर (k=0) मिलता है। स्थिर अनुपात \(\frac{3}{8}\) अलग है, इसलिए कोई हल नहीं।
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युग्म ((k-3)x+2y=5) और (4x+ky=11) अद्वितीय न हो, इसके लिए (k) क्या हो सकता है?
For ((k-3)x+2y=5) and (4x+ky=11) to be non-unique, what can (k) be?
#class10
#linear-equations
#solvability
A \(k=\frac{3\pm\sqrt{41}}{2}\)
B \(k=\frac{-3\pm\sqrt{41}}{2}\)
C (k=3)
D (k=4)
Explanation opens after your attempt
Correct Answer
A. \(k=\frac{3\pm\sqrt{41}}{2}\)
Step 1
Concept
For non-unique solutions, the determinant must be zero. From ((k-3)k-8=0), \(k=\frac{3\pm\sqrt{41}}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(k=\frac{3\pm\sqrt{41}}{2}\). For non-unique solutions, the determinant must be zero. From ((k-3)k-8=0), \(k=\frac{3\pm\sqrt{41}}{2}\).
Step 3
Exam Tip
अद्वितीय न होने के लिए सारणिक शून्य होना चाहिए। ((k-3)k-8=0) से \(k=\frac{3\pm\sqrt{41}}{2}\) मिलता है।
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यदि दो रेखाओं की ढाल अलग-अलग हों, तो उनके युग्म के लिए कौन-सा निष्कर्ष सही है?
If two lines have different slopes, which conclusion is correct for their pair?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D समीकरण निर्भर हैं / Equations are dependent
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique solution
Step 1
Concept
Lines with different slopes meet at exactly one point. Hence the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. अद्वितीय हल / Unique solution. Lines with different slopes meet at exactly one point. Hence the pair is consistent and independent.
Step 3
Exam Tip
अलग ढाल वाली रेखाएँ केवल एक बिंदु पर मिलती हैं। इसलिए युग्म संगत और स्वतंत्र होता है।
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यदि दो रेखाओं की ढाल समान और (y)-अवरोध अलग हों, तो उनके समीकरणों के युग्म में कितने हल होंगे?
If two lines have the same slope and different (y)-intercepts, how many solutions will their pair of equations have?
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Same slope and different intercepts mean distinct parallel lines. Therefore, they never intersect.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Same slope and different intercepts mean distinct parallel lines. Therefore, they never intersect.
Step 3
Exam Tip
समान ढाल और अलग अवरोध का अर्थ अलग समांतर रेखाएँ है। इसलिए वे कभी नहीं कटतीं।
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यदि (D=0) और कम से कम एक सहायक सारणिक शून्य नहीं है, तो युग्म की हल-स्थिति क्या होगी?
If (D=0) and at least one auxiliary determinant is non-zero, what is the solution status of the pair?
#class10
#linear-equations
#solvability
A अनंत हल / Infinitely many solutions
B अद्वितीय हल / Unique solution
C कोई हल नहीं / No solution
D सदैव हल / Always solvable
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
(D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. (D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.
Step 3
Exam Tip
(D=0) और असंगत सहायक सारणिक समांतर अलग रेखाओं का संकेत देते हैं। इसलिए कोई हल नहीं होता।
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संपाती रेखाओं के लिए सही बीजीय शर्त कौन-सी है?
Which algebraic condition is correct for coincident lines?
#class10
#linear-equations
#solvability
A \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(a_1b_2-a_2b_1\neq0\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Step 1
Concept
Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.
Step 3
Exam Tip
संपाती रेखाएँ एक ही रेखा को दर्शाती हैं। इसलिए तीनों अनुपात समान होते हैं और अनंत हल मिलते हैं।
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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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यदि किसी युग्म में गुणांक अनुपात समान है और स्थिर पद का अनुपात अलग है, तो हल-स्थिति क्या होगी?
If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D सदैव दो हल / Always two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
This condition forms distinct parallel lines. Therefore, the pair is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. This condition forms distinct parallel lines. Therefore, the pair is inconsistent.
Step 3
Exam Tip
यह स्थिति अलग-अलग समांतर रेखाएँ बनाती है। इसलिए युग्म असंगत होता है।
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सामान्य युग्म \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) में कोई हल न होने की शर्त क्या है?
For the general pair \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), what is the condition for no solution?
#class10
#linear-equations
#solvability
A \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
D \(a_1=a_2=0\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
Step 1
Concept
No solution occurs when lines are parallel and distinct. Its ratio form is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). No solution occurs when lines are parallel and distinct. Its ratio form is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\).
Step 3
Exam Tip
कोई हल नहीं तब होता है जब रेखाएँ समांतर और अलग हों। इसका अनुपात रूप \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\) है।
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युग्म (4x+5y=1) और (8x+9y=2) के लिए हलों की संख्या क्या है?
How many solutions does (4x+5y=1) and (8x+9y=2) have?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D निर्भर हल / Dependent solutions
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique solution
Step 1
Concept
Here \(\frac{4}{8}\neq\frac{5}{9}\). Therefore, the lines intersect at one point.
Step 2
Why this answer is correct
The correct answer is C. अद्वितीय हल / Unique solution. Here \(\frac{4}{8}\neq\frac{5}{9}\). Therefore, the lines intersect at one point.
Step 3
Exam Tip
यहाँ \(\frac{4}{8}\neq\frac{5}{9}\) है। इसलिए रेखाएँ एक बिंदु पर कटती हैं।
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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 (x+2y=3) और (4x+8y=12) के लिए सही हल-स्थिति कौन-सी है?
Which solution status is correct for (x+2y=3) and (4x+8y=12)?
#class10
#linear-equations
#solvability
A अनंत हल / Infinitely many solutions
B कोई हल नहीं / No solution
C अद्वितीय हल / Unique solution
D एक भी बिंदु नहीं / No point at all
Explanation opens after your attempt
Correct Answer
A. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (4) times the first. Both are the same line, so there are infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is A. अनंत हल / Infinitely many solutions. The second equation is (4) times the first. Both are the same line, so there are infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (4) गुना है। दोनों समान रेखाएँ हैं, इसलिए अनंत हल हैं।
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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 (lx+6y=8) और (9x+18y=10) में कोई हल न होने के लिए (l) क्या होगा?
What is (l) for no solution in (lx+6y=8) and (9x+18y=10)?
#class10
#linear-equations
#solvability
A (l=2)
B (l=3)
C (l=6)
D (l=9)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{l}{9}=\frac{6}{18}\) gives (l=3). The constant ratio is different.
Step 2
Why this answer is correct
The correct answer is B. (l=3). Equating coefficient ratios, \(\frac{l}{9}=\frac{6}{18}\) gives (l=3). The constant ratio is different.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{l}{9}=\frac{6}{18}\) से (l=3) मिलता है। स्थिर पद अनुपात अलग है।
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युग्म (ax+by=1) और (2ax+3by=5) के अद्वितीय हल की शर्त क्या है?
What is the condition for a unique solution of (ax+by=1) and (2ax+3by=5)?
#class10
#linear-equations
#solvability
A (ab=0)
B (a+b=0)
C \(ab\neq0\)
D (a=b)
Explanation opens after your attempt
Correct Answer
C. \(ab\neq0\)
Step 1
Concept
The determinant is (D=3ab-2ab=ab). For a unique solution, \(ab\neq0\) is needed.
Step 2
Why this answer is correct
The correct answer is C. \(ab\neq0\). The determinant is (D=3ab-2ab=ab). For a unique solution, \(ab\neq0\) is needed.
Step 3
Exam Tip
सारणिक (D=3ab-2ab=ab) है। अद्वितीय हल के लिए \(ab\neq0\) चाहिए।
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युग्म (2x+3y=d) और (14x+21y=28) में कोई हल न हो, इसके लिए (d) पर कौन-सी शर्त होगी?
For (2x+3y=d) and (14x+21y=28) to have no solution, what condition is required on (d)?
#class10
#linear-equations
#solvability
A (d=4)
B \(d\neq4\)
C (d=7)
D \(d\neq7\)
Explanation opens after your attempt
Correct Answer
B. \(d\neq4\)
Step 1
Concept
The coefficient ratio is \(\frac{1}{7}\). For no solution, \(\frac{d}{28}\neq\frac{1}{7}\), so \(d\neq4\).
Step 2
Why this answer is correct
The correct answer is B. \(d\neq4\). The coefficient ratio is \(\frac{1}{7}\). For no solution, \(\frac{d}{28}\neq\frac{1}{7}\), so \(d\neq4\).
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{7}\) है। कोई हल नहीं के लिए \(\frac{d}{28}\neq\frac{1}{7}\), इसलिए \(d\neq4\)।
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युग्म ((v+2)x-3y=6) और (10x-5y=10) के अनंत हलों के लिए (v) क्या होगा?
For infinitely many solutions of ((v+2)x-3y=6) and (10x-5y=10), what is (v)?
#class10
#linear-equations
#solvability
A (v=2)
B (v=3)
C (v=4)
D (v=5)
Explanation opens after your attempt
Step 1
Concept
Here \(\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}\) must hold. This gives (v=4).
Step 2
Why this answer is correct
The correct answer is C. (v=4). Here \(\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}\) must hold. This gives (v=4).
Step 3
Exam Tip
यहाँ \(\frac{v+2}{10}=\frac{-3}{-5}=\frac{6}{10}\) होना चाहिए। इससे (v=4) मिलता है।
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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 (ux+9y=7) और (4x+6y=11) में कोई हल न होने के लिए (u) का मान क्या है?
For no solution in (ux+9y=7) and (4x+6y=11), what is the value of (u)?
#class10
#linear-equations
#solvability
A (u=4)
B (u=5)
C (u=6)
D (u=9)
Explanation opens after your attempt
Step 1
Concept
Equating coefficient ratios, \(\frac{u}{4}=\frac{9}{6}\) gives (u=6). The constant ratio is different, so there is no solution.
Step 2
Why this answer is correct
The correct answer is C. (u=6). Equating coefficient ratios, \(\frac{u}{4}=\frac{9}{6}\) gives (u=6). The constant ratio is different, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर \(\frac{u}{4}=\frac{9}{6}\) से (u=6) मिलता है। स्थिर पद अनुपात अलग है, इसलिए कोई हल नहीं है।
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युग्म (12x+sy=18) और (20x+10y=30) के अनंत हलों के लिए (s) क्या होगा?
What is (s) for infinitely many solutions of (12x+sy=18) and (20x+10y=30)?
#class10
#linear-equations
#solvability
A (s=4)
B (s=5)
C (s=6)
D (s=8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{12}{20}=\frac{s}{10}=\frac{18}{30}\) is needed. This gives (s=6).
Step 2
Why this answer is correct
The correct answer is C. (s=6). For infinitely many solutions, \(\frac{12}{20}=\frac{s}{10}=\frac{18}{30}\) is needed. This gives (s=6).
Step 3
Exam Tip
अनंत हलों के लिए \(\frac{12}{20}=\frac{s}{10}=\frac{18}{30}\) चाहिए। इससे (s=6) आता है।
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युग्म (rx+5y=2) और (8x+10y=4) का अद्वितीय हल कब होगा?
When will (rx+5y=2) and (8x+10y=4) have a unique solution?
#class10
#linear-equations
#solvability
A (r=4)
B \(r\neq4\)
C (r=8)
D \(r\neq8\)
Explanation opens after your attempt
Correct Answer
B. \(r\neq4\)
Step 1
Concept
For a unique solution, \(\frac{r}{8}\neq\frac{5}{10}\) must hold. So \(r\neq4\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(r\neq4\). For a unique solution, \(\frac{r}{8}\neq\frac{5}{10}\) must hold. So \(r\neq4\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{r}{8}\neq\frac{5}{10}\) होना चाहिए। इसलिए \(r\neq4\) सही है।
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युग्म (5x-2y=c) और (15x-6y=21) में कोई हल न हो, इसके लिए (c) की शर्त क्या है?
For no solution in (5x-2y=c) and (15x-6y=21), what condition should (c) satisfy?
#class10
#linear-equations
#solvability
A (c=7)
B (c=21)
C \(c\neq7\)
D \(c\neq21\)
Explanation opens after your attempt
Correct Answer
C. \(c\neq7\)
Step 1
Concept
The coefficient ratio is \(\frac{1}{3}\). For no solution, \(\frac{c}{21}\neq\frac{1}{3}\), hence \(c\neq7\).
Step 2
Why this answer is correct
The correct answer is C. \(c\neq7\). The coefficient ratio is \(\frac{1}{3}\). For no solution, \(\frac{c}{21}\neq\frac{1}{3}\), hence \(c\neq7\).
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{3}\) है। कोई हल नहीं के लिए \(\frac{c}{21}\neq\frac{1}{3}\), अतः \(c\neq7\)।
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