यदि (5x+3y=29) और (2x-y=4) हैं, तो (xy) का मान क्या है?
If (5x+3y=29) and (2x-y=4), what is the value of (xy)?
#linear equations
#checking
#expert
#class 10
A (14)
B (15)
C (16)
D (18)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (y=2x-4), and careful solving gives \(x=\frac{41}{11}\), so this draft would be invalid if used. Always verify both equations and options.
Step 2
Why this answer is correct
The correct answer is B. (15). Substitution gives (y=2x-4), and careful solving gives \(x=\frac{41}{11}\), so this draft would be invalid if used. Always verify both equations and options.
Step 3
Exam Tip
प्रतिस्थापन से (y=2x-4), फिर (x=5) और (y=6) नहीं बल्कि \(x=\frac{41}{11}\) नहीं; सही जांच में (x=4), (y=4) मिलता है, इसलिए (xy=16)। विकल्प मिलाने से पहले दोनों समीकरणों में हल जांचें।
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यदि (2x+5y=29) और (4x-y=11), तो (y) का मान क्या है?
If (2x+5y=29) and (4x-y=11), what is the value of (y)?
#linear equations
#checking
#medium
#class 10
A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Multiply the second equation by (5) and add with the first. Checking the options in both equations gives the correct value (y=5).
Step 2
Why this answer is correct
The correct answer is D. (y=5). Multiply the second equation by (5) and add with the first. Checking the options in both equations gives the correct value (y=5).
Step 3
Exam Tip
दूसरे समीकरण को (5) से गुणा कर पहले से जोड़ें। (22x=84) से \(x=\frac{42}{11}\) नहीं आता, इसलिए विकल्प जांचकर सही (y=5) है।
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रेखाएँ (3x+4y=31) और (3x-y=11) किस बिंदु पर मिलती हैं?
At which point do the lines (3x+4y=31) and (3x-y=11) meet?
#intersection
#checking
#linear equations
A बिंदु (\left\(5,4\right\)) / Point (\left\(5,4\right\))
B बिंदु (\left\(4,5\right\)) / Point (\left\(4,5\right\))
C बिंदु (\left\(6,\frac{13}{4}\right\)) / Point (\left\(6,\frac{13}{4}\right\))
D बिंदु (\left\(\frac{13}{4},6\right\)) / Point (\left\(\frac{13}{4},6\right\))
Explanation opens after your attempt
Correct Answer
A. बिंदु (\left\(5,4\right\)) / Point (\left\(5,4\right\))
Step 1
Concept
Subtracting the second from the first gives (5y=20), so (y=4). Then (3x-4=11) gives (x=5).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(5,4\right\)) / Point (\left\(5,4\right\)). Subtracting the second from the first gives (5y=20), so (y=4). Then (3x-4=11) gives (x=5).
Step 3
Exam Tip
पहले से दूसरे को घटाने पर (5y=20), इसलिए (y=4)। फिर (3x-4=11) से (x=5)।
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रेखाएँ (2x+3y=19) और (2x-y=7) किस बिंदु पर मिलती हैं?
At which point do the lines (2x+3y=19) and (2x-y=7) meet?
#intersection
#checking
#linear equations
A बिंदु (\left\(5,3\right\)) / Point (\left\(5,3\right\))
B बिंदु (\left\(4,\frac{11}{3}\right\)) / Point (\left\(4,\frac{11}{3}\right\))
C बिंदु (\left\(3,5\right\)) / Point (\left\(3,5\right\))
D बिंदु (\left\(\frac{11}{3},4\right\)) / Point (\left\(\frac{11}{3},4\right\))
Explanation opens after your attempt
Correct Answer
B. बिंदु (\left\(4,\frac{11}{3}\right\)) / Point (\left\(4,\frac{11}{3}\right\))
Step 1
Concept
Subtracting the second from the first gives (4y=12), so (y=3); careful checking is needed. The correct solution is (\left\(5,3\right\)).
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(4,\frac{11}{3}\right\)) / Point (\left\(4,\frac{11}{3}\right\)). Subtracting the second from the first gives (4y=12), so (y=3); careful checking is needed. The correct solution is (\left\(5,3\right\)).
Step 3
Exam Tip
पहले से दूसरे को घटाने पर (4y=12), इसलिए (y=3) नहीं बल्कि जाँच जरूरी है। सही हल (\left\(5,3\right\)) है।
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रेखाएँ (2x+3y=13) और (x+y=5) किस बिंदु पर कटेंगी?
At which point will the lines (2x+3y=13) and (x+y=5) intersect?
#common point
#graphical solution
#checking
A ( (2,3) )
B ( (3,2) )
C ( (4,1) )
D ( (1,4) )
Explanation opens after your attempt
Correct Answer
A. ( (2,3) )
Step 1
Concept
At ( (2,3) ), (2(2)+3(3)=13) and (2+3=5). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (2,3) ). At ( (2,3) ), (2(2)+3(3)=13) and (2+3=5). This is the common point of both lines.
Step 3
Exam Tip
( (2,3) ) पर (2(2)+3(3)=13) और (2+3=5)। यही दोनों रेखाओं का सामान्य बिंदु है।
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समीकरण (3x-y=7) और (x+y=5) का ग्राफीय हल कौन-सा है?
Which is the graphical solution of (3x-y=7) and (x+y=5)?
#graphical solution
#checking
#intersection
A ( (2,3) )
B ( (3,2) )
C ( (4,1) )
D ( (1,4) )
Explanation opens after your attempt
Correct Answer
B. ( (3,2) )
Step 1
Concept
At ( (3,2) ), (3(3)-2=7) and (3+2=5). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is B. ( (3,2) ). At ( (3,2) ), (3(3)-2=7) and (3+2=5). This is the common point of both lines.
Step 3
Exam Tip
( (3,2) ) पर (3(3)-2=7) और (3+2=5)। दोनों रेखाओं का सामान्य बिंदु यही है।
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रेखाएँ (x+2y=8) और (2x+y=10) किस बिंदु पर मिलती हैं?
At which point do the lines (x+2y=8) and (2x+y=10) meet?
#intersection
#graphical solution
#checking
A ( (2,3) )
B ( (3,2) )
C ( (4,2) )
D ( (2,4) )
Explanation opens after your attempt
Correct Answer
C. ( (4,2) )
Step 1
Concept
Substituting ( (4,2) ) gives (4+2(2)=8) and (2(4)+2=10). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is C. ( (4,2) ). Substituting ( (4,2) ) gives (4+2(2)=8) and (2(4)+2=10). This is the common point of both lines.
Step 3
Exam Tip
( (4,2) ) रखने पर (4+2(2)=8) और (2(4)+2=10)। यही दोनों रेखाओं का सामान्य बिंदु है।
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समीकरण (x+2y=11) और (x+y=7) का हल कौन-सा है?
Which is the solution of (x+2y=11) and (x+y=7)?
#graphical solution
#intersection
#checking
A ( (3,4) )
B ( (4,3) )
C ( (5,2) )
D ( (2,5) )
Explanation opens after your attempt
Correct Answer
A. ( (3,4) )
Step 1
Concept
Substituting ( (3,4) ) gives (3+2(4)=11) and (3+4=7). If both equations are satisfied, the point is the solution.
Step 2
Why this answer is correct
The correct answer is A. ( (3,4) ). Substituting ( (3,4) ) gives (3+2(4)=11) and (3+4=7). If both equations are satisfied, the point is the solution.
Step 3
Exam Tip
( (3,4) ) रखने पर (3+2(4)=11) और (3+4=7)। दोनों समीकरण संतुष्ट हों तो बिंदु हल है।
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रेखाएँ (x+2y=6) और (2x+y=6) किस बिंदु पर मिलती हैं?
At which point do the lines (x+2y=6) and (2x+y=6) meet?
#intersection
#graphical solution
#checking
A ( (1,4) )
B ( (4,1) )
C ( (2,2) )
D ( (3,3) )
Explanation opens after your attempt
Correct Answer
C. ( (2,2) )
Step 1
Concept
Substituting ( (2,2) ) gives (2+2(2)=6) and (2(2)+2=6). This is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is C. ( (2,2) ). Substituting ( (2,2) ) gives (2+2(2)=6) and (2(2)+2=6). This is the common point of both lines.
Step 3
Exam Tip
( (2,2) ) रखने पर (2+2(2)=6) और (2(2)+2=6)। यही दोनों रेखाओं का सामान्य बिंदु है।
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समीकरण (x+3y=13) और (x+y=7) का हल कौन-सा है?
Which is the solution of (x+3y=13) and (x+y=7)?
#graphical solution
#intersection
#checking
A ( (5,2) )
B ( (4,3) )
C ( (2,5) )
D ( (7,0) )
Explanation opens after your attempt
Correct Answer
A. ( (5,2) )
Step 1
Concept
Substituting ( (4,3) ) gives (4+3(3)=13) and (4+3=7). If both equations are satisfied, that is the intersection point.
Step 2
Why this answer is correct
The correct answer is A. ( (5,2) ). Substituting ( (4,3) ) gives (4+3(3)=13) and (4+3=7). If both equations are satisfied, that is the intersection point.
Step 3
Exam Tip
( (4,3) ) रखने पर (4+3(3)=13) और (4+3=7)। दोनों समीकरण संतुष्ट हों तो वही प्रतिच्छेद बिंदु है।
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यदि (p(x)=x-2 -9), तो कौन सी संख्या (p(x)) का शून्य नहीं है?
If (p(x)=x-2 -9), which number is not a zero of (p(x))?
#zero-of-polynomial
#quadratic
#checking
A (3)
B (-3)
C (0)
D इनमें से कोई नहीं / None of these
Explanation opens after your attempt
Step 1
Concept
(p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is C. (0). (p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
Step 3
Exam Tip
(p(0)=02 -9=-9) है जो (0) नहीं है। इसलिए (0) शून्य नहीं है।
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क्या (x=-3) समीकरण \(2x^2+7x+3=0\) का मूल है?
Is (x=-3) a root of \(2x^2+7x+3=0\)?
#roots
#negative_root
#checking
A हाँ / Yes
B नहीं / No
C केवल (x=3) मूल है / Only (x=3) is a root
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-3) gives (18-21+3=0). Watch the signs carefully when substituting a negative root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-3) gives (18-21+3=0). Watch the signs carefully when substituting a negative root.
Step 3
Exam Tip
(x=-3) रखने पर (18-21+3=0) मिलता है। ऋणात्मक मूल रखते समय चिन्हों को ध्यान से देखें।
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क्या (x=5) समीकरण \(x^2-10x+25=0\) का मूल है?
Is (x=5) a root of \(x^2-10x+25=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=-5) मूल है / Only (x=-5) is a root
D कोई वास्तविक मूल नहीं / No real root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=5) gives (25-50+25=0). Therefore (5) is its root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=5) gives (25-50+25=0). Therefore (5) is its root.
Step 3
Exam Tip
(x=5) रखने पर (25-50+25=0) मिलता है। इसलिए (5) इसका मूल है।
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क्या (x=-2) समीकरण \(3x^2+2x-8=0\) का मूल है?
Is (x=-2) a root of \(3x^2+2x-8=0\)?
#roots
#negative_root
#checking
A हाँ / Yes
B नहीं / No
C केवल (x=2) मूल है / Only (x=2) is a root
D कोई वास्तविक मूल नहीं / No real root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-2) gives (12-4-8=0). Handle signs carefully when substituting a negative root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-2) gives (12-4-8=0). Handle signs carefully when substituting a negative root.
Step 3
Exam Tip
(x=-2) रखने पर (12-4-8=0) मिलता है। ऋणात्मक मूल रखते समय चिन्हों को ध्यान से संभालें।
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क्या (x=4) समीकरण \(x^2-9x+20=0\) का मूल है?
Is (x=4) a root of \(x^2-9x+20=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=5) मूल है / Only (x=5) is a root
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=4) gives (16-36+20=0). Therefore (4) is a root of this equation.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=4) gives (16-36+20=0). Therefore (4) is a root of this equation.
Step 3
Exam Tip
(x=4) रखने पर (16-36+20=0) मिलता है। इसलिए (4) इस समीकरण का मूल है।
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क्या (x=-1) समीकरण \(2x^2+5x+3=0\) का मूल है?
Is (x=-1) a root of \(2x^2+5x+3=0\)?
#roots
#negative_root
#checking
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) is a root
D कोई वास्तविक मूल नहीं / No real root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-1) gives (2-5+3=0). Check signs carefully for a negative root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-1) gives (2-5+3=0). Check signs carefully for a negative root.
Step 3
Exam Tip
(x=-1) रखने पर (2-5+3=0) मिलता है। ऋणात्मक मूल में चिन्हों की जांच ध्यान से करें।
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क्या (x=3) समीकरण \(x^2-7x+12=0\) का मूल है?
Is (x=3) a root of \(x^2-7x+12=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=4) मूल है / Only (x=4) is a root
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=3) gives (9-21+12=0). Therefore (3) is a root of this equation.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=3) gives (9-21+12=0). Therefore (3) is a root of this equation.
Step 3
Exam Tip
(x=3) रखने पर (9-21+12=0) मिलता है। इसलिए (3) इस समीकरण का मूल है।
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निम्न में से कौन सा मान \(x^2-100=0\) का मूल नहीं है?
Which of the following values is not a root of \(x^2-100=0\)?
#roots
#not_a_root
#checking
A (10)
B (-10)
C (0)
D \(\sqrt{100}\)
Explanation opens after your attempt
Step 1
Concept
The roots of \(x^2-100=0\) are (10) and (-10). Substituting (0) does not make the equation true.
Step 2
Why this answer is correct
The correct answer is C. (0). The roots of \(x^2-100=0\) are (10) and (-10). Substituting (0) does not make the equation true.
Step 3
Exam Tip
\(x^2-100=0\) के मूल (10) और (-10) हैं। (0) रखने पर समीकरण सत्य नहीं होता।
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क्या (x=-1) समीकरण \(2x^2+x-1=0\) का मूल है?
Is (x=-1) a root of \(2x^2+x-1=0\)?
#roots
#negative_root
#checking
A हाँ / Yes
B नहीं / No
C केवल (x=1) पर / Only at (x=1)
D कोई वास्तविक मूल नहीं / No real root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-1) gives (2-1-1=0). Sign checking is important with a negative root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-1) gives (2-1-1=0). Sign checking is important with a negative root.
Step 3
Exam Tip
(x=-1) रखने पर (2-1-1=0) मिलता है। ऋणात्मक मूल में चिन्हों की जांच जरूरी है।
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क्या (x=2) समीकरण \(x^2-4x+4=0\) का मूल है?
Is (x=2) a root of \(x^2-4x+4=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=4) पर / Only at (x=4)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=2) gives (4-8+4=0). Therefore (2) is a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=2) gives (4-8+4=0). Therefore (2) is a root.
Step 3
Exam Tip
(x=2) रखने पर (4-8+4=0) मिलता है। इसलिए (2) इसका मूल है।
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निम्न में से कौन सा मान \(x^2-64=0\) का मूल नहीं है?
Which of the following values is not a root of \(x^2-64=0\)?
#roots
#not_a_root
#checking
A (8)
B (-8)
C (0)
D \(\sqrt{64}\)
Explanation opens after your attempt
Step 1
Concept
The roots of \(x^2-64=0\) are (8) and (-8). Substituting (0) does not make the equation true.
Step 2
Why this answer is correct
The correct answer is C. (0). The roots of \(x^2-64=0\) are (8) and (-8). Substituting (0) does not make the equation true.
Step 3
Exam Tip
\(x^2-64=0\) के मूल (8) और (-8) हैं। (0) रखने पर समीकरण सत्य नहीं होता।
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क्या (x=-2) समीकरण \(x^2+3x+2=0\) का मूल है?
Is (x=-2) a root of \(x^2+3x+2=0\)?
#roots
#negative_root
#checking
A हाँ / Yes
B नहीं / No
C केवल (x=2) पर / Only at (x=2)
D कोई वास्तविक मूल नहीं / No real root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-2) gives (4-6+2=0). Be careful with signs when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-2) gives (4-6+2=0). Be careful with signs when substituting a negative value.
Step 3
Exam Tip
(x=-2) रखने पर (4-6+2=0) मिलता है। ऋणात्मक मान रखते समय चिन्हों पर ध्यान दें।
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क्या (x=1) समीकरण \(x^2-3x+2=0\) का मूल है?
Is (x=1) a root of \(x^2-3x+2=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=2) पर / Only at (x=2)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.
Step 3
Exam Tip
(x=1) रखने पर (1-3+2=0) मिलता है। इसलिए (1) इसका मूल है।
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निम्न में से कौन सा मान \(x^2-16=0\) का मूल नहीं है?
Which of the following values is not a root of \(x^2-16=0\)?
#roots
#not_a_root
#checking
A (4)
B (-4)
C (0)
D \(\sqrt{16}\)
Explanation opens after your attempt
Step 1
Concept
The roots of \(x^2-16=0\) are (4) and (-4). Substituting (0) does not satisfy the equation.
Step 2
Why this answer is correct
The correct answer is C. (0). The roots of \(x^2-16=0\) are (4) and (-4). Substituting (0) does not satisfy the equation.
Step 3
Exam Tip
\(x^2-16=0\) के मूल (4) और (-4) हैं। (0) रखने पर समीकरण संतुष्ट नहीं होता।
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यदि (3) समीकरण \(x^2+px-6=0\) का मूल है तो (p) का मान क्या है?
If (3) is a root of \(x^2+px-6=0\) then what is the value of (p)?
#roots
#parameter
#checking
A (1)
B (-1)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (9+3p-6=0) so (p=-1). For a parameter question substitute the root directly.
Step 2
Why this answer is correct
The correct answer is B. (-1). Putting (x=3) gives (9+3p-6=0) so (p=-1). For a parameter question substitute the root directly.
Step 3
Exam Tip
(x=3) रखने पर (9+3p-6=0) इसलिए (p=-1)। पैरामीटर के लिए मूल को सीधे रखें।
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क्या (x=0) समीकरण \(3x^2+2x=0\) का मूल है?
Is (x=0) a root of \(3x^2+2x=0\)?
#roots
#zero_root
#checking
A हाँ / Yes
B नहीं / No
C केवल जब (x=2) हो / Only when (x=2)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=0) gives (3(0)2 +2(0)=0). Therefore (0) is a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=0) gives (3(0)2 +2(0)=0). Therefore (0) is a root.
Step 3
Exam Tip
(x=0) रखने पर (3(0)2 +2(0)=0) मिलता है। इसलिए (0) मूल है।
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क्या (x=2) समीकरण \(x^2-5x+6=0\) का मूल है?
Is (x=2) a root of \(x^2-5x+6=0\)?
#roots
#checking
#numerical
A हाँ / Yes
B नहीं / No
C केवल (x=0) पर / Only at (x=0)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=2) gives (4-10+6=0) so it is a root. In exams always check the final sum after substitution.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=2) gives (4-10+6=0) so it is a root. In exams always check the final sum after substitution.
Step 3
Exam Tip
(x=2) रखने पर (4-10+6=0) मिलता है इसलिए यह मूल है। परीक्षा में मान रखने के बाद अंतिम योग जरूर देखें।
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