A. बिंदु (\left\(0,-5\right\))/Point (\left\(0,-5\right\))
Step 1
Concept
Substituting (\left\(0,-5\right\)) gives (5\left\(0\right\)-6\left\(-5\right\)=30). A negative (y)-intercept is plotted downward on the graph.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(0,-5\right\)) / Point (\left\(0,-5\right\)). Substituting (\left\(0,-5\right\)) gives (5\left\(0\right\)-6\left\(-5\right\)=30). A negative (y)-intercept is plotted downward on the graph.
Step 3
Exam Tip
(\left\(0,-5\right\)) रखने पर (5\left\(0\right\)-6\left\(-5\right\)=30)। ऋण (y)-अवरोध ग्राफ में नीचे की ओर लगाया जाता है।
A. बिंदु (\left\(0,-3\right\))/Point (\left\(0,-3\right\))
Step 1
Concept
Substituting (\left\(0,-3\right\)) gives (3\left\(0\right\)-4\left\(-3\right\)=12). A negative (y)-intercept is plotted downward on the graph.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(0,-3\right\)) / Point (\left\(0,-3\right\)). Substituting (\left\(0,-3\right\)) gives (3\left\(0\right\)-4\left\(-3\right\)=12). A negative (y)-intercept is plotted downward on the graph.
Step 3
Exam Tip
(\left\(0,-3\right\)) रखने पर (3\left\(0\right\)-4\left\(-3\right\)=12)। ऋण (y)-अवरोध ग्राफ में नीचे की ओर लगाया जाता है।
(x-2+20x+100=(x+10)2), so the touching point is ((-10,0)). Tip: change the sign in a perfect square to get the zero.
Step 2
Why this answer is correct
The correct answer is A. ((-10,0)). (x-2+20x+100=(x+10)2), so the touching point is ((-10,0)). Tip: change the sign in a perfect square to get the zero.
Step 3
Exam Tip
(x-2+20x+100=(x+10)2) है, इसलिए स्पर्श बिंदु ((-10,0)) है। टिप: पूर्ण वर्ग में चिह्न बदलकर शून्यक मिलता है।
A. (4) बहुपद का शून्यक है/(4) is a zero of the polynomial
Step 1
Concept
The point ((4,0)) means (p(x)=0) at (x=4). Tip: from ((a,0)) the zero is (a).
Step 2
Why this answer is correct
The correct answer is A. (4) बहुपद का शून्यक है / (4) is a zero of the polynomial. The point ((4,0)) means (p(x)=0) at (x=4). Tip: from ((a,0)) the zero is (a).
Step 3
Exam Tip
((4,0)) का अर्थ है (x=4) पर (p(x)=0)। टिप: ((a,0)) से शून्यक (a) मिलता है।
Real zeroes are obtained from common points of the graph and the (x)-axis. If there is no common point, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक शून्यक नहीं / No real zero. Real zeroes are obtained from common points of the graph and the (x)-axis. If there is no common point, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक ग्राफ और (x)-अक्ष के साझा बिंदुओं से मिलते हैं। साझा बिंदु न हो तो वास्तविक शून्यक नहीं होगा।
Perspective lines make depth logical by relating to vanishing point. Exam tip: check vanishing point direction.
Step 2
Why this answer is correct
The correct answer is A. गहराई असंगत लगेगी / Depth will look inconsistent. Perspective lines make depth logical by relating to vanishing point. Exam tip: check vanishing point direction.
Step 3
Exam Tip
परिप्रेक्ष्य रेखाएं लुप्त बिंदु से जुड़कर गहराई को तार्किक बनाती हैं। परीक्षा में vanishing point की दिशा जांचें।
One intersection point is the common solution of both equations. Therefore exactly one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. One intersection point is the common solution of both equations. Therefore exactly one unique solution is obtained.
Step 3
Exam Tip
कटने का एक बिंदु दोनों समीकरणों का सामान्य हल होता है। इसलिए केवल एक अद्वितीय हल मिलता है।
One common point gives one unique solution. Therefore it is a consistent and independent pair.
Step 2
Why this answer is correct
The correct answer is A. संगत और स्वतंत्र / Consistent and independent. One common point gives one unique solution. Therefore it is a consistent and independent pair.
Step 3
Exam Tip
एक सामान्य बिंदु होने से एक अद्वितीय हल मिलता है। इसलिए यह संगत और स्वतंत्र युग्म है।
\(3.75=\frac{15}{4}\) and \(-2.5=-\frac{5}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{15}{4},-\frac{5}{2}\right\)). \(3.75=\frac{15}{4}\) and \(-2.5=-\frac{5}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 3
Exam Tip
\(3.75=\frac{15}{4}\) और \(-2.5=-\frac{5}{2}\)। दशमलव निर्देशांक को सरल भिन्न में बदलना बेहतर रहता है।
The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 2
Why this answer is correct
The correct answer is B. \(x=-\frac{5}{2},\ y=3\). The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 3
Exam Tip
बिंदु में पहला निर्देशांक (x) और दूसरा (y) होता है। ऋण भिन्न निर्देशांक पढ़ते समय क्रम न बदलें।
\(2.25=\frac{9}{4}\) and \(-1.5=-\frac{3}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{9}{4},-\frac{3}{2}\right\)). \(2.25=\frac{9}{4}\) and \(-1.5=-\frac{3}{2}\). It is better to convert decimal coordinates into simplified fractions.
Step 3
Exam Tip
\(2.25=\frac{9}{4}\) और \(-1.5=-\frac{3}{2}\)। दशमलव निर्देशांक को सरल भिन्न में बदलना बेहतर रहता है।
The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 2
Why this answer is correct
The correct answer is B. \(x=-\frac{3}{2},\ y=4\). The first coordinate of a point is (x) and the second is (y). Do not change order while reading negative fraction coordinates.
Step 3
Exam Tip
बिंदु में पहला निर्देशांक (x) और दूसरा (y) होता है। ऋण भिन्न निर्देशांक पढ़ते समय क्रम न बदलें।
A. बिंदु (\left\(3.5,2.5\right\))/Point (\left\(3.5,2.5\right\))
Step 1
Concept
\(\frac{7}{2}=3.5\) and \(\frac{5}{2}=2.5\). While reading a graph, understand the relation between fraction and decimal forms.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(3.5,2.5\right\)) / Point (\left\(3.5,2.5\right\)). \(\frac{7}{2}=3.5\) and \(\frac{5}{2}=2.5\). While reading a graph, understand the relation between fraction and decimal forms.
Step 3
Exam Tip
\(\frac{7}{2}=3.5\) और \(\frac{5}{2}=2.5\)। ग्राफ पढ़ते समय भिन्न और दशमलव रूप का संबंध समझें।
\(4.5=\frac{9}{2}\) and \(1.5=\frac{3}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{9}{2},\frac{3}{2}\right\)). \(4.5=\frac{9}{2}\) and \(1.5=\frac{3}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 3
Exam Tip
\(4.5=\frac{9}{2}\) और \(1.5=\frac{3}{2}\)। ग्राफ से मिले दशमलव निर्देशांक को सरल भिन्न में लिखें।
In the point (\left\(-4,3\right\)), the first coordinate is (x) and the second is (y). Do not change order with negative coordinates.
Step 2
Why this answer is correct
The correct answer is A. (x=-4,\ y=3). In the point (\left\(-4,3\right\)), the first coordinate is (x) and the second is (y). Do not change order with negative coordinates.
Step 3
Exam Tip
बिंदु (\left\(-4,3\right\)) में पहला निर्देशांक (x) और दूसरा (y) होता है। ऋण निर्देशांक में क्रम न बदलें।
\(3.5=\frac{7}{2}\) and \(2.5=\frac{5}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{7}{2},\frac{5}{2}\right\) ). \(3.5=\frac{7}{2}\) and \(2.5=\frac{5}{2}\). Write decimal coordinates read from a graph as simplified fractions.
Step 3
Exam Tip
\(3.5=\frac{7}{2}\) और \(2.5=\frac{5}{2}\)। ग्राफ से मिले दशमलव निर्देशांक को सरल भिन्न में लिखें।
\(2.5=\frac{5}{2}\) and \(1.5=\frac{3}{2}\). When reading decimals from a graph, write them as simplified fractions.
Step 2
Why this answer is correct
The correct answer is A. ( \left\(\frac{5}{2},\frac{3}{2}\right\) ). \(2.5=\frac{5}{2}\) and \(1.5=\frac{3}{2}\). When reading decimals from a graph, write them as simplified fractions.
Step 3
Exam Tip
\(2.5=\frac{5}{2}\) और \(1.5=\frac{3}{2}\)। ग्राफ से दशमलव बिंदु पढ़ने पर सरल भिन्न में लिखें।
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।
One intersection point gives a unique solution. Hence, the pair is called 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 called consistent and independent.
Step 3
Exam Tip
एक प्रतिच्छेद बिंदु एक अद्वितीय हल देता है। इसलिए युग्म संगत और स्वतंत्र कहलाता है।
A. बराबर शून्यक (4) और (4)/Equal zeroes (4) and (4)
Step 1
Concept
When a quadratic graph touches at one point its two zeroes are equal. Treat it as a repeated zero in exams.
Step 2
Why this answer is correct
The correct answer is A. बराबर शून्यक (4) और (4) / Equal zeroes (4) and (4). When a quadratic graph touches at one point its two zeroes are equal. Treat it as a repeated zero in exams.
Step 3
Exam Tip
द्विघात ग्राफ एक बिंदु पर छूता है तो दोनों शून्यक समान होते हैं। परीक्षा में इसे दोहराया शून्यक मानें।
A. दो अलग वास्तविक शून्यक हैं/There are two distinct real zeroes
Step 1
Concept
Two distinct crossings give two distinct zeroes. Tip: distinct points show distinct (x)-values.
Step 2
Why this answer is correct
The correct answer is A. दो अलग वास्तविक शून्यक हैं / There are two distinct real zeroes. Two distinct crossings give two distinct zeroes. Tip: distinct points show distinct (x)-values.
Step 3
Exam Tip
दो अलग कटान दो अलग शून्यक देते हैं। टिप: अलग बिंदु अलग (x)-मान बताते हैं।
A. नहीं, क्योंकि \(y\neq 0\) है/No, because \(y\neq 0\)
Step 1
Concept
For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\). For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (y=0) होना चाहिए। ((0,4)) में (y=4) है, इसलिए (0) शून्यक नहीं है।
Substituting ((6,0)) gives \(2\cdot6+3\cdot0=12\), so it lies on the line. Intercept points are convenient for graphing.
Step 2
Why this answer is correct
The correct answer is A. ((6,0)). Substituting ((6,0)) gives \(2\cdot6+3\cdot0=12\), so it lies on the line. Intercept points are convenient for graphing.
Step 3
Exam Tip
((6,0)) रखने पर \(2\cdot6+3\cdot0=12\), इसलिए यह रेखा पर है। अक्ष-अवरोध वाले बिंदु ग्राफ के लिए सुविधाजनक होते हैं।
A. उसका कोई वास्तविक शून्यक नहीं है/It has no real zero
Step 1
Concept
A real zero appears only on the (x)-axis. Tip: check meeting the (x)-axis not distance from it.
Step 2
Why this answer is correct
The correct answer is A. उसका कोई वास्तविक शून्यक नहीं है / It has no real zero. A real zero appears only on the (x)-axis. Tip: check meeting the (x)-axis not distance from it.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष पर ही दिखता है। टिप: (x)-अक्ष से दूरी नहीं बल्कि मिलना देखें।
A. बिंदु (\left\(2,5\right\))/Point (\left\(2,5\right\))
Step 1
Concept
At (\left\(2,5\right\)), (3\left\(2\right\)+4\left\(5\right\)=26), but (2+5=7) also, so check fully. The correct non-common point is (\left\(4,\frac{7}{2}\right\)).
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(2,5\right\)) / Point (\left\(2,5\right\)). At (\left\(2,5\right\)), (3\left\(2\right\)+4\left\(5\right\)=26), but (2+5=7) also, so check fully. The correct non-common point is (\left\(4,\frac{7}{2}\right\)).
Step 3
Exam Tip
(\left\(2,5\right\)) पर (3\left\(2\right\)+4\left\(5\right\)=26), लेकिन (2+5=7) भी है, इसलिए जाँच पूरी करें। सही अलग बिंदु (\left\(4,\frac{7}{2}\right\)) है।
A. बिंदु (\left\(1,5\right\))/Point (\left\(1,5\right\))
Step 1
Concept
At (\left\(1,5\right\)), (2\left\(1\right\)+5\left\(5\right\)=27), but (1+5=6). To be a common solution, both equations must be true.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(1,5\right\)) / Point (\left\(1,5\right\)). At (\left\(1,5\right\)), (2\left\(1\right\)+5\left\(5\right\)=27), but (1+5=6). To be a common solution, both equations must be true.
Step 3
Exam Tip
(\left\(1,5\right\)) पर (2\left\(1\right\)+5\left\(5\right\)=27), लेकिन (1+5=6)। सामान्य हल बनने के लिए दोनों समीकरण सत्य होने चाहिए।
B. बिंदु (\left\(3,6\right\))/Point (\left\(3,6\right\))
Step 1
Concept
At (\left\(3,6\right\)), (2\left\(3\right\)+3\left\(6\right\)=24), but (3+6=9). For a common solution, both equations must be true.
Step 2
Why this answer is correct
The correct answer is B. बिंदु (\left\(3,6\right\)) / Point (\left\(3,6\right\)). At (\left\(3,6\right\)), (2\left\(3\right\)+3\left\(6\right\)=24), but (3+6=9). For a common solution, both equations must be true.
Step 3
Exam Tip
(\left\(3,6\right\)) पर (2\left\(3\right\)+3\left\(6\right\)=24), लेकिन (3+6=9)। सामान्य हल के लिए दोनों समीकरण सत्य होने चाहिए।
A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे/One that cuts the (x)-axis at ((1,0)) and ((-6,0))
Step 1
Concept
If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0)). If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 3
Exam Tip
शून्यक (1) और (-6) होने पर ग्राफ (x)-अक्ष को इन्हीं (x)-मानों पर काटेगा। इसलिए बिंदु ((1,0)) और ((-6,0)) होंगे।
In one-point perspective receding lines go toward one point on horizon. Exam tip: connect vanishing point with horizon.
Step 2
Why this answer is correct
The correct answer is A. क्षितिज रेखा पर / On the horizon line. In one-point perspective receding lines go toward one point on horizon. Exam tip: connect vanishing point with horizon.
Step 3
Exam Tip
एक बिंदु परिप्रेक्ष्य में दूर जाती रेखाएं क्षितिज पर एक बिंदु की ओर जाती हैं। परीक्षा में vanishing point को horizon से जोड़ें।
The value (p(a)=0) gives the point ((a,0)). Tip: (p(x)) is the (y)-coordinate on the graph.
Step 2
Why this answer is correct
The correct answer is C. ((a,0)) और ((b,0)) / ((a,0)) and ((b,0)). The value (p(a)=0) gives the point ((a,0)). Tip: (p(x)) is the (y)-coordinate on the graph.
Step 3
Exam Tip
(p(a)=0) का बिंदु ((a,0)) होता है। टिप: (p(x)) ग्राफ में (y)-निर्देशांक होता है।
The intersection point satisfies both equations. In a graph, one intersection means a unique solution.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. The intersection point satisfies both equations. In a graph, one intersection means a unique solution.
Step 3
Exam Tip
कटने का बिंदु दोनों समीकरणों को संतुष्ट करता है। ग्राफ में एक intersection का मतलब unique solution है।
Elimination gives (19x=112), so \(x=\frac{112}{19}\) and \(y=\frac{41}{19}\). A graphical solution may also have fractional coordinates.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{112}{19},\frac{41}{19}\right\)). Elimination gives (19x=112), so \(x=\frac{112}{19}\) and \(y=\frac{41}{19}\). A graphical solution may also have fractional coordinates.
Step 3
Exam Tip
उन्मूलन करने पर (19x=112), इसलिए \(x=\frac{112}{19}\) और \(y=\frac{41}{19}\)। ग्राफीय हल भिन्न निर्देशांक में भी हो सकता है।
From the second equation, (x=3y-11). Substituting gives (9y-33+2y=25), so (y=5). Then (x=5), so the intersection is ((5,5)).
Step 2
Why this answer is correct
The correct answer is A. ((5,5)). From the second equation, (x=3y-11). Substituting gives (9y-33+2y=25), so (y=5). Then (x=5), so the intersection is ((5,5)).
Step 3
Exam Tip
दूसरे से (x=3y-11), पहले में रखने पर (9y-33+2y=25), इसलिए (y=5)। फिर (x=5), अतः प्रतिच्छेद ((5,5)) है।
Putting (x=3y-4) gives (5(3y-4)+2y=23), so \(y=\frac{43}{17}\) and \(x=\frac{61}{17}\). Fractional coordinates can also be correct graphical solutions.
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{61}{17},\frac{43}{17}\right\)). Putting (x=3y-4) gives (5(3y-4)+2y=23), so \(y=\frac{43}{17}\) and \(x=\frac{61}{17}\). Fractional coordinates can also be correct graphical solutions.
Step 3
Exam Tip
(x=3y-4) रखने पर (5(3y-4)+2y=23), इसलिए \(y=\frac{43}{17}\) और \(x=\frac{61}{17}\)। भिन्न निर्देशांक भी सही ग्राफीय समाधान हो सकते हैं।
From (2x+y=13), (y=13-2x); substituting gives (10x=50), so ((5,3)). A graphical solution always satisfies both equations.
Step 2
Why this answer is correct
The correct answer is A. ((5,3)). From (2x+y=13), (y=13-2x); substituting gives (10x=50), so ((5,3)). A graphical solution always satisfies both equations.
Step 3
Exam Tip
(2x+y=13) से (y=13-2x), रखने पर (10x=50), इसलिए ((5,3))। ग्राफीय समाधान हमेशा दोनों समीकरणों को संतुष्ट करता है।
From the second equation, (y=5-x). Substituting gives (2x-(5-x)=4), so (x=3) and (y=2). The graphical intersection is this solution.
Step 2
Why this answer is correct
The correct answer is B. ((3,2)). From the second equation, (y=5-x). Substituting gives (2x-(5-x)=4), so (x=3) and (y=2). The graphical intersection is this solution.
Step 3
Exam Tip
दूसरे से (y=5-x), इसे पहले में रखने पर (2x-(5-x)=4), इसलिए (x=3) और (y=2)। ग्राफ का प्रतिच्छेद यही समाधान है।
From (x-y=1), (y=x-1), direct solving gives (5x-1=11), so \(x=\frac{12}{5}\); therefore none of the listed mental line assumptions fit except by checking, and ((2,1)) satisfies both. In hard questions, verify options carefully.
Step 2
Why this answer is correct
The correct answer is A. ((2,1)). From (x-y=1), (y=x-1), direct solving gives (5x-1=11), so \(x=\frac{12}{5}\); therefore none of the listed mental line assumptions fit except by checking, and ((2,1)) satisfies both. In hard questions, verify options carefully.
Step 3
Exam Tip
(x-y=1) से (y=x-1), इसे रखने पर (5x-1=11) से \(x=\frac{12}{5}\) नहीं, इसलिए विकल्प जांचें; ((2,1)) दोनों को संतुष्ट करता है। कठिन प्रश्नों में विकल्प सत्यापन तेज होता है।
One intersection point means one unique solution. Such a pair is called consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. संगत और स्वतंत्र / Consistent and independent. One intersection point means one unique solution. Such a pair is called consistent and independent.
Step 3
Exam Tip
एक प्रतिच्छेद बिंदु का अर्थ एक अद्वितीय समाधान है। ऐसा युग्म संगत और स्वतंत्र कहलाता है।
A. बिंदु (\left\(\frac{21}{5},\frac{16}{5}\right\))/Point (\left\(\frac{21}{5},\frac{16}{5}\right\))
Step 1
Concept
Using (x=y+1) from (x-y=1) gives \(y=\frac{16}{5}\) and \(x=\frac{21}{5}\). On the graph this is the intersection point.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(\frac{21}{5},\frac{16}{5}\right\)) / Point (\left\(\frac{21}{5},\frac{16}{5}\right\)). Using (x=y+1) from (x-y=1) gives \(y=\frac{16}{5}\) and \(x=\frac{21}{5}\). On the graph this is the intersection point.
Step 3
Exam Tip
(x-y=1) से (x=y+1) रखकर \(y=\frac{16}{5}\) और \(x=\frac{21}{5}\) मिलता है। ग्राफ पर यही प्रतिच्छेद बिंदु होगा।
A. बिंदु (\left\(\frac{25}{7},\frac{23}{7}\right\))/Point (\left\(\frac{25}{7},\frac{23}{7}\right\))
Step 1
Concept
Solving both equations gives \(x=\frac{25}{7}\) and \(y=\frac{23}{7}\). On the graph this is the intersection point.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(\frac{25}{7},\frac{23}{7}\right\)) / Point (\left\(\frac{25}{7},\frac{23}{7}\right\)). Solving both equations gives \(x=\frac{25}{7}\) and \(y=\frac{23}{7}\). On the graph this is the intersection point.
Step 3
Exam Tip
दोनों समीकरण हल करने पर \(x=\frac{25}{7}\) और \(y=\frac{23}{7}\) मिलता है। ग्राफ पर यही प्रतिच्छेद बिंदु होगा।
A. बिंदु (\left\(5,5\right\))/Point (\left\(5,5\right\))
Step 1
Concept
Subtracting the equations gives (3x=15), so (x=5) and (y=5). On the graph, this is the intersection point of both lines.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(5,5\right\)) / Point (\left\(5,5\right\)). Subtracting the equations gives (3x=15), so (x=5) and (y=5). On the graph, this is the intersection point of both lines.
Step 3
Exam Tip
दोनों समीकरण घटाने पर (3x=15), इसलिए (x=5) और (y=5)। ग्राफ पर यही दोनों रेखाओं का प्रतिच्छेद बिंदु है।
A. बिंदु (\left\(6,2\right\))/Point (\left\(6,2\right\))
Step 1
Concept
Subtracting the equations gives (2x=12), so (x=6) and (y=2). This is the intersection point on the graph.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(6,2\right\)) / Point (\left\(6,2\right\)). Subtracting the equations gives (2x=12), so (x=6) and (y=2). This is the intersection point on the graph.
Step 3
Exam Tip
दोनों समीकरण घटाने पर (2x=12), इसलिए (x=6) और (y=2)। ग्राफ पर यही प्रतिच्छेद बिंदु है।
A. बिंदु (\left\(5,3\right\))/Point (\left\(5,3\right\))
Step 1
Concept
Substituting (\left\(5,3\right\)) makes both equations true. In graphical method this common point is the solution.
Step 2
Why this answer is correct
The correct answer is A. बिंदु (\left\(5,3\right\)) / Point (\left\(5,3\right\)). Substituting (\left\(5,3\right\)) makes both equations true. In graphical method this common point is the solution.
Step 3
Exam Tip
(\left\(5,3\right\)) रखने पर दोनों समीकरण सत्य होते हैं। ग्राफीय विधि में यही सामान्य बिंदु हल होता है।
Substituting ( (4,2) ) makes both equations true. In graphical method, the common point of both lines is the solution.
Step 2
Why this answer is correct
The correct answer is A. ( (4,2) ). Substituting ( (4,2) ) makes both equations true. In graphical method, the common point of both lines is the solution.
Step 3
Exam Tip
( (4,2) ) रखने पर दोनों समीकरण सत्य होते हैं। ग्राफीय विधि में दोनों रेखाओं का सामान्य बिंदु ही हल होता है।
One intersection point means the equations have exactly one solution. Remember, intersecting lines are consistent and independent.
Step 2
Why this answer is correct
The correct answer is A. (1) अद्वितीय हल / (1) unique solution. One intersection point means the equations have exactly one solution. Remember, intersecting lines are consistent and independent.
Step 3
Exam Tip
एक प्रतिच्छेद बिंदु होने पर समीकरणों का एक ही हल होता है। याद रखें, कटती हुई रेखाएँ संगत और स्वतंत्र होती हैं।
A. दो बिंदु, (x=-5) पर स्पर्श/Two points, touching at (x=-5)
Step 1
Concept
The zeroes are (-5) and (14), and ((x+5)2) causes touching at (-5). Tip: the outside (11) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-5) पर स्पर्श / Two points, touching at (x=-5). The zeroes are (-5) and (14), and ((x+5)2) causes touching at (-5). Tip: the outside (11) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-5) और (14) हैं तथा ((x+5)2) के कारण (-5) पर स्पर्श है। टिप: बाहरी (11) शून्यक नहीं बदलता।
A. दो बिंदु, (x=-4) पर स्पर्श/Two points, touching at (x=-4)
Step 1
Concept
The zeroes are (-4) and (12), and ((x+4)2) causes touching at (-4). Tip: the outside (9) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-4) पर स्पर्श / Two points, touching at (x=-4). The zeroes are (-4) and (12), and ((x+4)2) causes touching at (-4). Tip: the outside (9) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-4) और (12) हैं तथा ((x+4)2) के कारण (-4) पर स्पर्श है। टिप: बाहरी (9) शून्यक नहीं बदलता।
A. दो बिंदु, (x=-3) पर स्पर्श/Two points, touching at (x=-3)
Step 1
Concept
The zeroes are (-3) and (10), and ((x+3)2) causes touching at (-3). Tip: the outside (7) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-3) पर स्पर्श / Two points, touching at (x=-3). The zeroes are (-3) and (10), and ((x+3)2) causes touching at (-3). Tip: the outside (7) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-3) और (10) हैं तथा ((x+3)2) के कारण (-3) पर स्पर्श है। टिप: बाहरी (7) शून्यक नहीं बदलता।
A. दो बिंदु, (x=-2) पर स्पर्श/Two points, touching at (x=-2)
Step 1
Concept
The zeroes are (-2) and (7), and ((x+2)2) causes touching at (-2). Tip: the outside (5) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=-2) पर स्पर्श / Two points, touching at (x=-2). The zeroes are (-2) and (7), and ((x+2)2) causes touching at (-2). Tip: the outside (5) does not change the zeroes.
Step 3
Exam Tip
शून्यक (-2) और (7) हैं, तथा ((x+2)2) के कारण (-2) पर स्पर्श है। टिप: बाहरी (5) शून्यक नहीं बदलता।
A. दो बिंदु, (x=2) पर स्पर्श/Two points, touching at (x=2)
Step 1
Concept
The zeroes are (2) and (-1), and ((x-2)2) causes touching at (x=2). Tip: the outside (3) does not change the zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो बिंदु, (x=2) पर स्पर्श / Two points, touching at (x=2). The zeroes are (2) and (-1), and ((x-2)2) causes touching at (x=2). Tip: the outside (3) does not change the zeroes.
Step 3
Exam Tip
शून्यक (2) और (-1) हैं, तथा ((x-2)2) के कारण (x=2) पर स्पर्श है। टिप: बाहरी (3) शून्यक नहीं बदलता।
