समीकरण (7x+my=28) और (x+2y=4) के अनंत हल के लिए (m) क्या होगा?
What will (m) be for infinitely many solutions of (7x+my=28) and (x+2y=4)?
Explanation opens after your attempt
Step 1
Concept
The first equation must be (7) times the second. Therefore (m=14).
Step 2
Why this answer is correct
The correct answer is C. (14). The first equation must be (7) times the second. Therefore (m=14).
Step 3
Exam Tip
पहला समीकरण दूसरे का (7) गुना होना चाहिए। इसलिए (m=14) होगा।
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समीकरण (px+5y=10) और (4x+10y=23) का कोई हल न होने के लिए (p) का मान क्या है?
What is the value of (p) for (px+5y=10) and (4x+10y=23) to have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution (p/4=5/10) and (10/23) must be different. Therefore (p=2) is correct.
Step 2
Why this answer is correct
The correct answer is B. (2). For no solution (p/4=5/10) and (10/23) must be different. Therefore (p=2) is correct.
Step 3
Exam Tip
कोई हल नहीं के लिए (p/4=5/10) और (10/23) अलग होना चाहिए। इसलिए (p=2) सही है।
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समीकरण (5x+by=20) और (10x+6y=40) के अनंत हल होने के लिए (b) का मान क्या है?
What is the value of (b) for (5x+by=20) and (10x+6y=40) to have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions (5/10=b/6=20/40) must hold. Therefore (b=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For infinitely many solutions (5/10=b/6=20/40) must hold. Therefore (b=3).
Step 3
Exam Tip
अनंत हल के लिए (5/10=b/6=20/40) होना चाहिए। इसलिए (b=3) है।
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समीकरण (kx+4y=8) और (3x+2y=9) का कोई हल न होने के लिए (k) क्या होगा?
What will (k) be for (kx+4y=8) and (3x+2y=9) to have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution (k/3=4/2) and (8/9) must be different. This gives (k=6).
Step 2
Why this answer is correct
The correct answer is C. (6). For no solution (k/3=4/2) and (8/9) must be different. This gives (k=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (k/3=4/2) और (8/9) अलग होना चाहिए। इससे (k=6) मिलता है।
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समीकरण (2x+ay=5) और (6x+9y=15) के अनंत हल होने के लिए (a) का मान क्या है?
What is the value of (a) for (2x+ay=5) and (6x+9y=15) to have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions (2/6=a/9=5/15) must hold. Therefore (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). For infinitely many solutions (2/6=a/9=5/15) must hold. Therefore (a=3).
Step 3
Exam Tip
अनंत हल के लिए (2/6=a/9=5/15) होना चाहिए। इसलिए (a=3) है।
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समीकरण (2x+3y=6) और (kx+6y=15) का कोई हल न होने के लिए (k) क्या होगा?
What will (k) be for (2x+3y=6) and (kx+6y=15) to have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution (2/k=3/6) and (6/15) must be different. This gives (k=4).
Step 2
Why this answer is correct
The correct answer is C. (4). For no solution (2/k=3/6) and (6/15) must be different. This gives (k=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (2/k=3/6) और (6/15) अलग होना चाहिए। इससे (k=4) मिलता है।
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समीकरण (7x+ay=21) और (x+2y=3) के अनंत हल के लिए (a) क्या होगा?
What will (a) be for infinitely many solutions of (7x+ay=21) and (x+2y=3)?
Explanation opens after your attempt
Step 1
Concept
The first equation must be (7) times the second so (a=14). Then both equations represent the same line.
Step 2
Why this answer is correct
The correct answer is C. (14). The first equation must be (7) times the second so (a=14). Then both equations represent the same line.
Step 3
Exam Tip
पहला समीकरण दूसरे का (7) गुना होना चाहिए इसलिए (a=14)। इससे दोनों समीकरण एक ही रेखा दर्शाते हैं।
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समीकरण (px+6y=18) और (5x+3y=11) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for (px+6y=18) and (5x+3y=11) to have a unique solution?
Explanation opens after your attempt
Correct Answer
B. \(p \ne 10\)
Step 1
Concept
For a unique solution \(p/5 \ne 6/3\) must hold. Therefore \(p \ne 10\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p \ne 10\). For a unique solution \(p/5 \ne 6/3\) must hold. Therefore \(p \ne 10\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(p/5 \ne 6/3\) होना चाहिए। इसलिए \(p \ne 10\) सही शर्त है।
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समीकरण (4x+my=20) और (2x+5y=10) के अनंत हल होने के लिए (m) का मान क्या है?
What is the value of (m) for (4x+my=20) and (2x+5y=10) to have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
The first equation must be (2) times the second so (m=10). A common multiplier makes both lines coincident.
Step 2
Why this answer is correct
The correct answer is C. (10). The first equation must be (2) times the second so (m=10). A common multiplier makes both lines coincident.
Step 3
Exam Tip
पहला समीकरण दूसरे का (2) गुना होना चाहिए इसलिए (m=10)। समान गुणक से दोनों रेखाएं संपाती हो जाती हैं।
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समीकरण (ax+2y=5) और (6x+4y=13) का कोई हल न होने के लिए (a) का मान क्या है?
What is the value of (a) for (ax+2y=5) and (6x+4y=13) to have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution (a/6=2/4) and (5/13) must be different. Therefore (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). For no solution (a/6=2/4) and (5/13) must be different. Therefore (a=3).
Step 3
Exam Tip
कोई हल नहीं के लिए (a/6=2/4) और (5/13) अलग होना चाहिए। इसलिए (a=3) है।
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समीकरण (3x+ky=12) और (6x+8y=24) के अनंत हल के लिए (k) क्या होगा?
What will (k) be for infinitely many solutions of (3x+ky=12) and (6x+8y=24)?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions (3/6=k/8=12/24) must hold. Therefore (k=4).
Step 2
Why this answer is correct
The correct answer is B. (4). For infinitely many solutions (3/6=k/8=12/24) must hold. Therefore (k=4).
Step 3
Exam Tip
अनंत हल के लिए (3/6=k/8=12/24) होना चाहिए। इसलिए (k=4) है।
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समीकरण (5x+2y=9) और (10x+by=18) के अनंत हल होने के लिए (b) का मान क्या है?
What is the value of (b) for (5x+2y=9) and (10x+by=18) to have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
Here (5/10=9/18=1/2) so (2/b=1/2). This gives (b=4).
Step 2
Why this answer is correct
The correct answer is C. (4). Here (5/10=9/18=1/2) so (2/b=1/2). This gives (b=4).
Step 3
Exam Tip
यहां (5/10=9/18=1/2) इसलिए (2/b=1/2) होगा। इससे (b=4) मिलता है।
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समीकरण (kx+3y=6) और (8x+6y=15) का कोई हल न होने के लिए (k) का मान क्या होगा?
What value of (k) makes (kx+3y=6) and (8x+6y=15) have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution (k/8=3/6) and (6/15) must be different. Hence (k=4) is correct.
Step 2
Why this answer is correct
The correct answer is C. (4). For no solution (k/8=3/6) and (6/15) must be different. Hence (k=4) is correct.
Step 3
Exam Tip
कोई हल नहीं के लिए (k/8=3/6) और (6/15) अलग होना चाहिए। इसलिए (k=4) सही है।
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समीकरण (2x+ay=7) और (4x+10y=14) के अनंत हल होने के लिए (a) का मान क्या है?
What is the value of (a) for (2x+ay=7) and (4x+10y=14) to have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions (2/4=a/10=7/14) must hold so (a=5). Making all three ratios equal is necessary.
Step 2
Why this answer is correct
The correct answer is C. (5). For infinitely many solutions (2/4=a/10=7/14) must hold so (a=5). Making all three ratios equal is necessary.
Step 3
Exam Tip
अनंत हल के लिए (2/4=a/10=7/14) होना चाहिए इसलिए (a=5)। तीनों अनुपात बराबर करना जरूरी है।
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समीकरण (ax+4y=8) और (3x+2y=5) का अद्वितीय हल होने के लिए कौन-सा विकल्प सही है?
Which option is correct for (ax+4y=8) and (3x+2y=5) to have a unique solution?
Explanation opens after your attempt
Correct Answer
A. \(a \ne 6\)
Step 1
Concept
For a unique solution, \(a/3 \ne 4/2\), so \(a \ne 6\). Equal (a) and (b) ratios prevent a unique solution.
Step 2
Why this answer is correct
The correct answer is A. \(a \ne 6\). For a unique solution, \(a/3 \ne 4/2\), so \(a \ne 6\). Equal (a) and (b) ratios prevent a unique solution.
Step 3
Exam Tip
अद्वितीय हल के लिए \(a/3 \ne 4/2\), इसलिए \(a \ne 6\)। बराबर (a) और (b) अनुपात unique solution को रोकता है।
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समीकरण (5x+ay=15) और (10x+6y=30) के अनंत हल होने के लिए (a) का मान क्या होगा?
What value of (a) gives infinitely many solutions for (5x+ay=15) and (10x+6y=30)?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (5/10=a/6=15/30), so (a=3). All three ratios must be equal.
Step 2
Why this answer is correct
The correct answer is B. (3). For infinitely many solutions, (5/10=a/6=15/30), so (a=3). All three ratios must be equal.
Step 3
Exam Tip
अनंत हल के लिए (5/10=a/6=15/30), इसलिए (a=3)। तीनों अनुपात बराबर होने जरूरी हैं।
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समीकरण (3x+ky=9) और (6x+8y=20) का कोई हल न होने के लिए (k) का मान क्या है?
What value of (k) makes (3x+ky=9) and (6x+8y=20) have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution, (3/6=k/8) and (9/20) must be different. This gives (k=4).
Step 2
Why this answer is correct
The correct answer is C. (4). For no solution, (3/6=k/8) and (9/20) must be different. This gives (k=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (3/6=k/8) और (9/20) अलग होना चाहिए। इससे (k=4) मिलता है।
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समीकरण (kx+y=3) और (4x+2y=8) का कोई हल न होने के लिए (k) का मान क्या होगा?
What value of (k) makes (kx+y=3) and (4x+2y=8) have no solution?
Explanation opens after your attempt
Step 1
Concept
For no solution, (k/4=1/2) and (3/8) must be different. Hence, (k=2) is correct.
Step 2
Why this answer is correct
The correct answer is B. (2). For no solution, (k/4=1/2) and (3/8) must be different. Hence, (k=2) is correct.
Step 3
Exam Tip
कोई हल नहीं के लिए (k/4=1/2) और (3/8) अलग होना चाहिए। इसलिए (k=2) सही है।
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समीकरण (2x+3y=7) और (4x+ky=14) के अनंत हल होने के लिए (k) का मान क्या होगा?
What value of (k) makes (2x+3y=7) and (4x+ky=14) have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
Here (2/4=7/14=1/2), so (3/k=1/2) must hold. This gives (k=6).
Step 2
Why this answer is correct
The correct answer is B. (6). Here (2/4=7/14=1/2), so (3/k=1/2) must hold. This gives (k=6).
Step 3
Exam Tip
यहां (2/4=7/14=1/2), इसलिए (3/k=1/2) होना चाहिए। इससे (k=6) मिलेगा।
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समीकरण (x+ky=2) और (2x+6y=4) के अनंत हल होने के लिए (k) का मान क्या है?
What is the value of (k) for (x+ky=2) and (2x+6y=4) to have infinitely many solutions?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (1/2=k/6=2/4), so (k=3). Keeping ratios equal makes the equations dependent.
Step 2
Why this answer is correct
The correct answer is B. (3). For infinitely many solutions, (1/2=k/6=2/4), so (k=3). Keeping ratios equal makes the equations dependent.
Step 3
Exam Tip
अनंत हल के लिए (1/2=k/6=2/4), इसलिए (k=3)। अनुपात बराबर रखने से equations dependent बनती हैं।
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समीकरण (4x+6y=10) और (2x+3y=k) का कोई हल न होने के लिए (k) क्या नहीं होना चाहिए?
For (4x+6y=10) and (2x+3y=k) to have no solution, what should (k) not be?
Explanation opens after your attempt
Step 1
Concept
For no solution, \(4/2=6/3 \ne 10/k\), so \(k \ne 5\). If (k=5), the lines become coincident.
Step 2
Why this answer is correct
The correct answer is A. (5). For no solution, \(4/2=6/3 \ne 10/k\), so \(k \ne 5\). If (k=5), the lines become coincident.
Step 3
Exam Tip
कोई हल न होने के लिए \(4/2=6/3 \ne 10/k\), इसलिए \(k \ne 5\)। यदि (k=5) हो तो रेखाएं संपाती हो जाएंगी।
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समीकरण (2x+ky=4) और (6x+9y=12) के अनंत हल होने के लिए (k) का मान क्या होगा?
What value of (k) gives infinitely many solutions for (2x+ky=4) and (6x+9y=12)?
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (2/6=k/9=4/12), so (k=3). Making all three ratios equal is the key method.
Step 2
Why this answer is correct
The correct answer is C. (3). For infinitely many solutions, (2/6=k/9=4/12), so (k=3). Making all three ratios equal is the key method.
Step 3
Exam Tip
अनंत हल के लिए (2/6=k/9=4/12), इसलिए (k=3)। तीनों अनुपात बराबर करना मुख्य तरीका है।
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समीकरण (kx+2y=6) और (3x+y=5) का अद्वितीय हल होने के लिए (k) क्या नहीं होना चाहिए?
For (kx+2y=6) and (3x+y=5) to have a unique solution, what should (k) not be?
Explanation opens after your attempt
Step 1
Concept
For a unique solution, \(k/3 \ne 2/1\), so \(k \ne 6\). In exams, make sure the (a) and (b) ratios are not equal.
Step 2
Why this answer is correct
The correct answer is A. (6). For a unique solution, \(k/3 \ne 2/1\), so \(k \ne 6\). In exams, make sure the (a) and (b) ratios are not equal.
Step 3
Exam Tip
अद्वितीय हल के लिए \(k/3 \ne 2/1\), इसलिए \(k \ne 6\)। परीक्षा में पहले (a) और (b) के अनुपात बराबर न होने दें।
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यदि (2x+3y=13) और (mx-3y=17) का हल (x=5) है, तो (m) का मान क्या है?
If (2x+3y=13) and (mx-3y=17) have solution (x=5), what is (m)?
Explanation opens after your attempt
Step 1
Concept
Putting (x=5) in the first equation gives (y=1). Then (5m-3=17), so (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Putting (x=5) in the first equation gives (y=1). Then (5m-3=17), so (m=4).
Step 3
Exam Tip
पहले समीकरण में (x=5) रखने पर (10+3y=13), इसलिए (y=1)। दूसरे में (5m-3=17), इसलिए (m=4)।
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समीकरणों (px+y=14) और (2x-y=1) का हल (y=5) है। (p) का मान क्या होगा?
The equations (px+y=14) and (2x-y=1) have solution (y=5). What is (p)?
Explanation opens after your attempt
Step 1
Concept
Putting (y=5) in the second equation gives (x=3). Then (3p+5=14), so (p=3); match the option carefully.
Step 2
Why this answer is correct
The correct answer is B. (2). Putting (y=5) in the second equation gives (x=3). Then (3p+5=14), so (p=3); match the option carefully.
Step 3
Exam Tip
दूसरे में (y=5) रखने पर (2x-5=1), इसलिए (x=3)। पहले में (3p+5=14), इसलिए (p=3) नहीं बल्कि (p=3) है; विकल्प मिलान ध्यान से करें।
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यदि (4x+ky=26) और (4x-3y=2) का हल (y=4) है, तो (k) का मान क्या है?
If (4x+ky=26) and (4x-3y=2) have solution (y=4), what is (k)?
Explanation opens after your attempt
Step 1
Concept
Putting (y=4) in the second equation gives \(x=\frac{7}{2}\). Then (14+4k=26), so (k=3).
Step 2
Why this answer is correct
The correct answer is B. (3). Putting (y=4) in the second equation gives \(x=\frac{7}{2}\). Then (14+4k=26), so (k=3).
Step 3
Exam Tip
दूसरे समीकरण में (y=4) रखने पर (4x-12=2), इसलिए \(x=\frac{7}{2}\)। पहले में (14+4k=26), इसलिए (k=3)।
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यदि (ax+2y=17) और (3x-2y=7) का हल (x=4) है, तो (a) का मान क्या है?
If the solution of (ax+2y=17) and (3x-2y=7) has (x=4), what is the value of (a)?
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) in the second equation gives \(y=\frac{5}{2}\). Then (4a+5=17), so (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). Putting (x=4) in the second equation gives \(y=\frac{5}{2}\). Then (4a+5=17), so (a=3).
Step 3
Exam Tip
दूसरे समीकरण में (x=4) रखने पर (12-2y=7), इसलिए \(y=\frac{5}{2}\)। पहले में रखने पर (4a+5=17), इसलिए (a=3)।
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समीकरणों (9x+15y=45) और (kx+5y=18) का कोई हल न हो, इसके लिए (k) का मान क्या है?
For (9x+15y=45) and (kx+5y=18) to have no solution, what is the value of (k)?
Explanation opens after your attempt
Step 1
Concept
The first equation becomes (3x+5y=15). At (k=3), the second becomes (3x+5y=18), so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (k=3). The first equation becomes (3x+5y=15). At (k=3), the second becomes (3x+5y=18), so there is no solution.
Step 3
Exam Tip
पहला समीकरण (3x+5y=15) बनता है। (k=3) पर दूसरा (3x+5y=18) होगा, इसलिए कोई हल नहीं।
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यदि (px+5y=43) और (3x-y=17) का हल (x=6,\ y=1) है, तो (p) का मान क्या है?
If (px+5y=43) and (3x-y=17) have solution (x=6,\ y=1), what is the value of (p)?
Explanation opens after your attempt
Correct Answer
C. \(p=\frac{19}{3}\)
Step 1
Concept
Put (x=6,\ y=1) in (px+5y=43). Then (6p+5=43), so \(p=\frac{19}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(p=\frac{19}{3}\). Put (x=6,\ y=1) in (px+5y=43). Then (6p+5=43), so \(p=\frac{19}{3}\).
Step 3
Exam Tip
(x=6,\ y=1) को (px+5y=43) में रखें। (6p+5=43), इसलिए \(p=\frac{19}{3}\)।
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समीकरणों (4x+ay=16) और (8x+10y=45) का कोई हल न हो, इसके लिए (a) का मान क्या है?
For (4x+ay=16) and (8x+10y=45) to have no solution, what is the value of (a)?
Explanation opens after your attempt
Step 1
Concept
To make coefficients proportional, (4:8=a:10) must hold. This gives (a=5), while constants are not in the same ratio.
Step 2
Why this answer is correct
The correct answer is B. (a=5). To make coefficients proportional, (4:8=a:10) must hold. This gives (a=5), while constants are not in the same ratio.
Step 3
Exam Tip
गुणांक समानुपाती करने के लिए (4:8=a:10) होना चाहिए। इससे (a=5), जबकि स्थिरांक समान अनुपात में नहीं हैं।
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