For no solution, coefficients must be proportional while constants are not. At (k=4), the left sides are proportional but (12) and (9) are not in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (4). For no solution, coefficients must be proportional while constants are not. At (k=4), the left sides are proportional but (12) and (9) are not in the same ratio.
Step 3
Exam Tip
कोई हल न होने के लिए गुणांक समानुपाती और स्थिरांक असमानुपाती होने चाहिए। (k=4) पर बायां पक्ष समानुपाती है, पर (12) और (9) अनुपात में नहीं हैं।
The second equation must be (3) times the first, so (k=126). In coincident lines, the constant term also changes in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (126). The second equation must be (3) times the first, so (k=126). In coincident lines, the constant term also changes in the same ratio.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना होना चाहिए, इसलिए (k=126)। संपाती रेखाओं में स्थिर पद भी उसी अनुपात में बदलता है।
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।
The second equation is (3) times the first, so (m=21). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (21). The second equation is (3) times the first, so (m=21). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है, इसलिए (m=21)। संपाती रेखा में (y) का गुणांक भी उसी अनुपात में बदलता है।
The first equation must be (4) times the second, so (a=20). In coincident lines, all terms change by the same multiplier.
Step 2
Why this answer is correct
The correct answer is C. (20). The first equation must be (4) times the second, so (a=20). In coincident lines, all terms change by the same multiplier.
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए, इसलिए (a=20)। संपाती रेखाओं में सभी पद समान गुणक से बदलते हैं।
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।
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।
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।
The second equation is (2) times the first, so (m=10). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (10). The second equation is (2) times the first, so (m=10). In a coincident line, the coefficient of (y) also changes in the same ratio.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए (m=10)। संपाती रेखा में (y) का गुणांक भी उसी अनुपात में बदलता है।
The first equation must be (3) times the second, so (a=12). In coincident lines, all terms change by the same multiplier.
Step 2
Why this answer is correct
The correct answer is C. (12). The first equation must be (3) times the second, so (a=12). In coincident lines, all terms change by the same multiplier.
Step 3
Exam Tip
पहला समीकरण दूसरे का (3) गुना होना चाहिए, इसलिए (a=12)। संपाती रेखाओं में सभी पद समान गुणक से बदलते हैं।
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।
