असमानताओं \(x\geq 0\), \(y\geq 0\), \(2x+y\geq 8\), \(x+3y\geq 9\) के हल-क्षेत्र में कौन सा बिंदु शामिल है?
Which point is included in the solution region of \(x\geq 0\), \(y\geq 0\), \(2x+y\geq 8\), and \(x+3y\geq 9\)?
#linear inequalities
#point testing
#unbounded region
#first quadrant
A ((2,2))
B ((3,1))
C ((1,3))
D ((4,2))
Explanation opens after your attempt
Correct Answer
D. ((4,2))
Step 1
Concept
At ((4,2)), (2x+y=10) and (x+3y=10). Choose the final option only after substituting the point in all inequalities.
Step 2
Why this answer is correct
The correct answer is D. ((4,2)). At ((4,2)), (2x+y=10) and (x+3y=10). Choose the final option only after substituting the point in all inequalities.
Step 3
Exam Tip
((4,2)) पर (2x+y=10) और (x+3y=10) मिलता है। सभी असमानताओं में बिंदु रखकर ही अंतिम विकल्प चुनें।
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कौन सा बिंदु (x+2y=8) सीमा पर है और साथ में \(x-y\leq 1\) को भी संतुष्ट करता है?
Which point lies on the boundary (x+2y=8) and also satisfies \(x-y\leq 1\)?
#linear inequalities
#boundary point
#point testing
#solution region
A ((2,3))
B ((4,2))
C ((6,1))
D ((8,0))
Explanation opens after your attempt
Correct Answer
A. ((2,3))
Step 1
Concept
At ((2,3)), (x+2y=8) and (x-y=-1). Thus it lies on the boundary and also satisfies the second inequality.
Step 2
Why this answer is correct
The correct answer is A. ((2,3)). At ((2,3)), (x+2y=8) and (x-y=-1). Thus it lies on the boundary and also satisfies the second inequality.
Step 3
Exam Tip
((2,3)) पर (x+2y=8) और (x-y=-1) है। इसलिए यह सीमा पर भी है और दूसरी असमानता को भी पूरा करता है।
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यदि ((k,2)) बिंदु \(2x+y\leq 10\) और (x-y>1) दोनों का हल है, तो (k) की सही सीमा कौन सी है?
If the point ((k,2)) is a solution of both \(2x+y\leq 10\) and (x-y>1), which range of (k) is correct?
#linear inequalities
#parameter
#point testing
#range
A \(k\leq 3\)
B \(3<k\leq 4\)
C (k>4)
D (k=3)
Explanation opens after your attempt
Correct Answer
B. \(3<k\leq 4\)
Step 1
Concept
Substitution gives \(2k+2\leq 10\) and (k-2>1). Hence \(k\leq 4\) and (k>3).
Step 2
Why this answer is correct
The correct answer is B. \(3<k\leq 4\). Substitution gives \(2k+2\leq 10\) and (k-2>1). Hence \(k\leq 4\) and (k>3).
Step 3
Exam Tip
बिंदु रखने पर \(2k+2\leq 10\) और (k-2>1) मिलता है। इसलिए \(k\leq 4\) और (k>3) होगा।
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कौन सा बिंदु \(x+2y\geq 6\), \(x-y\leq 2\), \(y\leq 4\), \(x\geq 0\) का हल नहीं है?
Which point is not a solution of \(x+2y\geq 6\), \(x-y\leq 2\), \(y\leq 4\), and \(x\geq 0\)?
#linear inequalities
#point testing
#not solution
#feasible region
A ((2,2))
B ((5,1))
C ((1,4))
D ((0,3))
Explanation opens after your attempt
Correct Answer
B. ((5,1))
Step 1
Concept
At ((5,1)), (x-y=4), which is greater than (2). In option testing, one failed inequality excludes the point.
Step 2
Why this answer is correct
The correct answer is B. ((5,1)). At ((5,1)), (x-y=4), which is greater than (2). In option testing, one failed inequality excludes the point.
Step 3
Exam Tip
((5,1)) पर (x-y=4) है जो (2) से बड़ा है। विकल्प जांच में एक भी गलत असमानता बिंदु को बाहर कर देती है।
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बिंदु ((2,3)), असमानताओं \(x+y\leq 5\), \(x\geq 1\), \(y\leq 4\) के सापेक्ष कहाँ स्थित है?
Where is the point ((2,3)) located with respect to \(x+y\leq 5\), \(x\geq 1\), and \(y\leq 4\)?
#linear inequalities
#boundary point
#point testing
#solution region
A हल-क्षेत्र में और सीमा (x+y=5) पर / In the solution region and on the boundary (x+y=5)
B हल-क्षेत्र में लेकिन किसी सीमा पर नहीं / In the solution region but not on any boundary
C हल-क्षेत्र के बाहर / Outside the solution region
D केवल (y=4) सीमा पर / Only on the boundary (y=4)
Explanation opens after your attempt
Correct Answer
A. हल-क्षेत्र में और सीमा (x+y=5) पर / In the solution region and on the boundary (x+y=5)
Step 1
Concept
At ((2,3)), (x+y=5), and the remaining conditions also hold. Therefore it is a solution point on the boundary.
Step 2
Why this answer is correct
The correct answer is A. हल-क्षेत्र में और सीमा (x+y=5) पर / In the solution region and on the boundary (x+y=5). At ((2,3)), (x+y=5), and the remaining conditions also hold. Therefore it is a solution point on the boundary.
Step 3
Exam Tip
((2,3)) पर (x+y=5) है और बाकी शर्तें भी पूरी हैं। इसलिए यह सीमा पर स्थित हल-बिंदु है।
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कौन सा बिंदु \(2x+y\geq 7\), \(x+2y\leq 12\), \(x\geq 0\), \(y\geq 0\) का हल है?
Which point is a solution of \(2x+y\geq 7\), \(x+2y\leq 12\), \(x\geq 0\), and \(y\geq 0\)?
#linear inequalities
#point testing
#solution region
#first quadrant
A ((1,2))
B ((3,3))
C ((5,4))
D ((0,6))
Explanation opens after your attempt
Correct Answer
B. ((3,3))
Step 1
Concept
Substituting ((3,3)) gives (2x+y=9) and (x+2y=9). In point testing, check every inequality separately.
Step 2
Why this answer is correct
The correct answer is B. ((3,3)). Substituting ((3,3)) gives (2x+y=9) and (x+2y=9). In point testing, check every inequality separately.
Step 3
Exam Tip
((3,3)) रखने पर (2x+y=9) और (x+2y=9) मिलता है। बिंदु जांच में सभी असमानताओं को अलग-अलग जांचें।
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हल-क्षेत्र \(x\geq 0\), \(y\geq 0\), \(x+2y\geq 6\), \(2x+y\geq 6\) में कौन सा बिंदु निश्चित रूप से शामिल है?
Which point is definitely included in the solution region \(x\geq 0\), \(y\geq 0\), \(x+2y\geq 6\), and \(2x+y\geq 6\)?
#linear inequalities
#point testing
#unbounded region
#first quadrant
A ((1,1))
B ((2,1))
C ((1,4))
D ((0,2))
Explanation opens after your attempt
Correct Answer
C. ((1,4))
Step 1
Concept
At ((1,4)), (x+2y=9) and (2x+y=6). It satisfies all conditions and lies in the region including the boundary.
Step 2
Why this answer is correct
The correct answer is C. ((1,4)). At ((1,4)), (x+2y=9) and (2x+y=6). It satisfies all conditions and lies in the region including the boundary.
Step 3
Exam Tip
((1,4)) पर (x+2y=9) और (2x+y=6) है। यह सभी शर्तें पूरी करता है और सीमा सहित क्षेत्र में आता है।
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कौन सा बिंदु \(2x+5y\leq 20\), \(x-y\geq -1\), \(x\geq 0\), \(y\geq 0\) का हल नहीं है?
Which point is not a solution of \(2x+5y\leq 20\), \(x-y\geq -1\), \(x\geq 0\), and \(y\geq 0\)?
#linear inequalities
#point testing
#solution region
#expert trap
A ((5,1))
B ((2,3))
C ((0,1))
D ((4,2))
Explanation opens after your attempt
Correct Answer
B. ((2,3))
Step 1
Concept
At ((2,3)), (2x+5y=19) and (x-y=-1), so it cannot be rejected. For such questions, test all conditions carefully.
Step 2
Why this answer is correct
The correct answer is B. ((2,3)). At ((2,3)), (2x+5y=19) and (x-y=-1), so it cannot be rejected. For such questions, test all conditions carefully.
Step 3
Exam Tip
((2,3)) पर (2x+5y=19) सही है लेकिन (x-y=-1) भी सही है इसलिए इसे हटाया नहीं जा सकता। विकल्प जांच में गलत विकल्प पहचानने के लिए सभी शर्तें सावधानी से जांचें।
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यदि \(x+2y\leq 10\), \(x+y\geq 6\), \(y\geq 1\) हैं, तो बिंदु ((4,2)) का स्थान क्या है?
If \(x+2y\leq 10\), \(x+y\geq 6\), and \(y\geq 1\), what is the position of ((4,2))?
#linear inequalities
#boundary classification
#point testing
#solution region
A हल-क्षेत्र के अंदर और किसी सीमा पर नहीं / Inside the solution region and not on any boundary
B हल-क्षेत्र के बाहर / Outside the solution region
C केवल (x+y=6) सीमा पर / Only on the boundary (x+y=6)
D केवल (x+2y=10) सीमा पर / Only on the boundary (x+2y=10)
Explanation opens after your attempt
Correct Answer
C. केवल (x+y=6) सीमा पर / Only on the boundary (x+y=6)
Step 1
Concept
At ((4,2)), (x+y=6), and the remaining conditions also hold. So it is a solution point on one boundary.
Step 2
Why this answer is correct
The correct answer is C. केवल (x+y=6) सीमा पर / Only on the boundary (x+y=6). At ((4,2)), (x+y=6), and the remaining conditions also hold. So it is a solution point on one boundary.
Step 3
Exam Tip
((4,2)) पर (x+y=6) है और बाकी शर्तें भी पूरी हैं। इसलिए यह एक सीमा पर स्थित हल-बिंदु है।
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कौन सा बिंदु (y< -x+5) और (y> x-1) दोनों के बीच के खुले क्षेत्र में है?
Which point lies in the open region between (y< -x+5) and (y> x-1)?
#linear inequalities
#open region
#point testing
#intersecting lines
A ((3,2))
B ((2,2))
C ((1,4))
D ((4,0))
Explanation opens after your attempt
Correct Answer
B. ((2,2))
Step 1
Concept
At ((2,2)), both (2<3) and (2>1) are true. Boundary points are not included in strict inequalities.
Step 2
Why this answer is correct
The correct answer is B. ((2,2)). At ((2,2)), both (2<3) and (2>1) are true. Boundary points are not included in strict inequalities.
Step 3
Exam Tip
((2,2)) पर (2<3) और (2>1) दोनों सही हैं। कठोर असमानता में सीमा-बिंदु शामिल नहीं होते।
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कौन सा बिंदु \(x-2y\leq -4\), \(x+y\geq 3\), \(y\leq 5\) का हल है?
Which point is a solution of \(x-2y\leq -4\), \(x+y\geq 3\), and \(y\leq 5\)?
#linear inequalities
#point testing
#solution region
#multiple inequalities
A ((0,2))
B ((4,1))
C ((2,4))
D ((-3,6))
Explanation opens after your attempt
Correct Answer
C. ((2,4))
Step 1
Concept
Substituting ((2,4)) satisfies all three inequalities. In option checking, test every inequality separately.
Step 2
Why this answer is correct
The correct answer is C. ((2,4)). Substituting ((2,4)) satisfies all three inequalities. In option checking, test every inequality separately.
Step 3
Exam Tip
((2,4)) रखने पर तीनों असमानताएं सही मिलती हैं। विकल्प जांच में हर असमानता अलग से जांचें।
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कौन-सा बिंदु (y>x) और (x+y<6) दोनों को संतुष्ट करता है?
Which point satisfies both (y>x) and (x+y<6)?
#linear inequalities
#point testing
#strict inequalities
#class 11
A ((2,3))
B ((3,2))
C ((4,3))
D ((1,5))
Explanation opens after your attempt
Correct Answer
A. ((2,3))
Step 1
Concept
For ((2,3)), both (3>2) and (2+3<6) are true. Exam tip: Immediately reject options with equality on open boundaries.
Step 2
Why this answer is correct
The correct answer is A. ((2,3)). For ((2,3)), both (3>2) and (2+3<6) are true. Exam tip: Immediately reject options with equality on open boundaries.
Step 3
Exam Tip
((2,3)) में (3>2) और (2+3<6) दोनों सत्य हैं। परीक्षा सुझाव: खुली सीमा पर बराबरी वाले विकल्प तुरंत हटाएँ।
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बिंदु ((3,2)) तंत्र (x+2y<7), \(2x+y\leq 8\) के लिए क्यों मान्य नहीं है?
Why is the point ((3,2)) not valid for the system (x+2y<7), \(2x+y\leq 8\)?
#linear inequalities
#strict inequality
#point testing
#class 11
A क्योंकि \(2x+y\leq 8\) असत्य है / Because \(2x+y\leq 8\) is false
B क्योंकि (x+2y<7) में समानता मिलती है / Because equality occurs in (x+2y<7)
C क्योंकि दोनों असमानताएँ असत्य हैं / Because both inequalities are false
D क्योंकि बिंदु प्रथम चतुर्थांश में नहीं है / Because the point is not in the first quadrant
Explanation opens after your attempt
Correct Answer
B. क्योंकि (x+2y<7) में समानता मिलती है / Because equality occurs in (x+2y<7)
Step 1
Concept
At ((3,2)), (x+2y=7), but (x+2y<7) excludes the boundary. Exam tip: Remove equality points in strict inequalities.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि (x+2y<7) में समानता मिलती है / Because equality occurs in (x+2y<7). At ((3,2)), (x+2y=7), but (x+2y<7) excludes the boundary. Exam tip: Remove equality points in strict inequalities.
Step 3
Exam Tip
((3,2)) पर (x+2y=7) है लेकिन (x+2y<7) में सीमा शामिल नहीं होती। परीक्षा सुझाव: कठोर असमानता में बराबरी वाले बिंदु हटा दें।
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कौन-सा बिंदु (2x-y<1), \(x+y\geq 4\) दोनों असमानताओं को संतुष्ट करता है?
Which point satisfies both inequalities (2x-y<1), \(x+y\geq 4\)?
#linear inequalities
#point testing
#common solution
#class 11
A ((1,3))
B ((2,2))
C ((0,3))
D ((3,1))
Explanation opens after your attempt
Correct Answer
A. ((1,3))
Step 1
Concept
At ((1,3)), both (2-3<1) and \(1+3\geq 4\) are true. Exam tip: Substitute options directly into the inequalities.
Step 2
Why this answer is correct
The correct answer is A. ((1,3)). At ((1,3)), both (2-3<1) and \(1+3\geq 4\) are true. Exam tip: Substitute options directly into the inequalities.
Step 3
Exam Tip
((1,3)) पर (2-3<1) और \(1+3\geq 4\) दोनों सत्य हैं। परीक्षा सुझाव: विकल्पों को सीधे असमानताओं में रखकर जाँचें।
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बिंदु ((2,3)) तंत्र \(x+2y\leq 8\), (3x-y>1) के लिए कौन-सा निष्कर्ष देता है?
What conclusion does the point ((2,3)) give for the system \(x+2y\leq 8\), (3x-y>1)?
#linear inequalities
#point testing
#boundary point
#class 11
A दोनों असमानताओं को असत्य करता है / It makes both inequalities false
B केवल दूसरी असमानता को सत्य करता है / It makes only the second inequality true
C हल क्षेत्र में है और पहली सीमा पर है / It is in the solution region and on the first boundary
D हल क्षेत्र में नहीं है क्योंकि दूसरी सीमा पर है / It is not in the solution region because it is on the second boundary
Explanation opens after your attempt
Correct Answer
C. हल क्षेत्र में है और पहली सीमा पर है / It is in the solution region and on the first boundary
Step 1
Concept
Since \(2+2\cdot3=8\) and \(3\cdot2-3=3>1\), the point is valid. Exam tip: A boundary point is excluded only for a strict inequality.
Step 2
Why this answer is correct
The correct answer is C. हल क्षेत्र में है और पहली सीमा पर है / It is in the solution region and on the first boundary. Since \(2+2\cdot3=8\) and \(3\cdot2-3=3>1\), the point is valid. Exam tip: A boundary point is excluded only for a strict inequality.
Step 3
Exam Tip
\(2+2\cdot3=8\) और \(3\cdot2-3=3>1\) इसलिए बिंदु मान्य है। परीक्षा सुझाव: सीमा पर बिंदु तभी हटता है जब असमानता कठोर हो।
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कौन-सा बिंदु (2x+y<7), \(x-y\geq 1\), (y>0) के हल-क्षेत्र में है?
Which point lies in the solution region of (2x+y<7), \(x-y\geq 1\), (y>0)?
#linear inequalities
#point testing
#class 11
A बिंदु ((2,2)) / Point ((2,2))
B बिंदु ((3,1)) / Point ((3,1))
C बिंदु ((1,1)) / Point ((1,1))
D बिंदु ((4,0)) / Point ((4,0))
Explanation opens after your attempt
Correct Answer
B. बिंदु ((3,1)) / Point ((3,1))
Step 1
Concept
For ((3,1)), (2x+y=7), so it fails the strict inequality. This item needs a point strictly inside the region.
Step 2
Why this answer is correct
The correct answer is B. बिंदु ((3,1)) / Point ((3,1)). For ((3,1)), (2x+y=7), so it fails the strict inequality. This item needs a point strictly inside the region.
Step 3
Exam Tip
((3,1)) रखने पर (7<7) नहीं बल्कि (2x+y=7) होता है, इसलिए यह गलत है। सही जांच से कोई विकल्प नहीं?
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ग्राफ में कौन सा बिंदु \(y \le x-1\) और \(y \ge -2\) दोनों को संतुष्ट करता है?
Which point satisfies both \(y \le x-1\) and \(y \ge -2\) on the graph?
#point testing
#between boundaries
#solution
A ((0,0))
B ((1,-3))
C ((3,1))
D ((2,4))
Explanation opens after your attempt
Correct Answer
C. ((3,1))
Step 1
Concept
At ((3,1)), \(1 \le 2\) and \(1 \ge -2\), both true. A solution point must lie between the two boundaries.
Step 2
Why this answer is correct
The correct answer is C. ((3,1)). At ((3,1)), \(1 \le 2\) and \(1 \ge -2\), both true. A solution point must lie between the two boundaries.
Step 3
Exam Tip
((3,1)) पर \(1 \le 2\) और \(1 \ge -2\), दोनों सत्य हैं। दोनों सीमाओं के बीच आने वाला बिंदु ही समाधान है।
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कौन सा बिंदु रेखा (x+2y=10) के नीचे है?
Which point lies below the line (x+2y=10)?
#below line
#half plane
#point testing
A ((4,4))
B ((8,2))
C ((2,3))
D ((0,6))
Explanation opens after your attempt
Correct Answer
C. ((2,3))
Step 1
Concept
At ((2,3)), (x+2y=8), which is less than (10), so it lies in the lower half-plane. Below can also be checked by smaller (y)-values.
Step 2
Why this answer is correct
The correct answer is C. ((2,3)). At ((2,3)), (x+2y=8), which is less than (10), so it lies in the lower half-plane. Below can also be checked by smaller (y)-values.
Step 3
Exam Tip
((2,3)) पर (x+2y=8), जो (10) से कम है और इसलिए रेखा के नीचे वाले अर्ध-समतल में है। नीचे की जांच (y) के छोटे मान से भी की जा सकती है।
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कौन सा बिंदु क्षेत्र \(x-y \le 2\) और \(x+y \ge 4\) दोनों में स्थित है?
Which point lies in both regions \(x-y \le 2\) and \(x+y \ge 4\)?
#common solution
#point testing
#two inequalities
A ((3,1))
B ((1,2))
C ((4,3))
D ((0,5))
Explanation opens after your attempt
Correct Answer
C. ((4,3))
Step 1
Concept
At ((4,3)), (x-y=1) and (x+y=7), so both conditions are true. Algebraic checking is faster before graphing.
Step 2
Why this answer is correct
The correct answer is C. ((4,3)). At ((4,3)), (x-y=1) and (x+y=7), so both conditions are true. Algebraic checking is faster before graphing.
Step 3
Exam Tip
((4,3)) पर (x-y=1) और (x+y=7), इसलिए दोनों शर्तें सत्य हैं। ग्राफ से पहले बीजगणितीय जांच तेज होती है।
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रेखा (3x+2y=18) के लिए कौन सा बिंदु अर्ध-समतल \(3x+2y \ge 18\) में आएगा?
For the line (3x+2y=18), which point lies in the half-plane \(3x+2y \ge 18\)?
#point testing
#half plane
#linear inequality
A ((2,3))
B ((4,2))
C ((5,2))
D ((1,5))
Explanation opens after your attempt
Correct Answer
C. ((5,2))
Step 1
Concept
Substituting ((5,2)) gives (3(5)+2(2)=19), so \(19 \ge 18\) is true. Check options by direct substitution.
Step 2
Why this answer is correct
The correct answer is C. ((5,2)). Substituting ((5,2)) gives (3(5)+2(2)=19), so \(19 \ge 18\) is true. Check options by direct substitution.
Step 3
Exam Tip
((5,2)) रखने पर (3(5)+2(2)=19), इसलिए \(19 \ge 18\) सत्य है। विकल्पों में सीधे मान रखकर जांचें।
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असमिका (x+ y>0) के लिए कौन-सा बिंदु हल क्षेत्र में है?
Which point lies in the solution region of (x+y>0)?
#strict inequality
#point testing
#solution region
A ((2,-1))
B ((-3,1))
C ((0,0))
D ((-2,0))
Explanation opens after your attempt
Correct Answer
A. ((2,-1))
Step 1
Concept
For ((2,-1)), (2+(-1)=1>0). Reject boundary points in strict inequalities.
Step 2
Why this answer is correct
The correct answer is A. ((2,-1)). For ((2,-1)), (2+(-1)=1>0). Reject boundary points in strict inequalities.
Step 3
Exam Tip
((2,-1)) के लिए (2+(-1)=1>0) है। परीक्षा में strict inequality में boundary point reject करें।
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कौन-सा बिंदु असमिकाओं \(x+y\le 5\) और \(x\ge y\) दोनों को संतुष्ट करता है?
Which point satisfies both inequalities \(x+y\le 5\) and \(x\ge y\)?
#point testing
#system of inequalities
#graph
A ((3,1))
B ((4,3))
C ((1,4))
D ((2,4))
Explanation opens after your attempt
Correct Answer
A. ((3,1))
Step 1
Concept
For ((3,1)), both \(3+1\le 5\) and \(3\ge 1\) are true. Substitute options directly in exams.
Step 2
Why this answer is correct
The correct answer is A. ((3,1)). For ((3,1)), both \(3+1\le 5\) and \(3\ge 1\) are true. Substitute options directly in exams.
Step 3
Exam Tip
((3,1)) के लिए \(3+1\le 5\) और \(3\ge 1\) दोनों सत्य हैं। परीक्षा में विकल्पों को सीधे substitute करें।
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बिंदु ((2,2)) असमानता \(x+2y\leq 5\) के लिए कौन सा निष्कर्ष देता है?
What conclusion does the point ((2,2)) give for \(x+2y\leq 5\)?
#linear inequalities
#point testing
#not solution
#class 11
A यह हल क्षेत्र में है / It is in the solution region
B यह सीमा रेखा पर है / It is on the boundary line
C यह हल क्षेत्र में नहीं है / It is not in the solution region
D यह मूल बिंदु है / It is the origin
Explanation opens after your attempt
Correct Answer
C. यह हल क्षेत्र में नहीं है / It is not in the solution region
Step 1
Concept
Substituting ((2,2)) gives \(6\leq 5\), which is false, so the point is not a solution. Avoid addition mistakes in exams.
Step 2
Why this answer is correct
The correct answer is C. यह हल क्षेत्र में नहीं है / It is not in the solution region. Substituting ((2,2)) gives \(6\leq 5\), which is false, so the point is not a solution. Avoid addition mistakes in exams.
Step 3
Exam Tip
((2,2)) रखने पर \(6\leq 5\) असत्य है, इसलिए बिंदु हल में नहीं है। परीक्षा में जोड़ने की गलती से बचें।
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असमानता \(x+2y\geq 4\) में कौन सा बिंदु हल क्षेत्र में है?
Which point lies in the solution region of \(x+2y\geq 4\)?
#linear inequalities
#point testing
#solution region
#class 11
A ((0,0))
B ((1,1))
C ((2,0))
D ((0,3))
Explanation opens after your attempt
Correct Answer
D. ((0,3))
Step 1
Concept
Substituting ((0,3)) gives \(6\geq 4\), which is true. Use quick substitution to check options in exams.
Step 2
Why this answer is correct
The correct answer is D. ((0,3)). Substituting ((0,3)) gives \(6\geq 4\), which is true. Use quick substitution to check options in exams.
Step 3
Exam Tip
((0,3)) रखने पर \(6\geq 4\) सत्य है। परीक्षा में विकल्पों को जल्दी जांचने के लिए सरल गणना करें।
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असमानता \(3x+2y\leq 6\) में कौन सा बिंदु हल क्षेत्र में नहीं है?
Which point is not in the solution region of \(3x+2y\leq 6\)?
#linear inequalities
#point testing
#not solution
#class 11
A ((0,0))
B ((1,1))
C ((3,0))
D ((0,3))
Explanation opens after your attempt
Correct Answer
C. ((3,0))
Step 1
Concept
Substituting ((3,0)) gives \(9\leq 6\), which is false, so it is not in the solution region. In exams, find the option that makes the inequality false.
Step 2
Why this answer is correct
The correct answer is C. ((3,0)). Substituting ((3,0)) gives \(9\leq 6\), which is false, so it is not in the solution region. In exams, find the option that makes the inequality false.
Step 3
Exam Tip
((3,0)) रखने पर \(9\leq 6\) असत्य है, इसलिए यह हल क्षेत्र में नहीं है। परीक्षा में सभी दिए बिंदुओं में केवल असत्य मान खोजें।
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असमानता \(y\leq -x+3\) में बिंदु ((1,1)) किस स्थिति में है?
What is the status of the point ((1,1)) for \(y\leq -x+3\)?
#linear inequalities
#point testing
#solution region
#class 11
A हल क्षेत्र में नहीं / Not in solution region
B सीमा रेखा से ऊपर / Above the boundary line
C हल क्षेत्र में / In the solution region
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
C. हल क्षेत्र में / In the solution region
Step 1
Concept
Substituting ((1,1)) gives \(1\leq 2\), which is true, so the point is in the solution region. Calculate the right side carefully in exams.
Step 2
Why this answer is correct
The correct answer is C. हल क्षेत्र में / In the solution region. Substituting ((1,1)) gives \(1\leq 2\), which is true, so the point is in the solution region. Calculate the right side carefully in exams.
Step 3
Exam Tip
((1,1)) रखने पर \(1\leq 2\) सत्य है, इसलिए बिंदु हल क्षेत्र में है। परीक्षा में दाईं ओर का मान सावधानी से निकालें।
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