For parallel lines, \(\frac{9}{27}=\frac{2}{m}\), so (m=6). Since \(\frac{18}{55}\neq\frac{1}{3}\), the lines are not coincident.
Step 2
Why this answer is correct
The correct answer is C. (6). For parallel lines, \(\frac{9}{27}=\frac{2}{m}\), so (m=6). Since \(\frac{18}{55}\neq\frac{1}{3}\), the lines are not coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{9}{27}=\frac{2}{m}\), इसलिए (m=6)। क्योंकि \(\frac{18}{55}\neq\frac{1}{3}\), रेखाएं संपाती नहीं हैं।
The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=90). For (k=88), the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=88). The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=90). For (k=88), the lines are distinct and parallel.
Step 3
Exam Tip
गुणांक का अनुपात \(\frac{1}{2}\) है, इसलिए संपाती होने के लिए (k=90) चाहिए। (k=88) पर रेखाएं समांतर अलग-अलग हैं।
\(\frac{3}{6}=\frac{-8}{-16}\neq\frac{11}{25}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई समाधान नहीं / No solution. \(\frac{3}{6}=\frac{-8}{-16}\neq\frac{11}{25}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 3
Exam Tip
\(\frac{3}{6}=\frac{-8}{-16}\neq\frac{11}{25}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे युग्म का कोई समाधान नहीं होता।
\(\frac{9}{3}=\frac{12}{4}\neq\frac{45}{20}\), so the lines are distinct and parallel. Check the constant term ratio also.
Step 2
Why this answer is correct
The correct answer is C. समांतर अलग-अलग / Distinct parallel. \(\frac{9}{3}=\frac{12}{4}\neq\frac{45}{20}\), so the lines are distinct and parallel. Check the constant term ratio also.
Step 3
Exam Tip
\(\frac{9}{3}=\frac{12}{4}\neq\frac{45}{20}\), इसलिए रेखाएं समांतर अलग-अलग हैं। अनुपातों में स्थिर पद को भी देखें।
The coefficient ratio is \(\frac{1}{2}\); coincidence needs (k=54). For (k=50), the lines will be distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=50). The coefficient ratio is \(\frac{1}{2}\); coincidence needs (k=54). For (k=50), the lines will be distinct and parallel.
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{2}\) है; संपाती होने के लिए (k=54) चाहिए। (k=50) पर रेखाएं समांतर अलग-अलग होंगी।
Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 3
Exam Tip
समान ढाल और अलग (y)-अवरोध वाली रेखाएं समांतर होती हैं। इसलिए उनका कोई प्रतिच्छेद नहीं होता।
For parallel lines, \(\frac{3}{9}=\frac{a}{12}\), so (a=4). Since \(\frac{15}{47}\neq\frac{1}{3}\), they will not be coincident.
Step 2
Why this answer is correct
The correct answer is C. (a=4). For parallel lines, \(\frac{3}{9}=\frac{a}{12}\), so (a=4). Since \(\frac{15}{47}\neq\frac{1}{3}\), they will not be coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{3}{9}=\frac{a}{12}\), इसलिए (a=4)। चूंकि \(\frac{15}{47}\neq\frac{1}{3}\), वे संपाती नहीं होंगी।
\(\frac{4}{8}=\frac{9}{18}\neq\frac{36}{75}\), so the lines are distinct and parallel. Distinct parallel lines have no common point.
Step 2
Why this answer is correct
The correct answer is A. समांतर अलग-अलग / Distinct parallel. \(\frac{4}{8}=\frac{9}{18}\neq\frac{36}{75}\), so the lines are distinct and parallel. Distinct parallel lines have no common point.
Step 3
Exam Tip
\(\frac{4}{8}=\frac{9}{18}\neq\frac{36}{75}\), इसलिए रेखाएं समांतर अलग-अलग हैं। समांतर अलग-अलग रेखाओं का कोई साझी बिंदु नहीं होता।
For parallel lines, \(\frac{7}{14}=\frac{b}{10}\), so (b=5). Since \(\frac{21}{50}\neq\frac{1}{2}\), the lines are not coincident.
Step 2
Why this answer is correct
The correct answer is B. (5). For parallel lines, \(\frac{7}{14}=\frac{b}{10}\), so (b=5). Since \(\frac{21}{50}\neq\frac{1}{2}\), the lines are not coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{7}{14}=\frac{b}{10}\), इसलिए (b=5)। क्योंकि \(\frac{21}{50}\neq\frac{1}{2}\), रेखाएं संपाती नहीं हैं।
The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=42). For (k=40), the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=40). The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=42). For (k=40), the lines are distinct and parallel.
Step 3
Exam Tip
गुणांक का अनुपात \(\frac{1}{2}\) है, इसलिए संपाती होने के लिए (k=42) चाहिए। (k=40) पर रेखाएं समांतर अलग-अलग हैं।
\(\frac{2}{4}=\frac{-5}{-10}\neq\frac{7}{16}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई समाधान नहीं / No solution. \(\frac{2}{4}=\frac{-5}{-10}\neq\frac{7}{16}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 3
Exam Tip
\(\frac{2}{4}=\frac{-5}{-10}\neq\frac{7}{16}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे युग्म का कोई समाधान नहीं होता।
\(\frac{5}{1}=\frac{10}{2}\neq\frac{25}{6}\), so the lines are distinct and parallel. Check the constant term ratio also.
Step 2
Why this answer is correct
The correct answer is C. समांतर अलग-अलग / Distinct parallel. \(\frac{5}{1}=\frac{10}{2}\neq\frac{25}{6}\), so the lines are distinct and parallel. Check the constant term ratio also.
Step 3
Exam Tip
\(\frac{5}{1}=\frac{10}{2}\neq\frac{25}{6}\), इसलिए रेखाएं समांतर अलग-अलग हैं। अनुपातों में स्थिर पद को भी देखें।
The coefficient ratio is \(\frac{1}{2}\); coincidence needs (k=34). For (k=30), the lines will be distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=30). The coefficient ratio is \(\frac{1}{2}\); coincidence needs (k=34). For (k=30), the lines will be distinct and parallel.
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{2}\) है; संपाती होने के लिए (k=34) चाहिए। (k=30) पर रेखाएं समांतर अलग-अलग होंगी।
Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 3
Exam Tip
समान ढाल और अलग (y)-अवरोध वाली रेखाएं समांतर होती हैं। इसलिए उनका कोई प्रतिच्छेद नहीं होता।
For parallel lines, \(\frac{4}{8}=\frac{a}{10}\), so (a=5). Since \(\frac{16}{35}\neq\frac{1}{2}\), they will not be coincident.
Step 2
Why this answer is correct
The correct answer is B. (a=5). For parallel lines, \(\frac{4}{8}=\frac{a}{10}\), so (a=5). Since \(\frac{16}{35}\neq\frac{1}{2}\), they will not be coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{4}{8}=\frac{a}{10}\), इसलिए (a=5)। चूंकि \(\frac{16}{35}\neq\frac{1}{2}\), वे संपाती नहीं होंगी।
\(\frac{2}{4}=\frac{7}{14}\neq\frac{14}{31}\), so the lines are distinct and parallel. Such a graph has no common point.
Step 2
Why this answer is correct
The correct answer is A. समांतर अलग-अलग / Distinct parallel. \(\frac{2}{4}=\frac{7}{14}\neq\frac{14}{31}\), so the lines are distinct and parallel. Such a graph has no common point.
Step 3
Exam Tip
\(\frac{2}{4}=\frac{7}{14}\neq\frac{14}{31}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे ग्राफ में कोई साझी बिंदु नहीं होता।
The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=24). For (k=20), the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=20). The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=24). For (k=20), the lines are distinct and parallel.
Step 3
Exam Tip
गुणांक का अनुपात \(\frac{1}{2}\) है, इसलिए संपाती होने के लिए (k=24) चाहिए। (k=20) पर रेखाएं समांतर अलग-अलग हैं।
\(\frac{1}{2}=\frac{-3}{-6}\neq\frac{2}{9}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई समाधान नहीं / No solution. \(\frac{1}{2}=\frac{-3}{-6}\neq\frac{2}{9}\), so the lines are distinct and parallel. Such a pair has no solution.
Step 3
Exam Tip
\(\frac{1}{2}=\frac{-3}{-6}\neq\frac{2}{9}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसे युग्म का कोई समाधान नहीं होता।
\(\frac{4}{2}=\frac{6}{3}\neq\frac{18}{10}\), so the lines are distinct and parallel. Do not ignore the constant ratio.
Step 2
Why this answer is correct
The correct answer is C. समांतर अलग-अलग / Distinct parallel. \(\frac{4}{2}=\frac{6}{3}\neq\frac{18}{10}\), so the lines are distinct and parallel. Do not ignore the constant ratio.
Step 3
Exam Tip
\(\frac{4}{2}=\frac{6}{3}\neq\frac{18}{10}\), इसलिए रेखाएं समांतर अलग-अलग हैं। अनुपातों में स्थिर पद को नजरअंदाज न करें।
The coefficient ratio is \(\frac{1}{2}\); coincidence needs (k=26). For (k=13), the lines are distinct and parallel, so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (k=13). The coefficient ratio is \(\frac{1}{2}\); coincidence needs (k=26). For (k=13), the lines are distinct and parallel, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात \(\frac{1}{2}\) है; संपाती के लिए (k=26) चाहिए। (k=13) पर रेखाएं समांतर अलग-अलग हैं, इसलिए कोई समाधान नहीं।
Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 3
Exam Tip
समान ढाल और अलग (y)-अवरोध वाली रेखाएं समांतर होती हैं। इसलिए उनका कोई प्रतिच्छेद नहीं होता।
The coefficient ratios of (x) and (y) are equal, but the constant ratio is different. Hence the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is C. समांतर अलग-अलग / Distinct parallel. The coefficient ratios of (x) and (y) are equal, but the constant ratio is different. Hence the lines are distinct and parallel.
Step 3
Exam Tip
(x) और (y) के गुणांक अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है। इसलिए रेखाएं समांतर अलग-अलग होती हैं।
C. रेखाएं समांतर अलग-अलग हों/The lines are distinct and parallel
Step 1
Concept
Distinct parallel lines have no common point. If there is no common point on the graph, there is no solution.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं समांतर अलग-अलग हों / The lines are distinct and parallel. Distinct parallel lines have no common point. If there is no common point on the graph, there is no solution.
Step 3
Exam Tip
समांतर अलग-अलग रेखाओं में कोई साझी बिंदु नहीं होता। ग्राफ में साझी बिंदु न होने पर कोई समाधान नहीं होता।
For parallel lines, \(\frac{2}{6}=\frac{a}{9}\), so (a=3). Since \(\frac{10}{31}\neq\frac{1}{3}\), the lines are not coincident.
Step 2
Why this answer is correct
The correct answer is B. (a=3). For parallel lines, \(\frac{2}{6}=\frac{a}{9}\), so (a=3). Since \(\frac{10}{31}\neq\frac{1}{3}\), the lines are not coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{2}{6}=\frac{a}{9}\), इसलिए (a=3)। चूंकि \(\frac{10}{31}\neq\frac{1}{3}\), रेखाएं संपाती नहीं होंगी।
\(\frac{3}{6}=\frac{5}{10}\neq\frac{15}{32}\), so the lines are distinct and parallel. In exams, compare all three ratios first.
Step 2
Why this answer is correct
The correct answer is B. समांतर अलग-अलग रेखाएं / Distinct parallel lines. \(\frac{3}{6}=\frac{5}{10}\neq\frac{15}{32}\), so the lines are distinct and parallel. In exams, compare all three ratios first.
Step 3
Exam Tip
\(\frac{3}{6}=\frac{5}{10}\neq\frac{15}{32}\), इसलिए रेखाएं समांतर अलग-अलग हैं। परीक्षा में तीनों अनुपातों की तुलना पहले करें।
\(\frac{2}{6}=\frac{1}{3}\neq\frac{7}{20}\), so the lines are distinct and parallel. This case gives no solution.
Step 2
Why this answer is correct
The correct answer is B. समांतर अलग-अलग / Parallel distinct. \(\frac{2}{6}=\frac{1}{3}\neq\frac{7}{20}\), so the lines are distinct and parallel. This case gives no solution.
Step 3
Exam Tip
\(\frac{2}{6}=\frac{1}{3}\neq\frac{7}{20}\), इसलिए रेखाएं समांतर अलग-अलग हैं। यह स्थिति कोई समाधान नहीं देती।
\(\frac{1}{2}=\frac{4}{8}\neq\frac{9}{21}\), so the lines are distinct parallel lines. Such lines have no solution.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. \(\frac{1}{2}=\frac{4}{8}\neq\frac{9}{21}\), so the lines are distinct parallel lines. Such lines have no solution.
Step 3
Exam Tip
\(\frac{1}{2}=\frac{4}{8}\neq\frac{9}{21}\), इसलिए रेखाएं समांतर अलग-अलग हैं। ऐसी रेखाओं का कोई समाधान नहीं होता।
\(\frac{1}{2}=\frac{3}{6}\neq\frac{6}{15}\), so the lines are parallel. Parallel lines never meet.
Step 2
Why this answer is correct
The correct answer is B. वे समांतर हैं / They are parallel. \(\frac{1}{2}=\frac{3}{6}\neq\frac{6}{15}\), so the lines are parallel. Parallel lines never meet.
Step 3
Exam Tip
\(\frac{1}{2}=\frac{3}{6}\neq\frac{6}{15}\), इसलिए रेखाएं समांतर हैं। समांतर रेखाएं कभी नहीं मिलतीं।
Here \(\frac{2}{4}=\frac{3}{6}\neq\frac{12}{18}\), so the lines are parallel. In exams, check ratios first.
Step 2
Why this answer is correct
The correct answer is A. कोई समाधान नहीं / No solution. Here \(\frac{2}{4}=\frac{3}{6}\neq\frac{12}{18}\), so the lines are parallel. In exams, check ratios first.
Step 3
Exam Tip
यहां \(\frac{2}{4}=\frac{3}{6}\neq\frac{12}{18}\), इसलिए रेखाएं समांतर हैं। परीक्षा में पहले अनुपात जांचें।
