यदि दो रेखाओं का सामान्य बिंदु ( (4,6) ) है, तो ग्राफीय हल क्या होगा?
If the common point of two lines is ( (4,6) ), what will be the graphical solution?
#graphical method
#solution
#coordinates
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A (x=4,\ y=6)
B (x=6,\ y=4)
C (x=4,\ y=4)
D (x=6,\ y=6)
Explanation opens after your attempt
Correct Answer
A. (x=4,\ y=6)
Step 1
Concept
The coordinates of the common point are the solution. Always write the answer in the order (x,y).
Step 2
Why this answer is correct
The correct answer is A. (x=4,\ y=6). The coordinates of the common point are the solution. Always write the answer in the order (x,y).
Step 3
Exam Tip
सामान्य बिंदु के निर्देशांक ही हल होते हैं। उत्तर हमेशा (x,y) के क्रम में लिखें।
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रेखा (x+y=13) पर (x=5) रखने पर कौन-सा बिंदु मिलेगा?
For the line (x+y=13), which point is obtained when (x=5)?
#linear equations
#table values
#graph plotting
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A ( (5,8) )
B ( (8,5) )
C ( (5,13) )
D ( (13,5) )
Explanation opens after your attempt
Correct Answer
A. ( (5,8) )
Step 1
Concept
From (5+y=13), (y=8), so the point is ( (5,8) ). While drawing a graph, write the point as ( (x,y) ).
Step 2
Why this answer is correct
The correct answer is A. ( (5,8) ). From (5+y=13), (y=8), so the point is ( (5,8) ). While drawing a graph, write the point as ( (x,y) ).
Step 3
Exam Tip
(5+y=13) से (y=8), इसलिए बिंदु ( (5,8) ) है। ग्राफ बनाते समय बिंदु को ( (x,y) ) रूप में लिखें।
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समीकरण (2x+y=14) में (x=3) रखने पर (y) का मान क्या होगा?
In (2x+y=14), what is the value of (y) when (x=3)?
#substitution
#graph plotting
#linear equations
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A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (2(3)+y=14), we get (y=8). Choosing simple values is useful while making a table.
Step 2
Why this answer is correct
The correct answer is B. (8). From (2(3)+y=14), we get (y=8). Choosing simple values is useful while making a table.
Step 3
Exam Tip
(2(3)+y=14) से (y=8) मिलता है। तालिका बनाते समय सरल मान चुनना उपयोगी होता है।
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समीकरण (3x+y=18) का (y)-अवरोध कौन-सा है?
What is the (y)-intercept of (3x+y=18)?
#y intercept
#graphical method
#linear equations
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A ( (18,0) )
B ( (3,0) )
C ( (0,18) )
D ( (0,3) )
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Correct Answer
C. ( (0,18) )
Step 1
Concept
For the (y)-intercept, (x=0), so (y=18). Every point on the (y)-axis has (x)-coordinate (0).
Step 2
Why this answer is correct
The correct answer is C. ( (0,18) ). For the (y)-intercept, (x=0), so (y=18). Every point on the (y)-axis has (x)-coordinate (0).
Step 3
Exam Tip
(y)-अवरोध के लिए (x=0), इसलिए (y=18)। (y)-अक्ष पर हर बिंदु का (x)-निर्देशांक (0) होता है।
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समीकरण (5x+y=30) का (x)-अवरोध कौन-सा है?
What is the (x)-intercept of (5x+y=30)?
#x intercept
#graph plotting
#linear equations
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A ( (0,30) )
B ( (5,0) )
C ( (0,6) )
D ( (6,0) )
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Correct Answer
D. ( (6,0) )
Step 1
Concept
For the (x)-intercept, (y=0), so (5x=30) and (x=6). On the (x)-axis, (y=0).
Step 2
Why this answer is correct
The correct answer is D. ( (6,0) ). For the (x)-intercept, (y=0), so (5x=30) and (x=6). On the (x)-axis, (y=0).
Step 3
Exam Tip
(x)-अवरोध के लिए (y=0), इसलिए (5x=30) और (x=6)। (x)-अक्ष पर (y=0) होता है।
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रेखाएँ (x+3y=15) और (x+3y=21) ग्राफ पर कैसी होंगी?
How will the lines (x+3y=15) and (x+3y=21) appear on the graph?
#parallel lines
#no solution
#graphical method
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A समांतर रेखाएँ / Parallel lines
B संपाती रेखाएँ / Coincident lines
C एक बिंदु पर कटती रेखाएँ / Lines intersecting at one point
D अक्षों जैसी रेखाएँ / Lines like axes
Explanation opens after your attempt
Correct Answer
A. समांतर रेखाएँ / Parallel lines
Step 1
Concept
Both have the same coefficients of (x) and (y), but different constants. So the lines are parallel and have no solution.
Step 2
Why this answer is correct
The correct answer is A. समांतर रेखाएँ / Parallel lines. Both have the same coefficients of (x) and (y), but different constants. So the lines are parallel and have no solution.
Step 3
Exam Tip
दोनों में (x) और (y) के गुणांक समान हैं लेकिन नियतांक अलग हैं। इसलिए रेखाएँ समांतर होंगी और कोई हल नहीं होगा।
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समीकरण (8x+4y=20) को सरल करने पर कौन-सा समीकरण मिलेगा?
Which equation is obtained by simplifying (8x+4y=20)?
#simplification
#linear equations
#graphical method
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A (4x+y=20)
B (2x+y=5)
C (x+4y=5)
D (2x+4y=20)
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Correct Answer
B. (2x+y=5)
Step 1
Concept
Dividing the whole equation by (4) gives (2x+y=5). The simplified form makes line comparison easier.
Step 2
Why this answer is correct
The correct answer is B. (2x+y=5). Dividing the whole equation by (4) gives (2x+y=5). The simplified form makes line comparison easier.
Step 3
Exam Tip
पूरे समीकरण को (4) से भाग देने पर (2x+y=5) मिलता है। सरल रूप से रेखाओं की तुलना आसान होती है।
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रेखाएँ (2x+y=5) और (8x+4y=20) कैसी होंगी?
What type of lines are (2x+y=5) and (8x+4y=20)?
#coincident lines
#infinite solutions
#graphical method
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A समांतर रेखाएँ / Parallel lines
B एक बिंदु पर कटेंगी / They will intersect at one point
C संपाती रेखाएँ / Coincident lines
D लंब रेखाएँ / Perpendicular lines
Explanation opens after your attempt
Correct Answer
C. संपाती रेखाएँ / Coincident lines
Step 1
Concept
The second equation is (4) times the first, so both are the same line. Such lines have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. संपाती रेखाएँ / Coincident lines. The second equation is (4) times the first, so both are the same line. Such lines have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (4) गुना है, इसलिए दोनों एक ही रेखा हैं। ऐसी रेखाओं के अनंत हल होते हैं।
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बिंदु ( (3,7) ) किस समीकरण को संतुष्ट करता है?
Which equation is satisfied by the point ( (3,7) )?
#point checking
#linear equations
#graph
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A (x+y=10)
B (x+y=12)
C (x-y=10)
D (2x+y=16)
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Correct Answer
A. (x+y=10)
Step 1
Concept
Substituting ( (3,7) ) gives (3+7=10), so (x+y=10) is correct. To check a point, substitute it in the equation.
Step 2
Why this answer is correct
The correct answer is A. (x+y=10). Substituting ( (3,7) ) gives (3+7=10), so (x+y=10) is correct. To check a point, substitute it in the equation.
Step 3
Exam Tip
( (3,7) ) रखने पर (3+7=10), इसलिए (x+y=10) सही है। बिंदु जाँचने के लिए उसे समीकरण में रखें।
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समीकरण (y=x+5) पर कौन-सा बिंदु स्थित है?
Which point lies on the equation (y=x+5)?
#point on line
#substitution
#graphical method
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A ( (5,5) )
B ( (2,7) )
C ( (7,2) )
D ( (0,4) )
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Correct Answer
B. ( (2,7) )
Step 1
Concept
Putting (x=2) gives (y=2+5=7), so ( (2,7) ) is correct. Substitute values to check a point on a line.
Step 2
Why this answer is correct
The correct answer is B. ( (2,7) ). Putting (x=2) gives (y=2+5=7), so ( (2,7) ) is correct. Substitute values to check a point on a line.
Step 3
Exam Tip
(x=2) रखने पर (y=2+5=7), इसलिए ( (2,7) ) सही है। रेखा पर बिंदु जाँचने के लिए मान रखें।
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समीकरण (y=4x-2) के लिए (x=3) होने पर कौन-सा बिंदु मिलेगा?
For (y=4x-2), which point is obtained when (x=3)?
#table values
#ordered pair
#linear equations
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A ( (3,8) )
B ( (8,3) )
C ( (3,10) )
D ( (10,3) )
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Correct Answer
C. ( (3,10) )
Step 1
Concept
(y=4(3)-2=10), so the point is ( (3,10) ). Do not change the coordinate order after calculation.
Step 2
Why this answer is correct
The correct answer is C. ( (3,10) ). (y=4(3)-2=10), so the point is ( (3,10) ). Do not change the coordinate order after calculation.
Step 3
Exam Tip
(y=4(3)-2=10), इसलिए बिंदु ( (3,10) ) है। गणना के बाद निर्देशांक क्रम न बदलें।
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समीकरण (x=11) किस प्रकार की रेखा दर्शाता है?
What type of line does (x=11) represent?
#vertical line
#axis
#graph
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A मूलबिंदु से गुजरने वाली रेखा / Line passing through origin
B (x)-अक्ष के समांतर रेखा / Line parallel to (x)-axis
C कोई रेखा नहीं / No line
D (y)-अक्ष के समांतर रेखा / Line parallel to (y)-axis
Explanation opens after your attempt
Correct Answer
D. (y)-अक्ष के समांतर रेखा / Line parallel to (y)-axis
Step 1
Concept
In (x=11), (x) is fixed and (y) can vary. Hence, it is a vertical line parallel to the (y)-axis.
Step 2
Why this answer is correct
The correct answer is D. (y)-अक्ष के समांतर रेखा / Line parallel to (y)-axis. In (x=11), (x) is fixed and (y) can vary. Hence, it is a vertical line parallel to the (y)-axis.
Step 3
Exam Tip
(x=11) में (x) स्थिर रहता है और (y) बदल सकता है। इसलिए यह (y)-अक्ष के समांतर ऊर्ध्वाधर रेखा है।
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समीकरण (y=8) किस प्रकार की रेखा दर्शाता है?
What type of line does (y=8) represent?
#horizontal line
#axis
#graphical method
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A (x)-अक्ष के समांतर रेखा / Line parallel to (x)-axis
B (y)-अक्ष के समांतर रेखा / Line parallel to (y)-axis
C मूलबिंदु से गुजरने वाली रेखा / Line passing through origin
D केवल एक बिंदु / Only one point
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के समांतर रेखा / Line parallel to (x)-axis
Step 1
Concept
In (y=8), (y) is fixed and (x) can vary. Hence, it is a horizontal line parallel to the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के समांतर रेखा / Line parallel to (x)-axis. In (y=8), (y) is fixed and (x) can vary. Hence, it is a horizontal line parallel to the (x)-axis.
Step 3
Exam Tip
(y=8) में (y) स्थिर रहता है और (x) बदल सकता है। इसलिए यह (x)-अक्ष के समांतर क्षैतिज रेखा है।
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रेखाएँ (x=4) और (y=9) किस बिंदु पर मिलेंगी?
At which point will the lines (x=4) and (y=9) meet?
#vertical horizontal lines
#intersection
#solution
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A ( (9,4) )
B ( (4,9) )
C ( (4,0) )
D ( (0,9) )
Explanation opens after your attempt
Correct Answer
B. ( (4,9) )
Step 1
Concept
On the first line (x=4), and on the second line (y=9). Therefore, their common point is ( (4,9) ).
Step 2
Why this answer is correct
The correct answer is B. ( (4,9) ). On the first line (x=4), and on the second line (y=9). Therefore, their common point is ( (4,9) ).
Step 3
Exam Tip
पहली रेखा पर (x=4) और दूसरी रेखा पर (y=9) है। इसलिए उनका सामान्य बिंदु ( (4,9) ) है।
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समीकरण (6x+y=36) में (y=0) रखने पर कौन-सा बिंदु मिलेगा?
For (6x+y=36), which point is obtained when (y=0)?
#x intercept
#graph plotting
#linear equations
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A ( (0,36) )
B ( (36,0) )
C ( (6,0) )
D ( (0,6) )
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Correct Answer
C. ( (6,0) )
Step 1
Concept
From (6x+0=36), (x=6), so the point is ( (6,0) ). This is the (x)-intercept.
Step 2
Why this answer is correct
The correct answer is C. ( (6,0) ). From (6x+0=36), (x=6), so the point is ( (6,0) ). This is the (x)-intercept.
Step 3
Exam Tip
(6x+0=36) से (x=6), इसलिए बिंदु ( (6,0) ) है। यह (x)-अवरोध है।
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समीकरण (x+6y=36) में (x=0) रखने पर कौन-सा बिंदु मिलेगा?
For (x+6y=36), which point is obtained when (x=0)?
#y intercept
#graph plotting
#linear equations
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A ( (6,0) )
B ( (36,0) )
C ( (0,36) )
D ( (0,6) )
Explanation opens after your attempt
Correct Answer
D. ( (0,6) )
Step 1
Concept
From (0+6y=36), (y=6), so the point is ( (0,6) ). This is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is D. ( (0,6) ). From (0+6y=36), (y=6), so the point is ( (0,6) ). This is the (y)-intercept.
Step 3
Exam Tip
(0+6y=36) से (y=6), इसलिए बिंदु ( (0,6) ) है। यह (y)-अवरोध है।
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रेखाएँ (x+y=16) और (x-y=6) का सामान्य बिंदु कौन-सा है?
What is the common point of the lines (x+y=16) and (x-y=6)?
#graphical solution
#common point
#linear equations
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A ( (11,5) )
B ( (5,11) )
C ( (8,8) )
D ( (10,6) )
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Correct Answer
A. ( (11,5) )
Step 1
Concept
At ( (11,5) ), (11+5=16) and (11-5=6). This is the intersection point of both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (11,5) ). At ( (11,5) ), (11+5=16) and (11-5=6). This is the intersection point of both lines.
Step 3
Exam Tip
( (11,5) ) पर (11+5=16) और (11-5=6)। यही दोनों रेखाओं का प्रतिच्छेद 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
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A ( (3,4) )
B ( (4,3) )
C ( (5,2) )
D ( (2,5) )
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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 (2x+y=13) और (x+y=9) कहाँ मिलती हैं?
Where do the lines (2x+y=13) and (x+y=9) meet?
#intersection point
#graphical method
#linear equations
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A ( (2,7) )
B ( (3,6) )
C ( (4,5) )
D ( (5,4) )
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Correct Answer
C. ( (4,5) )
Step 1
Concept
At ( (4,5) ), (2(4)+5=13) and (4+5=9). Therefore, this is the common point of both lines.
Step 2
Why this answer is correct
The correct answer is C. ( (4,5) ). At ( (4,5) ), (2(4)+5=13) and (4+5=9). Therefore, this is the common point of both lines.
Step 3
Exam Tip
( (4,5) ) पर (2(4)+5=13) और (4+5=9)। इसलिए यह दोनों रेखाओं का सामान्य बिंदु है।
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एक सीधी रेखा का ग्राफ बनाने के लिए कम से कम कितने बिंदु चाहिए?
At least how many points are needed to draw the graph of a straight line?
#straight line
#two points
#graph construction
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A (3)
B (4)
C (1)
D (2)
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Step 1
Concept
Two correct points are sufficient to draw a straight line. A third point may be used only for checking.
Step 2
Why this answer is correct
The correct answer is D. (2). Two correct points are sufficient to draw a straight line. A third point may be used only for checking.
Step 3
Exam Tip
एक सीधी रेखा खींचने के लिए (2) सही बिंदु पर्याप्त होते हैं। तीसरा बिंदु केवल जाँच के लिए लिया जा सकता है।
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यदि दो रेखाएँ अलग-अलग समांतर हैं, तो हलों की संख्या क्या होगी?
If two lines are distinct and parallel, how many solutions will there be?
#parallel lines
#no solution
#inconsistent
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A कोई हल नहीं / No solution
B एक हल / One solution
C दो हल / Two solutions
D अनंत हल / Infinitely many solutions
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Distinct parallel lines have no common point. Therefore, such a pair has no solution.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Distinct parallel lines have no common point. Therefore, such a pair has no solution.
Step 3
Exam Tip
अलग-अलग समांतर रेखाओं का कोई सामान्य बिंदु नहीं होता। इसलिए ऐसे युग्म का कोई हल नहीं होता।
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यदि ग्राफ पर दोनों रेखाएँ बिल्कुल एक ही रेखा बनती हैं, तो हलों की संख्या क्या होगी?
If both lines on a graph form exactly the same line, how many solutions will there be?
#coincident lines
#infinite solutions
#consistent dependent
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A एक हल / One solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D केवल दो हल / Only two solutions
Explanation opens after your attempt
Correct Answer
B. अनंत हल / Infinitely many solutions
Step 1
Concept
All points on the same line satisfy both equations. Therefore, there are infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. अनंत हल / Infinitely many solutions. All points on the same line satisfy both equations. Therefore, there are infinitely many solutions.
Step 3
Exam Tip
एक ही रेखा के सभी बिंदु दोनों समीकरणों को संतुष्ट करते हैं। इसलिए अनंत हल मिलते हैं।
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ग्राफ पर दो रेखाएँ एक ही बिंदु पर कटें, तो युग्म कैसा कहलाता है?
If two lines cut at exactly one point on a graph, what is the pair called?
#consistent independent
#unique solution
#graph
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A असंगत / Inconsistent
B संगत और आश्रित / Consistent and dependent
C संगत और स्वतंत्र / Consistent and independent
D संपाती / Coincident
Explanation opens after your attempt
Correct Answer
C. संगत और स्वतंत्र / Consistent and independent
Step 1
Concept
One intersection point gives a unique solution. Hence, the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. संगत और स्वतंत्र / Consistent and independent. One intersection point gives a unique solution. Hence, the pair is consistent and independent.
Step 3
Exam Tip
एक प्रतिच्छेद बिंदु एक अद्वितीय हल देता है। इसलिए युग्म संगत और स्वतंत्र होता है।
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समीकरण (3x+3y=24) और (x+y=8) के ग्राफ का संबंध क्या है?
What is the relation between the graphs of (3x+3y=24) and (x+y=8)?
#same line
#coincident
#graphical method
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A समांतर और अलग / Parallel and distinct
B एक बिंदु पर कटते / Intersect at one point
C एक ही रेखा / Same line
D लंब रेखाएँ / Perpendicular lines
Explanation opens after your attempt
Correct Answer
C. एक ही रेखा / Same line
Step 1
Concept
Dividing the first equation by (3) gives (x+y=8). Therefore, both are the same line.
Step 2
Why this answer is correct
The correct answer is C. एक ही रेखा / Same line. Dividing the first equation by (3) gives (x+y=8). Therefore, both are the same line.
Step 3
Exam Tip
पहला समीकरण (3) से भाग देने पर (x+y=8) बनता है। इसलिए दोनों एक ही रेखा हैं।
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रेखाएँ (4x+y=9) और (4x+y=17) कैसी हैं?
What type of lines are (4x+y=9) and (4x+y=17)?
#parallel lines
#inconsistent
#no solution
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A संपाती / Coincident
B प्रतिच्छेदी / Intersecting
C समांतर / Parallel
D एक ही अक्ष / Same axis
Explanation opens after your attempt
Correct Answer
C. समांतर / Parallel
Step 1
Concept
Both have the same coefficients of (x) and (y), but different constants. Therefore, they are distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. समांतर / Parallel. Both have the same coefficients of (x) and (y), but different constants. Therefore, they are distinct parallel lines.
Step 3
Exam Tip
दोनों में (x) और (y) के गुणांक समान हैं लेकिन नियतांक अलग हैं। इसलिए वे अलग-अलग समांतर रेखाएँ हैं।
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रेखा (x-y=8) पर (y=3) रखने पर कौन-सा बिंदु मिलेगा?
For the line (x-y=8), which point is obtained when (y=3)?
#table value
#ordered pair
#graph plotting
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A ( (3,11) )
B ( (11,3) )
C ( (8,3) )
D ( (5,3) )
Explanation opens after your attempt
Correct Answer
B. ( (11,3) )
Step 1
Concept
From (x-3=8), (x=11), so the point is ( (11,3) ). Watch signs carefully in subtraction equations.
Step 2
Why this answer is correct
The correct answer is B. ( (11,3) ). From (x-3=8), (x=11), so the point is ( (11,3) ). Watch signs carefully in subtraction equations.
Step 3
Exam Tip
(x-3=8) से (x=11), इसलिए बिंदु ( (11,3) ) है। घटाव वाले समीकरणों में चिह्न ध्यान से देखें।
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समीकरण (3x-y=2) के लिए कौन-सा बिंदु रेखा पर है?
Which point lies on the line (3x-y=2)?
#point on line
#substitution
#linear equations
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A ( (2,2) )
B ( (1,2) )
C ( (3,7) )
D ( (4,8) )
Explanation opens after your attempt
Correct Answer
C. ( (3,7) )
Step 1
Concept
Substituting ( (3,7) ) gives (3(3)-7=2). The correct point is the one that satisfies the equation.
Step 2
Why this answer is correct
The correct answer is C. ( (3,7) ). Substituting ( (3,7) ) gives (3(3)-7=2). The correct point is the one that satisfies the equation.
Step 3
Exam Tip
( (3,7) ) रखने पर (3(3)-7=2)। सही बिंदु वही है जो समीकरण को संतुष्ट करे।
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बिंदु ( (0,12) ) किस अक्ष पर स्थित है?
On which axis does the point ( (0,12) ) lie?
#coordinate axes
#graph reading
#point
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A (x)-अक्ष / (x)-axis
B दोनों अक्ष / Both axes
C किसी अक्ष पर नहीं / On no axis
D (y)-अक्ष / (y)-axis
Explanation opens after your attempt
Correct Answer
D. (y)-अक्ष / (y)-axis
Step 1
Concept
In the point ( (0,12) ), (x=0), so it lies on the (y)-axis. Identifying axes helps in reading graphs.
Step 2
Why this answer is correct
The correct answer is D. (y)-अक्ष / (y)-axis. In the point ( (0,12) ), (x=0), so it lies on the (y)-axis. Identifying axes helps in reading graphs.
Step 3
Exam Tip
बिंदु ( (0,12) ) में (x=0), इसलिए यह (y)-अक्ष पर है। अक्ष पहचानना ग्राफ पढ़ने में मदद करता है।
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बिंदु ( (14,0) ) किस अक्ष पर स्थित है?
On which axis does the point ( (14,0) ) lie?
#coordinate axes
#x axis
#graph reading
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A (x)-अक्ष / (x)-axis
B (y)-अक्ष / (y)-axis
C दोनों अक्ष / Both axes
D किसी अक्ष पर नहीं / On no axis
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष / (x)-axis
Step 1
Concept
In the point ( (14,0) ), (y=0), so it lies on the (x)-axis. This is useful in intercept questions.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष / (x)-axis. In the point ( (14,0) ), (y=0), so it lies on the (x)-axis. This is useful in intercept questions.
Step 3
Exam Tip
बिंदु ( (14,0) ) में (y=0), इसलिए यह (x)-अक्ष पर है। अवरोधों के प्रश्नों में यह बात उपयोगी है।
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समीकरण (x+y=18) की रेखा किन दो अवरोधों से होकर गुजरती है?
Through which two intercepts does the line (x+y=18) pass?
#intercepts
#graph plotting
#linear equations
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A ( (9,0) ) और ( (0,9) )
B ( (18,0) ) और ( (0,18) )
C ( (1,18) ) और ( (18,1) )
D ( (0,0) ) और ( (18,18) )
Explanation opens after your attempt
Correct Answer
B. ( (18,0) ) और ( (0,18) )
Step 1
Concept
When (y=0), (x=18), and when (x=0), (y=18). These two intercepts are enough to draw the line.
Step 2
Why this answer is correct
The correct answer is B. ( (18,0) ) और ( (0,18) ). When (y=0), (x=18), and when (x=0), (y=18). These two intercepts are enough to draw the line.
Step 3
Exam Tip
(y=0) पर (x=18) और (x=0) पर (y=18)। ये दो अवरोध रेखा बनाने के लिए पर्याप्त हैं।
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समीकरण (3x+6y=24) की रेखा किन बिंदुओं से खींची जा सकती है?
Using which points can the line (3x+6y=24) be drawn?
#two points
#intercepts
#graph construction
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A ( (0,8) ) और ( (4,0) )
B ( (8,0) ) और ( (0,2) )
C ( (8,0) ) और ( (0,4) )
D ( (2,4) ) और ( (4,2) )
Explanation opens after your attempt
Correct Answer
C. ( (8,0) ) और ( (0,4) )
Step 1
Concept
When (y=0), (x=8), and when (x=0), (y=4). Once two correct points are found, the line is easy to draw.
Step 2
Why this answer is correct
The correct answer is C. ( (8,0) ) और ( (0,4) ). When (y=0), (x=8), and when (x=0), (y=4). Once two correct points are found, the line is easy to draw.
Step 3
Exam Tip
(y=0) पर (x=8) और (x=0) पर (y=4)। दो सही बिंदु मिलने पर रेखा आसानी से बनती है।
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रेखाएँ (x=5) और (x=12) के बारे में सही कथन कौन-सा है?
Which statement is correct about the lines (x=5) and (x=12)?
#vertical lines
#parallel
#no solution
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A दोनों मिलती हैं / Both intersect
B दोनों संपाती हैं / Both coincide
C दोनों (x)-अक्ष हैं / Both are (x)-axis
D दोनों समांतर हैं / Both are parallel
Explanation opens after your attempt
Correct Answer
D. दोनों समांतर हैं / Both are parallel
Step 1
Concept
Both are vertical lines but have different (x)-values. Therefore, they are parallel and do not meet.
Step 2
Why this answer is correct
The correct answer is D. दोनों समांतर हैं / Both are parallel. Both are vertical lines but have different (x)-values. Therefore, they are parallel and do not meet.
Step 3
Exam Tip
दोनों ऊर्ध्वाधर रेखाएँ हैं लेकिन उनके (x) मान अलग हैं। इसलिए वे समांतर हैं और नहीं मिलतीं।
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रेखाएँ (y=3) और (y=11) के लिए हलों की संख्या क्या होगी?
For the lines (y=3) and (y=11), how many solutions will there be?
#horizontal lines
#no solution
#parallel
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A अनंत हल / Infinitely many solutions
B कोई हल नहीं / No solution
C एक हल / One solution
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं / No solution
Step 1
Concept
Both horizontal lines are at different levels. They are parallel, so there is no common point.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Both horizontal lines are at different levels. They are parallel, so there is no common point.
Step 3
Exam Tip
दोनों क्षैतिज रेखाएँ अलग-अलग स्तरों पर हैं। वे समांतर हैं, इसलिए कोई सामान्य बिंदु नहीं है।
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यदि ग्राफ पर प्रतिच्छेद बिंदु ( (7,13) ) है, तो (y) का मान क्या है?
If the intersection point on the graph is ( (7,13) ), what is the value of (y)?
#coordinates
#graph reading
#solution
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A (7)
B (20)
C (13)
D (6)
Explanation opens after your attempt
Step 1
Concept
In the point ( (7,13) ), the second coordinate is (y). Therefore, (y=13).
Step 2
Why this answer is correct
The correct answer is C. (13). In the point ( (7,13) ), the second coordinate is (y). Therefore, (y=13).
Step 3
Exam Tip
बिंदु ( (7,13) ) में दूसरा निर्देशांक (y) होता है। इसलिए (y=13) है।
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यदि ग्राफ पर प्रतिच्छेद बिंदु ( (15,2) ) है, तो (x) का मान क्या है?
If the intersection point on the graph is ( (15,2) ), what is the value of (x)?
#coordinates
#graphical solution
#graph reading
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A (2)
B (13)
C (17)
D (15)
Explanation opens after your attempt
Step 1
Concept
In the point ( (15,2) ), the first coordinate is (x). Therefore, (x=15).
Step 2
Why this answer is correct
The correct answer is D. (15). In the point ( (15,2) ), the first coordinate is (x). Therefore, (x=15).
Step 3
Exam Tip
बिंदु ( (15,2) ) में पहला निर्देशांक (x) होता है। इसलिए (x=15) है।
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समीकरण (x+y=7) और (3x+3y=21) का ग्राफीय हल कैसा होगा?
What will be the graphical solution type of (x+y=7) and (3x+3y=21)?
#infinite solutions
#coincident lines
#graphical method
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A अनंत हल / Infinitely many solutions
B कोई हल नहीं / No solution
C एक हल / One solution
D केवल दो हल / Only two solutions
Explanation opens after your attempt
Correct Answer
A. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first, so the lines are coincident. Coincident lines have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is A. अनंत हल / Infinitely many solutions. The second equation is (3) times the first, so the lines are coincident. Coincident lines have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है, इसलिए रेखाएँ संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं।
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समीकरण (x-y=7) और (3x-3y=24) की रेखाएँ कैसी होंगी?
What type of lines are (x-y=7) and (3x-3y=24)?
#parallel lines
#no solution
#comparison
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A संपाती / Coincident
B समांतर / Parallel
C एक बिंदु पर कटती / Intersecting at one point
D एक ही अक्ष / Same axis
Explanation opens after your attempt
Correct Answer
B. समांतर / Parallel
Step 1
Concept
Multiplying the first equation by (3) gives (3x-3y=21), which differs from (3x-3y=24). Therefore, the lines are parallel.
Step 2
Why this answer is correct
The correct answer is B. समांतर / Parallel. Multiplying the first equation by (3) gives (3x-3y=21), which differs from (3x-3y=24). Therefore, the lines are parallel.
Step 3
Exam Tip
पहले समीकरण को (3) से गुणा करने पर (3x-3y=21) मिलता है, जो (3x-3y=24) से अलग है। इसलिए रेखाएँ समांतर हैं।
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रेखा (x+5y=15) पर (x=5) रखने पर कौन-सा बिंदु मिलेगा?
For the line (x+5y=15), which point is obtained when (x=5)?
#value table
#graph plotting
#linear equations
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A ( (5,2) )
B ( (2,5) )
C ( (5,1) )
D ( (1,5) )
Explanation opens after your attempt
Correct Answer
A. ( (5,2) )
Step 1
Concept
From (5+5y=15), (5y=10) and (y=2). Therefore, the point is ( (5,2) ).
Step 2
Why this answer is correct
The correct answer is A. ( (5,2) ). From (5+5y=15), (5y=10) and (y=2). Therefore, the point is ( (5,2) ).
Step 3
Exam Tip
(5+5y=15) से (5y=10) और (y=2)। इसलिए बिंदु ( (5,2) ) है।
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रेखा (5x+y=26) पर (y=1) रखने पर कौन-सा बिंदु मिलेगा?
For the line (5x+y=26), which point is obtained when (y=1)?
#substitution
#ordered pair
#graph plotting
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A ( (5,1) )
B ( (1,5) )
C ( (26,1) )
D ( (1,26) )
Explanation opens after your attempt
Correct Answer
A. ( (5,1) )
Step 1
Concept
From (5x+1=26), (5x=25) and (x=5). Therefore, the point is ( (5,1) ).
Step 2
Why this answer is correct
The correct answer is A. ( (5,1) ). From (5x+1=26), (5x=25) and (x=5). Therefore, the point is ( (5,1) ).
Step 3
Exam Tip
(5x+1=26) से (5x=25) और (x=5)। इसलिए बिंदु ( (5,1) ) 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
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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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रेखाएँ (x+4y=17) और (2x+4y=22) कहाँ मिलती हैं?
Where do the lines (x+4y=17) and (2x+4y=22) meet?
#graphical solution
#intersection
#linear equations
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A ( (5,3) )
B ( (3,5) )
C ( (4,4) )
D ( (6,2) )
Explanation opens after your attempt
Correct Answer
A. ( (5,3) )
Step 1
Concept
At ( (5,3) ), (5+4(3)=17) and (2(5)+4(3)=22). Hence, this is the graphical solution.
Step 2
Why this answer is correct
The correct answer is A. ( (5,3) ). At ( (5,3) ), (5+4(3)=17) and (2(5)+4(3)=22). Hence, this is the graphical solution.
Step 3
Exam Tip
( (5,3) ) पर (5+4(3)=17) और (2(5)+4(3)=22)। इसलिए यह ग्राफीय हल है।
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ग्राफीय विधि में पैमाना गलत लेने से सबसे पहले किसमें गलती हो सकती है?
In graphical method, taking a wrong scale can first cause an error in what?
#scale
#graph plotting
#common mistake
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A बिंदुओं को सही स्थान पर लगाने में / Plotting points at correct positions
B समीकरण लिखने में / Writing equations
C रेखा का नाम रखने में / Naming the line
D प्रश्न पढ़ने में / Reading the question
Explanation opens after your attempt
Correct Answer
A. बिंदुओं को सही स्थान पर लगाने में / Plotting points at correct positions
Step 1
Concept
A wrong scale can make point positions incorrect. So choose a clear scale before drawing the graph.
Step 2
Why this answer is correct
The correct answer is A. बिंदुओं को सही स्थान पर लगाने में / Plotting points at correct positions. A wrong scale can make point positions incorrect. So choose a clear scale before drawing the graph.
Step 3
Exam Tip
गलत पैमाना बिंदुओं की स्थिति गलत कर सकता है। इसलिए ग्राफ बनाने से पहले स्पष्ट पैमाना चुनें।
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यदि विद्यार्थी ( (9,4) ) को ( (4,9) ) लिख देता है, तो मुख्य गलती क्या है?
If a student writes ( (9,4) ) as ( (4,9) ), what is the main mistake?
#common mistake
#coordinates
#graph reading
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A अक्षों को नाम न देना / Not naming axes
B निर्देशांक उलटे लिखना / Writing coordinates in reverse order
C रेखा न खींचना / Not drawing the line
D पैमाना सही लेना / Taking correct scale
Explanation opens after your attempt
Correct Answer
B. निर्देशांक उलटे लिखना / Writing coordinates in reverse order
Step 1
Concept
A point is always written in ( (x,y) ) order. Reversing coordinates can make the solution wrong.
Step 2
Why this answer is correct
The correct answer is B. निर्देशांक उलटे लिखना / Writing coordinates in reverse order. A point is always written in ( (x,y) ) order. Reversing coordinates can make the solution wrong.
Step 3
Exam Tip
बिंदु हमेशा ( (x,y) ) क्रम में लिखा जाता है। निर्देशांक उलटे लिखने से हल गलत हो सकता है।
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रेखा (2x+2y=0) किस बिंदु से होकर अवश्य गुजरेगी?
The line (2x+2y=0) must pass through which point?
#origin
#point on line
#graph
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A ( (1,1) )
B ( (0,1) )
C ( (0,0) )
D ( (1,0) )
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Correct Answer
C. ( (0,0) )
Step 1
Concept
Substituting ( (0,0) ) gives (2(0)+2(0)=0), so the line passes through the origin. Checking the origin is easy.
Step 2
Why this answer is correct
The correct answer is C. ( (0,0) ). Substituting ( (0,0) ) gives (2(0)+2(0)=0), so the line passes through the origin. Checking the origin is easy.
Step 3
Exam Tip
( (0,0) ) रखने पर (2(0)+2(0)=0), इसलिए रेखा मूलबिंदु से गुजरती है। मूलबिंदु की जाँच आसान होती है।
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रेखा (3x-4y=0) पर कौन-सा बिंदु स्थित है?
Which point lies on the line (3x-4y=0)?
#point checking
#substitution
#linear equations
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A ( (3,4) )
B ( (4,3) )
C ( (1,2) )
D ( (2,1) )
Explanation opens after your attempt
Correct Answer
B. ( (4,3) )
Step 1
Concept
Substituting ( (4,3) ) gives (3(4)-4(3)=0). Substituting options in the equation is the fastest method.
Step 2
Why this answer is correct
The correct answer is B. ( (4,3) ). Substituting ( (4,3) ) gives (3(4)-4(3)=0). Substituting options in the equation is the fastest method.
Step 3
Exam Tip
( (4,3) ) रखने पर (3(4)-4(3)=0)। विकल्पों को समीकरण में रखना सबसे तेज तरीका है।
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ग्राफीय विधि में ठीक एक हल कब मिलता है?
When does graphical method give exactly one solution?
#unique solution
#intersecting lines
#graphical method
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A जब रेखाएँ संपाती हों / When lines are coincident
B जब रेखाएँ समांतर हों / When lines are parallel
C जब रेखाएँ एक बिंदु पर कटें / When lines intersect at one point
D जब अक्ष न बनाए जाएँ / When axes are not drawn
Explanation opens after your attempt
Correct Answer
C. जब रेखाएँ एक बिंदु पर कटें / When lines intersect at one point
Step 1
Concept
Exactly one solution is obtained when both lines intersect at one point. That point is the common solution of both equations.
Step 2
Why this answer is correct
The correct answer is C. जब रेखाएँ एक बिंदु पर कटें / When lines intersect at one point. Exactly one solution is obtained when both lines intersect at one point. That point is the common solution of both equations.
Step 3
Exam Tip
ठीक एक हल तब मिलता है जब दोनों रेखाएँ एक ही बिंदु पर कटती हैं। वही बिंदु दोनों समीकरणों का सामान्य हल होता है।
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ग्राफीय विधि में कोई हल कब नहीं मिलता?
When does graphical method give no solution?
#no solution
#parallel lines
#inconsistent
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A जब रेखाएँ एक बिंदु पर कटें / When lines intersect at one point
B जब रेखाएँ संपाती हों / When lines coincide
C जब रेखाएँ अलग-अलग समांतर हों / When lines are distinct parallel
D जब अक्षों को नाम दिया जाए / When axes are named
Explanation opens after your attempt
Correct Answer
C. जब रेखाएँ अलग-अलग समांतर हों / When lines are distinct parallel
Step 1
Concept
Distinct parallel lines never meet. Therefore, they have no common point.
Step 2
Why this answer is correct
The correct answer is C. जब रेखाएँ अलग-अलग समांतर हों / When lines are distinct parallel. Distinct parallel lines never meet. Therefore, they have no common point.
Step 3
Exam Tip
अलग-अलग समांतर रेखाएँ कभी नहीं मिलतीं। इसलिए उनका कोई सामान्य बिंदु नहीं होता।
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ग्राफीय विधि में अनंत हल कब मिलते हैं?
When does graphical method give infinitely many solutions?
#infinite solutions
#coincident lines
#graphical method
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A जब रेखाएँ अलग-अलग समांतर हों / When lines are distinct parallel
B जब रेखाएँ एक ही रेखा हों / When lines are the same line
C जब रेखाएँ केवल अक्षों को काटें / When lines only cut axes
D जब केवल एक बिंदु दिया हो / When only one point is given
Explanation opens after your attempt
Correct Answer
B. जब रेखाएँ एक ही रेखा हों / When lines are the same line
Step 1
Concept
All points on the same line satisfy both equations. Therefore, there are infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. जब रेखाएँ एक ही रेखा हों / When lines are the same line. All points on the same line satisfy both equations. Therefore, there are infinitely many solutions.
Step 3
Exam Tip
एक ही रेखा के सभी बिंदु दोनों समीकरणों को संतुष्ट करते हैं। इसलिए अनंत हल मिलते हैं।
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समीकरण (x+3y=15) और (x+y=7) का ग्राफीय हल कौन-सा है?
Which is the graphical solution of (x+3y=15) and (x+y=7)?
#graphical solution
#intersection
#linear equations
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A ( (3,4) )
B ( (4,3) )
C ( (5,2) )
D ( (6,1) )
Explanation opens after your attempt
Correct Answer
A. ( (3,4) )
Step 1
Concept
At ( (3,4) ), (3+3(4)=15) and (3+4=7). This is the intersection point of both lines.
Step 2
Why this answer is correct
The correct answer is A. ( (3,4) ). At ( (3,4) ), (3+3(4)=15) and (3+4=7). This is the intersection point of both lines.
Step 3
Exam Tip
( (3,4) ) पर (3+3(4)=15) और (3+4=7)। यही दोनों रेखाओं का प्रतिच्छेद बिंदु है।
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यदि रेखाएँ (2x+y=16) और (x+y=10) ग्राफ पर खींची जाएँ, तो उनका प्रतिच्छेद बिंदु कौन-सा होगा?
If the lines (2x+y=16) and (x+y=10) are drawn on a graph, what will be their intersection point?
#intersection point
#graphical solution
#linear equations
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A ( (4,6) )
B ( (5,5) )
C ( (6,4) )
D ( (7,3) )
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Correct Answer
C. ( (6,4) )
Step 1
Concept
At ( (6,4) ), (2(6)+4=16) and (6+4=10). Therefore, this is the graphical solution.
Step 2
Why this answer is correct
The correct answer is C. ( (6,4) ). At ( (6,4) ), (2(6)+4=16) and (6+4=10). Therefore, this is the graphical solution.
Step 3
Exam Tip
( (6,4) ) पर (2(6)+4=16) और (6+4=10)। इसलिए यही ग्राफीय हल है।
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