100 results found for "brush variables" in Class 10.
मोटे ब्रश स्ट्रोक से किस तरह की बनावट दिख सकती है?
What kind of texture can thick brush strokes show?
#brush stroke
#texture
#raised
A दूरी / Distance
B रंग चक्र / Colour wheel
C उभरी हुई सतह / Raised surface
D केवल खालीपन / Only emptiness
Explanation opens after your attempt
Correct Answer
C. उभरी हुई सतह / Raised surface
Step 1
Concept
Thick brush strokes can make the surface look raised. Exam tip: understand brush stroke as texture effect.
Step 2
Why this answer is correct
The correct answer is C. उभरी हुई सतह / Raised surface. Thick brush strokes can make the surface look raised. Exam tip: understand brush stroke as texture effect.
Step 3
Exam Tip
मोटे ब्रश स्ट्रोक सतह को उभरा हुआ दिखा सकते हैं। परीक्षा में brush stroke को texture effect समझें।
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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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रेखा की गति और ब्रश की गति में संबंध क्या है?
What is the relation between line movement and brush movement?
#visual-art
#line
#hard
#class-10
A ब्रश की गति रेखा के स्वभाव और ऊर्जा को प्रभावित करती है / Brush movement affects character and energy of line
B ब्रश की गति का कोई प्रभाव नहीं / Brush movement has no effect
C रेखा हमेशा समान रहती है / Line always remains same
D माध्यम हमेशा बदल जाता है / Medium always changes
Explanation opens after your attempt
Correct Answer
A. ब्रश की गति रेखा के स्वभाव और ऊर्जा को प्रभावित करती है / Brush movement affects character and energy of line
Step 1
Concept
Fast or slow brush movement changes the mood of line. In exams understand both tool and hand movement.
Step 2
Why this answer is correct
The correct answer is A. ब्रश की गति रेखा के स्वभाव और ऊर्जा को प्रभावित करती है / Brush movement affects character and energy of line. Fast or slow brush movement changes the mood of line. In exams understand both tool and hand movement.
Step 3
Exam Tip
तेज या धीमी ब्रश गति रेखा का भाव बदलती है। परीक्षा में साधन और हाथ की गति दोनों समझें।
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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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युग्म (3x+ay=6) और (9x+12y=b) के अनंत हलों के लिए ((a,b)) क्या होगा?
For infinitely many solutions of (3x+ay=6) and (9x+12y=b), what is ((a,b))?
#class10
#linear-equations
#solvability
A (a=3,\ b=12)
B (a=4,\ b=18)
C (a=6,\ b=18)
D (a=4,\ b=12)
Explanation opens after your attempt
Correct Answer
B. (a=4,\ b=18)
Step 1
Concept
All three ratios must be \(\frac{1}{3}\). So (a=4) and (b=18).
Step 2
Why this answer is correct
The correct answer is B. (a=4,\ b=18). All three ratios must be \(\frac{1}{3}\). So (a=4) and (b=18).
Step 3
Exam Tip
तीनों अनुपात \(\frac{1}{3}\) होने चाहिए। इसलिए (a=4) और (b=18) है।
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युग्म ((p-2)x+9y=4) और (5x+15y=12) का अद्वितीय हल कब होगा?
When will ((p-2)x+9y=4) and (5x+15y=12) have a unique solution?
#class10
#linear-equations
#solvability
A (p=5)
B (p=2)
C \(p\neq5\)
D \(p\neq2\)
Explanation opens after your attempt
Correct Answer
C. \(p\neq5\)
Step 1
Concept
For a unique solution, \(\frac{p-2}{5}\neq\frac{9}{15}\) is needed. Hence \(p\neq5\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(p\neq5\). For a unique solution, \(\frac{p-2}{5}\neq\frac{9}{15}\) is needed. Hence \(p\neq5\) is correct.
Step 3
Exam Tip
अद्वितीय हल के लिए \(\frac{p-2}{5}\neq\frac{9}{15}\) चाहिए। इसलिए \(p\neq5\) सही है।
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युग्म (7x+(m-4 )y=13) और (14x+6y=26) के अनंत हलों के लिए (m) का मान बताइए।
Find (m) for infinitely many solutions of (7x+(m-4 )y=13) and (14x+6y=26).
#class10
#linear-equations
#solvability
A (m=6)
B (m=7)
C (m=8)
D (m=10)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, \(\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}\) must hold. This gives (m=7).
Step 2
Why this answer is correct
The correct answer is B. (m=7). For infinitely many solutions, \(\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}\) must hold. This gives (m=7).
Step 3
Exam Tip
अनंत हलों में \(\frac{7}{14}=\frac{m-4}{6}=\frac{13}{26}\) होना चाहिए। इससे (m=7) मिलता है।
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युग्म ((k+1)x+4y=9) और (6x+8y=15) में कोई हल न होने के लिए (k) क्या होगा?
For no solution in ((k+1)x+4y=9) and (6x+8y=15), what is (k)?
#class10
#linear-equations
#solvability
A (k=1)
B (k=2)
C (k=3)
D (k=5)
Explanation opens after your attempt
Step 1
Concept
Making coefficient ratios equal gives (k=2). The constant ratio is different, so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (k=2). Making coefficient ratios equal gives (k=2). The constant ratio is different, so there is no solution.
Step 3
Exam Tip
गुणांक अनुपात समान करने पर (k=2) आता है। स्थिर अनुपात अलग है, इसलिए कोई हल नहीं होगा।
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युग्म (5x+2y=6) और (15x+7y=18) के लिए हलों की संख्या क्या है?
How many solutions does the pair (5x+2y=6) and (15x+7y=18) have?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D ठीक (2) हल / Exactly (2) solutions
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique solution
Step 1
Concept
Here \(5\times7-15\times2\neq0\). Therefore, the pair has a unique solution.
Step 2
Why this answer is correct
The correct answer is C. अद्वितीय हल / Unique solution. Here \(5\times7-15\times2\neq0\). Therefore, the pair has a unique solution.
Step 3
Exam Tip
यहाँ \(5\times7-15\times2\neq0\) है। इसलिए युग्म का अद्वितीय हल है।
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युग्म (9x-4y=11) और (18x-8y=21) की प्रकृति क्या है?
What is the nature of the pair (9x-4y=11) and (18x-8y=21)?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D हर मान हल है / Every value is a solution
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
The coefficient ratio is equal but the constant ratio is not equal. In exams, treat this as distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. The coefficient ratio is equal but the constant ratio is not equal. In exams, treat this as distinct parallel lines.
Step 3
Exam Tip
गुणांक अनुपात समान है लेकिन स्थिर पद का अनुपात समान नहीं है। परीक्षा में इसे समांतर अलग रेखाओं का संकेत मानें।
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युग्म (2x+3y=5) और (4x+6y=10) के लिए कौन-सा कथन सही है?
Which statement is correct for (2x+3y=5) and (4x+6y=10)?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अद्वितीय हल / Unique solution
C हल केवल (x=0) पर है / Solution only at (x=0)
D अनंत हल / Infinitely many solutions
Explanation opens after your attempt
Correct Answer
D. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (2) times the first. Thus both are the same line and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is D. अनंत हल / Infinitely many solutions. The second equation is (2) times the first. Thus both are the same line and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों एक ही रेखा हैं और अनंत हल हैं।
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