If (p>0), the (x)-intercept \(\frac{6}{p}\) is finite. If \(p\leq 0\), the region is not bounded in the (x)-direction in the first quadrant.
Step 2
Why this answer is correct
The correct answer is C. (p>0). If (p>0), the (x)-intercept \(\frac{6}{p}\) is finite. If \(p\leq 0\), the region is not bounded in the (x)-direction in the first quadrant.
Step 3
Exam Tip
यदि (p>0), तो (x)-अवरोध \(\frac{6}{p}\) सीमित होता है। \(p\leq 0\) होने पर प्रथम चतुर्थांश में क्षेत्र (x) दिशा में सीमित नहीं रहता।
If \(a\geq 0\), at least ((0,0)) is in the solution and the region remains bounded. If (a<0), there is no solution in the first quadrant.
Step 2
Why this answer is correct
The correct answer is B. \(a\geq 0\). If \(a\geq 0\), at least ((0,0)) is in the solution and the region remains bounded. If (a<0), there is no solution in the first quadrant.
Step 3
Exam Tip
यदि \(a\geq 0\) है तो कम से कम ((0,0)) हल में आता है और क्षेत्र सीमित रहता है। (a<0) होने पर प्रथम चतुर्थांश में कोई हल नहीं मिलेगा।
The width is (7-2=5) and height is (5-1=4), so it is a rectangle. Parallel axis-aligned lines form a rectangle.
Step 2
Why this answer is correct
The correct answer is B. आयत / Rectangle. The width is (7-2=5) and height is (5-1=4), so it is a rectangle. Parallel axis-aligned lines form a rectangle.
Step 3
Exam Tip
चौड़ाई (7-2=5) और ऊंचाई (5-1=4) है, इसलिए यह आयत है। समानांतर अक्षीय रेखाएं आयत बनाती हैं।
The upper bound \(2x+3y\le 18\) and the first quadrant make the region bounded. The lower line \(x+y\ge 4\) only cuts an inner part.
Step 2
Why this answer is correct
The correct answer is A. सीमित / Bounded. The upper bound \(2x+3y\le 18\) and the first quadrant make the region bounded. The lower line \(x+y\ge 4\) only cuts an inner part.
Step 3
Exam Tip
ऊपरी सीमा \(2x+3y\le 18\) और प्रथम चतुर्थांश क्षेत्र को सीमित करते हैं। निचली रेखा \(x+y\ge 4\) केवल अंदर का हिस्सा काटती है।
The rectangle has length (5-1=4) and width (6-2=4), so the area is (16). For parallel bounds, take differences to get dimensions.
Step 2
Why this answer is correct
The correct answer is C. (16). The rectangle has length (5-1=4) and width (6-2=4), so the area is (16). For parallel bounds, take differences to get dimensions.
Step 3
Exam Tip
आयत की लंबाई (5-1=4) और चौड़ाई (6-2=4), इसलिए क्षेत्रफल (16) है। समानांतर सीमाओं में अंतर लेकर आयाम निकालें।
From \(x-1\leq 3\), we get \(x\leq 4\), and all boundaries are included. Exam tip: A hidden upper bound may come from comparing inequalities.
Step 2
Why this answer is correct
The correct answer is C. सीमित और बंद / Bounded and closed. From \(x-1\leq 3\), we get \(x\leq 4\), and all boundaries are included. Exam tip: A hidden upper bound may come from comparing inequalities.
Step 3
Exam Tip
\(x-1\leq 3\) से \(x\leq 4\) मिलता है और सभी सीमाएँ शामिल हैं। परीक्षा सुझाव: छिपी हुई ऊपरी सीमा तुलना से मिलती है।
The line (x+y=6) is not included, but the region remains within a triangle. Exam tip: A strict inequality changes closedness.
Step 2
Why this answer is correct
The correct answer is A. सीमित लेकिन बंद नहीं / Bounded but not closed. The line (x+y=6) is not included, but the region remains within a triangle. Exam tip: A strict inequality changes closedness.
Step 3
Exam Tip
रेखा (x+y=6) शामिल नहीं है पर क्षेत्र त्रिभुज के भीतर सीमित है। परीक्षा सुझाव: कठोर असमानता बंदपन को बदल देती है।
The three boundary lines give vertices ((1,2)), ((6,2)), and ((1,7)). A closed region from three lines is generally a triangle.
Step 2
Why this answer is correct
The correct answer is A. त्रिभुज / Triangle. The three boundary lines give vertices ((1,2)), ((6,2)), and ((1,7)). A closed region from three lines is generally a triangle.
Step 3
Exam Tip
तीन सीमा रेखाएं तीन शीर्ष ((1,2)), ((6,2)), और ((1,7)) देती हैं। तीन रेखाओं से बंद क्षेत्र सामान्यतः त्रिभुज बनता है।
The small bounded region with axes is in the first quadrant and below the line. Use the origin test in exams.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 0\), \(y\ge 0\), \(x+2y\le 4\). The small bounded region with axes is in the first quadrant and below the line. Use the origin test in exams.
Step 3
Exam Tip
axes के साथ छोटा bounded region पहले चतुर्थांश में और रेखा के नीचे होता है। परीक्षा में origin test करें।
(x) lies between two vertical boundaries and (y) lies between two horizontal boundaries. Hence a closed rectangle is formed.
Step 2
Why this answer is correct
The correct answer is C. आयत / rectangle. (x) lies between two vertical boundaries and (y) lies between two horizontal boundaries. Hence a closed rectangle is formed.
Step 3
Exam Tip
(x) दो ऊर्ध्वाधर सीमाओं और (y) दो क्षैतिज सीमाओं के बीच है। इसलिए बंद आयत बनता है।
The line intercepts are ((8,0)) and ((0,6)), and the axes meet at ((0,0)). These are the triangle vertices in the first quadrant.
Step 2
Why this answer is correct
The correct answer is A. ((0,0)), ((8,0)), ((0,6)). The line intercepts are ((8,0)) and ((0,6)), and the axes meet at ((0,0)). These are the triangle vertices in the first quadrant.
Step 3
Exam Tip
रेखा के अवरोध ((8,0)) और ((0,6)) हैं तथा अक्षों का प्रतिच्छेद ((0,0)) है। प्रथम चतुर्थांश में ये त्रिभुज के शीर्ष हैं।
The axes and the line (x+2y=10) form a closed triangle. First-quadrant conditions can make the region bounded.
Step 2
Why this answer is correct
The correct answer is A. त्रिभुज / triangle. The axes and the line (x+2y=10) form a closed triangle. First-quadrant conditions can make the region bounded.
Step 3
Exam Tip
अक्षों और रेखा (x+2y=10) से बंद त्रिभुज बनता है। प्रथम चतुर्थांश की शर्तें क्षेत्र को सीमित कर सकती हैं।
