B. बिंदु (\left\(\frac{8}{3},\frac{8}{3}\right\))/Point (\left\(\frac{8}{3},\frac{8}{3}\right\))
Step 1
Concept
Solving the two boundary lines together gives \(x=y=\frac{8}{3}\). In exams, find vertices by treating boundary lines as equations.
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(\frac{8}{3},\frac{8}{3}\right\)) / Point (\left\(\frac{8}{3},\frac{8}{3}\right\)). Solving the two boundary lines together gives \(x=y=\frac{8}{3}\). In exams, find vertices by treating boundary lines as equations.
Step 3
Exam Tip
दोनों रेखाओं को साथ हल करने पर \(x=y=\frac{8}{3}\) मिलता है। परीक्षा में शीर्ष निकालने के लिए सीमा रेखाओं को समीकरण मानें।
A. सीमा रेखा ठोस होगी और मूलबिंदु वाला भाग छायांकित होगा/Boundary is solid and the side containing origin is shaded
Step 1
Concept
Since \(0 \le 12\) is true, the half-plane containing the origin is taken. In exams, check the boundary line first and then use a test point.
Step 2
Why this answer is correct
The correct answer is A. सीमा रेखा ठोस होगी और मूलबिंदु वाला भाग छायांकित होगा / Boundary is solid and the side containing origin is shaded. Since \(0 \le 12\) is true, the half-plane containing the origin is taken. In exams, check the boundary line first and then use a test point.
Step 3
Exam Tip
\(0 \le 12\) सत्य है, इसलिए मूलबिंदु वाला अर्ध-तल लिया जाता है। परीक्षा में पहले सीमा रेखा और फिर परीक्षण-बिंदु जांचें।
D. (3x+y=6) टूटी और (x-y=2) ठोस होगी/(3x+y=6) dashed and (x-y=2) solid
Step 1
Concept
A strict inequality (>) excludes the boundary, so its line is dashed. The inequality \(\leq\) includes the boundary, so its line is solid.
Step 2
Why this answer is correct
The correct answer is D. (3x+y=6) टूटी और (x-y=2) ठोस होगी / (3x+y=6) dashed and (x-y=2) solid. A strict inequality (>) excludes the boundary, so its line is dashed. The inequality \(\leq\) includes the boundary, so its line is solid.
Step 3
Exam Tip
कड़ी असमानता (>) के लिए सीमा शामिल नहीं होती, इसलिए रेखा टूटी होती है। \(\leq\) में सीमा शामिल होती है, इसलिए रेखा ठोस होती है।
A. वह आधा तल जिसमें ((0,0)) है/The half-plane containing ((0,0))
Step 1
Concept
Substituting ((0,0)) gives \(0\geq 6\), which is false, so the half-plane containing the origin is rejected. In exams, choose a test point not lying on the boundary.
Step 2
Why this answer is correct
The correct answer is A. वह आधा तल जिसमें ((0,0)) है / The half-plane containing ((0,0)). Substituting ((0,0)) gives \(0\geq 6\), which is false, so the half-plane containing the origin is rejected. In exams, choose a test point not lying on the boundary.
Step 3
Exam Tip
((0,0)) रखने पर \(0\geq 6\) गलत है, इसलिए मूल वाला आधा तल हटेगा। परीक्षा में जांच-बिंदु सीमा रेखा पर नहीं होना चाहिए।
From \(3x-2y \ge 6\), we get \(y \le \frac{3x-6}{2}\). When dividing by a negative number, the inequality sign reverses.
Step 2
Why this answer is correct
The correct answer is B. \(y \le \frac{3x-6}{2}\). From \(3x-2y \ge 6\), we get \(y \le \frac{3x-6}{2}\). When dividing by a negative number, the inequality sign reverses.
Step 3
Exam Tip
\(3x-2y \ge 6\) से \(y \le \frac{3x-6}{2}\) मिलता है। ऋणात्मक संख्या से भाग देते समय असमानता का चिन्ह बदलता है।
Boundary intersections give ((2,3)), ((4,1)), and ((4,3)). On a graph, keep only intersections satisfying all inequalities.
Step 2
Why this answer is correct
The correct answer is B. ((2,3)), ((4,1)), ((4,3)). Boundary intersections give ((2,3)), ((4,1)), and ((4,3)). On a graph, keep only intersections satisfying all inequalities.
Step 3
Exam Tip
सीमाओं के प्रतिच्छेद से ((2,3)), ((4,1)), ((4,3)) मिलते हैं। ग्राफ में केवल वे प्रतिच्छेद लें जो सभी असमानताओं को संतुष्ट करें।
B. रेखा (4x+y=10) बिंदुदार होगी/The line (4x+y=10) is dotted
Step 1
Concept
The sign (<) is strict, so the boundary line is not included. Such a boundary is drawn dotted in the graph.
Step 2
Why this answer is correct
The correct answer is B. रेखा (4x+y=10) बिंदुदार होगी / The line (4x+y=10) is dotted. The sign (<) is strict, so the boundary line is not included. Such a boundary is drawn dotted in the graph.
Step 3
Exam Tip
(<) सख्त असमानता है, इसलिए सीमा रेखा शामिल नहीं होती। ग्राफ में ऐसी सीमा रेखा बिंदुदार बनाते हैं।
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?
At ( (3,2) ), (8<10) and (9<12), so it is strictly inside. A boundary point must make at least one inequality an equality.
Step 2
Why this answer is correct
The correct answer is C. ( (3,2) ). At ( (3,2) ), (8<10) and (9<12), so it is strictly inside. A boundary point must make at least one inequality an equality.
Step 3
Exam Tip
( (3,2) ) पर (8<10) और (9<12), इसलिए यह अंदर है। सीमा पर होने के लिए कम से कम एक असमानता बराबरी बननी चाहिए।
B. मूलबिंदु वाला भाग स्वीकार होगा/The side containing origin is accepted
Step 1
Concept
Since \(0\ge-5\) is true, the side containing the origin is the solution region. A simple test point quickly decides the shading.
Step 2
Why this answer is correct
The correct answer is B. मूलबिंदु वाला भाग स्वीकार होगा / The side containing origin is accepted. Since \(0\ge-5\) is true, the side containing the origin is the solution region. A simple test point quickly decides the shading.
Step 3
Exam Tip
\(0\ge-5\) सत्य है, इसलिए मूलबिंदु वाला भाग हल क्षेत्र है। सरल परीक्षण-बिंदु से छायांकन जल्दी तय होता है।
D. किसी भी असमानता को संतुष्ट नहीं करता/It satisfies neither inequality
Step 1
Concept
At ( (2,2) ), both left sides equal (6), which is less than (10). In a combined solution, all inequalities must be true together.
Step 2
Why this answer is correct
The correct answer is D. किसी भी असमानता को संतुष्ट नहीं करता / It satisfies neither inequality. At ( (2,2) ), both left sides equal (6), which is less than (10). In a combined solution, all inequalities must be true together.
Step 3
Exam Tip
( (2,2) ) पर दोनों पक्षों में मान (6) आता है, जो (10) से कम है। संयुक्त हल में सभी असमानताएं एक साथ सत्य होनी चाहिए।
In the first quadrant, the region above (x+y=5) extends without bound. In such questions, check both direction and axis restrictions.
Step 2
Why this answer is correct
The correct answer is C. असीमित क्षेत्र / Unbounded region. In the first quadrant, the region above (x+y=5) extends without bound. In such questions, check both direction and axis restrictions.
Step 3
Exam Tip
पहले चतुर्थांश में रेखा (x+y=5) के ऊपर का भाग असीमित फैलता है। ऐसे प्रश्न में दिशा और अक्षों की शर्त साथ देखें।
From \(x\le4\) and \(y\le3\), the maximum possible (x+y) is (7). Hence \(x+y\le8\) does not further reduce the region.
Step 2
Why this answer is correct
The correct answer is C. \(x+y\le8\). From \(x\le4\) and \(y\le3\), the maximum possible (x+y) is (7). Hence \(x+y\le8\) does not further reduce the region.
Step 3
Exam Tip
\(x\le4\) और \(y\le3\) से अधिकतम (x+y=7) हो सकता है। इसलिए \(x+y\le8\) अलग से क्षेत्र नहीं घटाती।
From (5x-2y<10), we get \(y>\frac{5x-10}{2}\). Do not forget to reverse the sign when removing a negative coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(y>\frac{5x-10}{2}\). From (5x-2y<10), we get \(y>\frac{5x-10}{2}\). Do not forget to reverse the sign when removing a negative coefficient.
Step 3
Exam Tip
(5x-2y<10) से \(y>\frac{5x-10}{2}\) मिलता है। ऋणात्मक गुणांक हटाते समय चिन्ह पलटना न भूलें।
A. ( (10,0) ) और ( (0,4) )/( (10,0) ) and ( (0,4) )
Step 1
Concept
The boundary line is (2x+5y=20), giving intercepts (x=10) and (y=4). Drawing the line first is the base of graphical solution.
Step 2
Why this answer is correct
The correct answer is A. ( (10,0) ) और ( (0,4) ) / ( (10,0) ) and ( (0,4) ). The boundary line is (2x+5y=20), giving intercepts (x=10) and (y=4). Drawing the line first is the base of graphical solution.
Step 3
Exam Tip
सीमा रेखा (2x+5y=20) है, जिससे (x=10) और (y=4) प्रतिच्छेद मिलते हैं। पहले रेखा बनाना ग्राफीय हल का आधार है।
C. हल क्षेत्र के विपरीत तरफ/On the opposite side of the solution region
Step 1
Concept
At the origin, (0>24) is false, so the side containing the origin is not the solution. If the test point fails, shade the other side.
Step 2
Why this answer is correct
The correct answer is C. हल क्षेत्र के विपरीत तरफ / On the opposite side of the solution region. At the origin, (0>24) is false, so the side containing the origin is not the solution. If the test point fails, shade the other side.
Step 3
Exam Tip
मूलबिंदु पर (0>24) असत्य है, इसलिए मूलबिंदु वाला भाग हल नहीं है। असत्य परीक्षण-बिंदु मिलने पर दूसरी तरफ छायांकन करें।
The conditions \(x\le5\) and \(y\le4\) with the axes form a bounded rectangular region. A bounded region needs closing boundaries in all directions.
Step 2
Why this answer is correct
The correct answer is C. \(x\ge0\), \(y\ge0\), \(x\le5\), \(y\le4\). The conditions \(x\le5\) and \(y\le4\) with the axes form a bounded rectangular region. A bounded region needs closing boundaries in all directions.
Step 3
Exam Tip
\(x\le5\) और \(y\le4\) अक्षों के साथ आयताकार सीमित क्षेत्र बनाते हैं। सीमित क्षेत्र के लिए सभी दिशाओं में बंद सीमा चाहिए।
Putting (x=0) gives \(4y\le16\), so \(y\le4\). To find an axis intercept limit, put the other variable equal to zero.
Step 2
Why this answer is correct
The correct answer is C. ( (0,4) ). Putting (x=0) gives \(4y\le16\), so \(y\le4\). To find an axis intercept limit, put the other variable equal to zero.
Step 3
Exam Tip
(x=0) रखने पर \(4y\le16\), इसलिए \(y\le4\) है। अक्षों पर अधिकतम बिंदु निकालने के लिए दूसरे चर को शून्य रखें।
Writing the line as \(y=\frac{18-2x}{3}\), the upper side is \(y\ge\frac{18-2x}{3}\). This is equivalent to \(2x+3y\ge18\).
Step 2
Why this answer is correct
The correct answer is B. \(2x+3y\ge18\). Writing the line as \(y=\frac{18-2x}{3}\), the upper side is \(y\ge\frac{18-2x}{3}\). This is equivalent to \(2x+3y\ge18\).
Step 3
Exam Tip
रेखा को \(y=\frac{18-2x}{3}\) लिखने पर ऊपर का भाग \(y\ge\frac{18-2x}{3}\) है। यह \(2x+3y\ge18\) के बराबर है।
The conditions \(0\le x\le6\) and \(0\le y\le5\) restrict the region inside a rectangle. The inequality \(x+y\ge4\) only cuts off one corner.
Step 2
Why this answer is correct
The correct answer is B. सीमित / Bounded. The conditions \(0\le x\le6\) and \(0\le y\le5\) restrict the region inside a rectangle. The inequality \(x+y\ge4\) only cuts off one corner.
Step 3
Exam Tip
\(0\le x\le6\) और \(0\le y\le5\) क्षेत्र को आयत में सीमित करते हैं। \(x+y\ge4\) केवल उसका एक कोना काटता है।
Solving (x+2y=9) and (3x+y=11) gives \(x=\frac{13}{5}\), \(y=\frac{16}{5}\). Fractional vertices are common in graphical solutions.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{13}{5},\frac{16}{5}\right\) ). Solving (x+2y=9) and (3x+y=11) gives \(x=\frac{13}{5}\), \(y=\frac{16}{5}\). Fractional vertices are common in graphical solutions.
Step 3
Exam Tip
(x+2y=9) और (3x+y=11) हल करने पर \(x=\frac{13}{5}\), \(y=\frac{16}{5}\) मिलता है। भिन्नात्मक शीर्ष भी ग्राफीय हल में सामान्य हैं।
A. दो समानांतर रेखाओं के बीच का पट्टी क्षेत्र/A strip between two parallel lines
Step 1
Concept
Both lines have slope (3), so they are parallel. The inequalities give a strip-like region between them.
Step 2
Why this answer is correct
The correct answer is A. दो समानांतर रेखाओं के बीच का पट्टी क्षेत्र / A strip between two parallel lines. Both lines have slope (3), so they are parallel. The inequalities give a strip-like region between them.
Step 3
Exam Tip
दोनों रेखाओं की ढाल (3) है, इसलिए वे समानांतर हैं। असमानताएं उनके बीच का पट्टी क्षेत्र देती हैं।
The intercepts are ( (6,0) ) and ( (0,4) ), so the area is \(\frac{1}{2}\times6\times4=12\). For a triangular region, identify base and height.
Step 2
Why this answer is correct
The correct answer is A. (12) वर्ग इकाई / (12) square units. The intercepts are ( (6,0) ) and ( (0,4) ), so the area is \(\frac{1}{2}\times6\times4=12\). For a triangular region, identify base and height.
Step 3
Exam Tip
अक्षों पर प्रतिच्छेद ( (6,0) ) और ( (0,4) ) हैं, इसलिए क्षेत्रफल \(\frac{1}{2}\times6\times4=12\) है। त्रिभुज क्षेत्र के लिए आधार और ऊंचाई पहचानें।
The boundaries (x=1), (y=2), and (x+y=8) give ( (1,2) ), ( (6,2) ), and ( (1,7) ). Do not treat shifted restrictions as simple \(x\ge0\), \(y\ge0\).
Step 2
Why this answer is correct
The correct answer is A. ( (1,2) ), ( (6,2) ), ( (1,7) ). The boundaries (x=1), (y=2), and (x+y=8) give ( (1,2) ), ( (6,2) ), and ( (1,7) ). Do not treat shifted restrictions as simple \(x\ge0\), \(y\ge0\).
Step 3
Exam Tip
सीमाएं (x=1), (y=2) और (x+y=8) से ( (1,2) ), ( (6,2) ), ( (1,7) ) मिलते हैं। बदले हुए अक्षीय प्रतिबंधों को साधारण \(x\ge0\), \(y\ge0\) न मानें।
It is impossible for (x+y) to be both less than and greater than (5) at the same time. Opposite inequalities can make the solution empty.
Step 2
Why this answer is correct
The correct answer is C. रिक्त समुच्चय / Empty set. It is impossible for (x+y) to be both less than and greater than (5) at the same time. Opposite inequalities can make the solution empty.
Step 3
Exam Tip
एक ही समय में (x+y) का (5) से कम और अधिक होना असंभव है। विरोधी असमानताएं मिलने पर हल रिक्त हो सकता है।
The vertices are ( (0,0) ), ( (3,0) ), ( (2,2) ), and ( (0,3) ), so every listed point is a vertex. The correct choice should have been none of these.
Step 2
Why this answer is correct
The correct answer is D. ( (0,3) ). The vertices are ( (0,0) ), ( (3,0) ), ( (2,2) ), and ( (0,3) ), so every listed point is a vertex. The correct choice should have been none of these.
Step 3
Exam Tip
इस क्षेत्र के शीर्ष ( (0,0) ), ( (3,0) ), ( (2,2) ), ( (0,3) ) हैं, इसलिए दिया गया हर बिंदु शीर्ष है। प्रश्न में सही उत्तर कोई नहीं होना चाहिए।
From \(x-3y\le9\), we get \(-3y\le9-x\), hence \(y\ge\frac{x-9}{3}\). Dividing by a negative reverses the sign.
Step 2
Why this answer is correct
The correct answer is A. \(y\ge\frac{x-9}{3}\). From \(x-3y\le9\), we get \(-3y\le9-x\), hence \(y\ge\frac{x-9}{3}\). Dividing by a negative reverses the sign.
Step 3
Exam Tip
\(x-3y\le9\) से \(-3y\le9-x\), इसलिए \(y\ge\frac{x-9}{3}\) है। ऋणात्मक से भाग देने पर चिन्ह उलटता है।
At ( (2,2) ), both left sides equal (10), which is less than (12). Therefore this option cannot be correct and true solutions must make both values at least (12).
Step 2
Why this answer is correct
The correct answer is A. ( (2,2) ). At ( (2,2) ), both left sides equal (10), which is less than (12). Therefore this option cannot be correct and true solutions must make both values at least (12).
Step 3
Exam Tip
( (2,2) ) पर दोनों असमानताओं में मान (10) आता है, जो (12) से कम है। इसलिए यह विकल्प सही नहीं हो सकता और सही हलों के लिए दोनों मान कम से कम (12) होने चाहिए।
At (x=2), (y=4); at (y=1), (x=8). Intersect the boundary line with the given lower limits.
Step 2
Why this answer is correct
The correct answer is A. ( (2,4) ) और ( (8,1) ) / ( (2,4) ) and ( (8,1) ). At (x=2), (y=4); at (y=1), (x=8). Intersect the boundary line with the given lower limits.
Step 3
Exam Tip
(x=2) पर (y=4) और (y=1) पर (x=8) मिलता है। सीमा रेखा को दी गई निचली सीमाओं के साथ काटें।
Adding the equations gives (4x+4y=30), and by symmetry \(x=y=\frac{15}{4}\). Use symmetry when boundary lines have a similar structure.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{15}{4},\frac{15}{4}\right\) ). Adding the equations gives (4x+4y=30), and by symmetry \(x=y=\frac{15}{4}\). Use symmetry when boundary lines have a similar structure.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (4x+4y=30) और सममिति से \(x=y=\frac{15}{4}\) है। समान संरचना वाली रेखाओं में सममिति का उपयोग करें।
B. हल क्षेत्र रिक्त है/The solution region is empty
Step 1
Concept
The value (x+y) cannot be at most (4) and at least (7) simultaneously. Parallel bounds in opposite positions can give an empty region.
Step 2
Why this answer is correct
The correct answer is B. हल क्षेत्र रिक्त है / The solution region is empty. The value (x+y) cannot be at most (4) and at least (7) simultaneously. Parallel bounds in opposite positions can give an empty region.
Step 3
Exam Tip
(x+y) एक साथ (4) से कम या बराबर और (7) से अधिक या बराबर नहीं हो सकता। समान दिशा की समानांतर सीमाएं खाली क्षेत्र दे सकती हैं।
At ( (1,4) ), \(1\le3\) and \(4\ge3\) are true. Check both the vertical boundary and the oblique boundary for each option.
Step 2
Why this answer is correct
The correct answer is C. ( (1,4) ). At ( (1,4) ), \(1\le3\) and \(4\ge3\) are true. Check both the vertical boundary and the oblique boundary for each option.
Step 3
Exam Tip
( (1,4) ) पर \(1\le3\) और \(4\ge3\) सत्य हैं। हर विकल्प में ऊर्ध्वाधर सीमा और तिरछी सीमा दोनों जांचें।
The two equations give (x=y) and (3x=14), so the vertex is ( \left\(\frac{14}{3},\frac{14}{3}\right\) ). Symmetric boundaries can quickly give (x=y).
Step 2
Why this answer is correct
The correct answer is C. ( \left\(\frac{14}{3},\frac{14}{3}\right\) ). The two equations give (x=y) and (3x=14), so the vertex is ( \left\(\frac{14}{3},\frac{14}{3}\right\) ). Symmetric boundaries can quickly give (x=y).
Step 3
Exam Tip
दोनों समीकरणों से (x=y) और (3x=14), इसलिए शीर्ष ( \left\(\frac{14}{3},\frac{14}{3}\right\) ) है। सममित सीमाओं में (x=y) जल्दी मिल सकता है।
B. रेखा के नीचे या रेखा सहित/Below the line including the line
Step 1
Concept
An inequality in the form \(y\le\) represents the region below the line. The equality part means the boundary line is included.
Step 2
Why this answer is correct
The correct answer is B. रेखा के नीचे या रेखा सहित / Below the line including the line. An inequality in the form \(y\le\) represents the region below the line. The equality part means the boundary line is included.
Step 3
Exam Tip
\(y\le\) रूप में असमानता रेखा के नीचे वाले भाग को दर्शाती है। बराबरी होने से सीमा रेखा भी शामिल होती है।
Both inequalities select regions above the boundary lines, and the common region extends indefinitely. Conditions with \(\ge\) can often create an unbounded region.
Step 2
Why this answer is correct
The correct answer is B. असीमित क्षेत्र / Unbounded region. Both inequalities select regions above the boundary lines, and the common region extends indefinitely. Conditions with \(\ge\) can often create an unbounded region.
Step 3
Exam Tip
दोनों असमानताएं रेखाओं के ऊपर की ओर क्षेत्र देती हैं और क्षेत्र दूर तक फैलता है। \(\ge\) वाली सीमाएं अक्सर असीमित क्षेत्र बना सकती हैं।
Left of (x=4) is \(x\le4\), and above (y=-1) is \(y\ge-1\). For vertical and horizontal boundaries, identify direction separately.
Step 2
Why this answer is correct
The correct answer is B. \(x\le4\), \(y\ge-1\). Left of (x=4) is \(x\le4\), and above (y=-1) is \(y\ge-1\). For vertical and horizontal boundaries, identify direction separately.
Step 3
Exam Tip
रेखा (x=4) के बाईं ओर \(x\le4\) और (y=-1) के ऊपर \(y\ge-1\) होता है। ऊर्ध्वाधर और क्षैतिज सीमाओं के लिए दिशा अलग-अलग पहचानें।
At ( (1,1) ), (x+y=2), which is less than (3). In multi-inequality questions, one false condition is enough to reject a point.
Step 2
Why this answer is correct
The correct answer is C. ( (1,1) ). At ( (1,1) ), (x+y=2), which is less than (3). In multi-inequality questions, one false condition is enough to reject a point.
Step 3
Exam Tip
( (1,1) ) पर (x+y=2), जो (3) से कम है। बहु-असमानता प्रश्नों में अस्वीकृति के लिए एक असत्य शर्त काफी है।
At (y=1), \(x\le8\) and \(x\le4\), so the tighter limit is (x=4). For the right endpoint, choose the smaller upper bound from all constraints.
Step 2
Why this answer is correct
The correct answer is B. ( (4,1) ). At (y=1), \(x\le8\) and \(x\le4\), so the tighter limit is (x=4). For the right endpoint, choose the smaller upper bound from all constraints.
Step 3
Exam Tip
(y=1) पर \(x\le8\) और \(x\le4\), इसलिए कड़ी सीमा (x=4) है। दाएं अंतिम बिंदु के लिए सभी ऊपरी सीमाओं में छोटी सीमा चुनें।
At ( (3,3) ), (6+9=15<18), so it is inside and not on the axes. For an interior point, look for a strict inequality value.
Step 2
Why this answer is correct
The correct answer is B. ( (3,3) ). At ( (3,3) ), (6+9=15<18), so it is inside and not on the axes. For an interior point, look for a strict inequality value.
Step 3
Exam Tip
( (3,3) ) पर (6+9=15<18), इसलिए यह अंदर है और अक्षों पर नहीं है। अंदरूनी बिंदु के लिए सख्त कम मान देखें।
Two vertical and two horizontal boundaries together form a closed rectangle. In a graph, pairs of parallel boundaries help identify the shape quickly.
Step 2
Why this answer is correct
The correct answer is B. आयत / Rectangle. Two vertical and two horizontal boundaries together form a closed rectangle. In a graph, pairs of parallel boundaries help identify the shape quickly.
Step 3
Exam Tip
दो ऊर्ध्वाधर और दो क्षैतिज सीमाएं मिलकर बंद आयत बनाती हैं। ग्राफ में समानांतर सीमाओं की जोड़ी से आकार तुरंत पहचाना जा सकता है।
From (x+2=-x+4), (2x=2), so (x=1) and (y=3). The intersection of slant boundaries can mark the start or a corner of a region.
Step 2
Why this answer is correct
The correct answer is A. ( (1,3) ). From (x+2=-x+4), (2x=2), so (x=1) and (y=3). The intersection of slant boundaries can mark the start or a corner of a region.
Step 3
Exam Tip
(x+2=-x+4) से (2x=2), इसलिए (x=1) और (y=3) है। तिरछी सीमाओं का प्रतिच्छेद क्षेत्र की शुरुआत या कोना बता सकता है।
