A. (\left\(3,0\right\)) और (\left\(0,-8\right\))/(\left\(3,0\right\)) and (\left\(0,-8\right\))
Step 1
Concept
At (y=0), (x=3), and at (x=0), (y=-8). Plot the negative intercept in the correct direction on the graph.
Step 2
Why this answer is correct
The correct answer is A. (\left\(3,0\right\)) और (\left\(0,-8\right\)) / (\left\(3,0\right\)) and (\left\(0,-8\right\)). At (y=0), (x=3), and at (x=0), (y=-8). Plot the negative intercept in the correct direction on the graph.
Step 3
Exam Tip
(y=0) पर (x=3) और (x=0) पर (y=-8)। ऋण अवरोध को ग्राफ में सही दिशा में अंकित करें।
A. (\left\(0,-4\right\)) और (\left\(16,0\right\))/(\left\(0,-4\right\)) and (\left\(16,0\right\))
Step 1
Concept
At (x=0), (y=-4), and at (y=0), (x=16). While finding intercepts, note which variable is kept zero.
Step 2
Why this answer is correct
The correct answer is A. (\left\(0,-4\right\)) और (\left\(16,0\right\)) / (\left\(0,-4\right\)) and (\left\(16,0\right\)). At (x=0), (y=-4), and at (y=0), (x=16). While finding intercepts, note which variable is kept zero.
Step 3
Exam Tip
(x=0) पर (y=-4) और (y=0) पर (x=16)। अवरोध निकालते समय कौन-सा चर शून्य रखा है, यह ध्यान रखें।
A. (\left\(5,0\right\)) और (\left\(0,-9\right\))/(\left\(5,0\right\)) and (\left\(0,-9\right\))
Step 1
Concept
At (y=0), (x=5), and at (x=0), (y=-9). Plot the negative intercept in the correct direction.
Step 2
Why this answer is correct
The correct answer is A. (\left\(5,0\right\)) और (\left\(0,-9\right\)) / (\left\(5,0\right\)) and (\left\(0,-9\right\)). At (y=0), (x=5), and at (x=0), (y=-9). Plot the negative intercept in the correct direction.
Step 3
Exam Tip
(y=0) पर (x=5) और (x=0) पर (y=-9)। ऋण अवरोध को सही दिशा में अंकित करें।
A. (\left\(0,-4\right\)) और (\left\(12,0\right\))/(\left\(0,-4\right\)) and (\left\(12,0\right\))
Step 1
Concept
At (x=0), (y=-4), and at (y=0), (x=12). While finding intercepts, note which variable is kept zero.
Step 2
Why this answer is correct
The correct answer is A. (\left\(0,-4\right\)) और (\left\(12,0\right\)) / (\left\(0,-4\right\)) and (\left\(12,0\right\)). At (x=0), (y=-4), and at (y=0), (x=12). While finding intercepts, note which variable is kept zero.
Step 3
Exam Tip
(x=0) पर (y=-4) और (y=0) पर (x=12)। अवरोध निकालते समय कौन-सा चर शून्य रखा है, यह ध्यान रखें।
A. (\left\(4,0\right\)) और (\left\(0,-7\right\))/(\left\(4,0\right\)) and (\left\(0,-7\right\))
Step 1
Concept
At (y=0), (x=4), and at (x=0), (y=-7). Plot the negative intercept in the correct direction.
Step 2
Why this answer is correct
The correct answer is A. (\left\(4,0\right\)) और (\left\(0,-7\right\)) / (\left\(4,0\right\)) and (\left\(0,-7\right\)). At (y=0), (x=4), and at (x=0), (y=-7). Plot the negative intercept in the correct direction.
Step 3
Exam Tip
(y=0) पर (x=4) और (x=0) पर (y=-7)। ऋण अवरोध को सही दिशा में अंकित करें।
A. (\left\(10,0\right\)) और (\left\(0,6\right\))/(\left\(10,0\right\)) and (\left\(0,6\right\))
Step 1
Concept
Putting (y=0) gives (x=10), and putting (x=0) gives (y=6). Intercepts make line drawing easier.
Step 2
Why this answer is correct
The correct answer is A. (\left\(10,0\right\)) और (\left\(0,6\right\)) / (\left\(10,0\right\)) and (\left\(0,6\right\)). Putting (y=0) gives (x=10), and putting (x=0) gives (y=6). Intercepts make line drawing easier.
Step 3
Exam Tip
(y=0) रखने पर (x=10) और (x=0) रखने पर (y=6)। अवरोधों से रेखा खींचना आसान होता है।
A. ( (10,0) ) और ( (0,4) )/( (10,0) ) and ( (0,4) )
Step 1
Concept
Putting (y=0) gives (x=10), and putting (x=0) gives (y=4). Intercepts make the graph quick and clear.
Step 2
Why this answer is correct
The correct answer is A. ( (10,0) ) और ( (0,4) ) / ( (10,0) ) and ( (0,4) ). Putting (y=0) gives (x=10), and putting (x=0) gives (y=4). Intercepts make the graph quick and clear.
Step 3
Exam Tip
(y=0) रखने पर (x=10) और (x=0) रखने पर (y=4)। अवरोधों से ग्राफ जल्दी और साफ बनता है।
At (y=0), (x=4), and at (x=0), (y=6). Intercepts help draw the line quickly.
Step 2
Why this answer is correct
The correct answer is B. ( (4,0) ) और ( (0,6) ) / ( (4,0) ) and ( (0,6) ). At (y=0), (x=4), and at (x=0), (y=6). Intercepts help draw the line quickly.
Step 3
Exam Tip
(y=0) पर (x=4) और (x=0) पर (y=6)। अवरोधों से रेखा जल्दी खींची जा सकती है।
Three distinct (x)-values give three distinct (x)-axis points. Tip: distinct zeroes make distinct intersection points.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. Three distinct (x)-values give three distinct (x)-axis points. Tip: distinct zeroes make distinct intersection points.
Step 3
Exam Tip
तीन अलग (x)-मान तीन अलग (x)-अक्ष बिंदु देते हैं। टिप: अलग शून्यक अलग कटान बिंदु बनाते हैं।
Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 3
Exam Tip
अलग शून्यक अलग (x)-अक्ष मिलने वाले बिंदुओं की संख्या से मिलते हैं। टिप: घात से अधिकतम संख्या मिलती है, वास्तविक गिनती ग्राफ से पढ़ें।
Same slope and different intercepts make the lines distinct parallel. Therefore, the pair is inconsistent.
Step 2
Why this answer is correct
The correct answer is B. असंगत / Inconsistent. Same slope and different intercepts make the lines distinct parallel. Therefore, the pair is inconsistent.
Step 3
Exam Tip
समान ढाल और अलग अवरोध रेखाओं को अलग समानांतर बनाते हैं। इसलिए युग्म असंगत होता है।
Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.
Step 3
Exam Tip
समान ढाल और अलग अवरोध रेखाओं को अलग समानांतर बनाते हैं। इसलिए कोई सामान्य हल नहीं होता।
Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.
Step 3
Exam Tip
समान ढाल और अलग अवरोध रेखाओं को अलग समानांतर बनाते हैं। इसलिए कोई सामान्य हल नहीं होता।
Same slope and different intercepts make the lines parallel and distinct. Therefore there is no common solution.
Step 2
Why this answer is correct
The correct answer is B. असंगत / Inconsistent. Same slope and different intercepts make the lines parallel and distinct. Therefore there is no common solution.
Step 3
Exam Tip
समान ढाल और अलग अवरोध से रेखाएं समानांतर और अलग होती हैं। इसलिए कोई सामान्य हल नहीं होता।
Same slope and different intercepts make the lines parallel. Distinct parallel lines give no solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं / No solution. Same slope and different intercepts make the lines parallel. Distinct parallel lines give no solution.
Step 3
Exam Tip
समान ढाल और अलग अवरोध रेखाओं को समानांतर बनाते हैं। समानांतर अलग रेखाएं कोई हल नहीं देतीं।
Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 3
Exam Tip
समान ढाल और अलग (y)-अवरोध वाली रेखाएं समांतर होती हैं। इसलिए उनका कोई प्रतिच्छेद नहीं होता।
Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 3
Exam Tip
समान ढाल और अलग (y)-अवरोध वाली रेखाएं समांतर होती हैं। इसलिए उनका कोई प्रतिच्छेद नहीं होता।
Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 2
Why this answer is correct
The correct answer is B. कोई समाधान नहीं / No solution. Lines with equal slopes and different (y)-intercepts are parallel. Therefore they have no intersection.
Step 3
Exam Tip
समान ढाल और अलग (y)-अवरोध वाली रेखाएं समांतर होती हैं। इसलिए उनका कोई प्रतिच्छेद नहीं होता।
The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=90). For (k=88), the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=88). The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=90). For (k=88), the lines are distinct and parallel.
Step 3
Exam Tip
गुणांक का अनुपात \(\frac{1}{2}\) है, इसलिए संपाती होने के लिए (k=90) चाहिए। (k=88) पर रेखाएं समांतर अलग-अलग हैं।
For parallel lines, \(\frac{3}{9}=\frac{a}{12}\), so (a=4). Since \(\frac{15}{47}\neq\frac{1}{3}\), they will not be coincident.
Step 2
Why this answer is correct
The correct answer is C. (a=4). For parallel lines, \(\frac{3}{9}=\frac{a}{12}\), so (a=4). Since \(\frac{15}{47}\neq\frac{1}{3}\), they will not be coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{3}{9}=\frac{a}{12}\), इसलिए (a=4)। चूंकि \(\frac{15}{47}\neq\frac{1}{3}\), वे संपाती नहीं होंगी।
The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=42). For (k=40), the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=40). The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=42). For (k=40), the lines are distinct and parallel.
Step 3
Exam Tip
गुणांक का अनुपात \(\frac{1}{2}\) है, इसलिए संपाती होने के लिए (k=42) चाहिए। (k=40) पर रेखाएं समांतर अलग-अलग हैं।
For parallel lines, \(\frac{4}{8}=\frac{a}{10}\), so (a=5). Since \(\frac{16}{35}\neq\frac{1}{2}\), they will not be coincident.
Step 2
Why this answer is correct
The correct answer is B. (a=5). For parallel lines, \(\frac{4}{8}=\frac{a}{10}\), so (a=5). Since \(\frac{16}{35}\neq\frac{1}{2}\), they will not be coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{4}{8}=\frac{a}{10}\), इसलिए (a=5)। चूंकि \(\frac{16}{35}\neq\frac{1}{2}\), वे संपाती नहीं होंगी।
The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=24). For (k=20), the lines are distinct and parallel.
Step 2
Why this answer is correct
The correct answer is B. (k=20). The coefficient ratio is \(\frac{1}{2}\), so coincidence needs (k=24). For (k=20), the lines are distinct and parallel.
Step 3
Exam Tip
गुणांक का अनुपात \(\frac{1}{2}\) है, इसलिए संपाती होने के लिए (k=24) चाहिए। (k=20) पर रेखाएं समांतर अलग-अलग हैं।
For parallel lines, \(\frac{2}{6}=\frac{a}{9}\), so (a=3). Since \(\frac{10}{31}\neq\frac{1}{3}\), the lines are not coincident.
Step 2
Why this answer is correct
The correct answer is B. (a=3). For parallel lines, \(\frac{2}{6}=\frac{a}{9}\), so (a=3). Since \(\frac{10}{31}\neq\frac{1}{3}\), the lines are not coincident.
Step 3
Exam Tip
समांतर के लिए \(\frac{2}{6}=\frac{a}{9}\), इसलिए (a=3)। चूंकि \(\frac{10}{31}\neq\frac{1}{3}\), रेखाएं संपाती नहीं होंगी।
The coefficient ratio is \(\frac{3}{6}=\frac{2}{4}=\frac{1}{2}\); for coincidence, (k=14) is needed. With (k=7), the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is B. (7). The coefficient ratio is \(\frac{3}{6}=\frac{2}{4}=\frac{1}{2}\); for coincidence, (k=14) is needed. With (k=7), the lines are parallel and distinct.
Step 3
Exam Tip
गुणांक अनुपात \(\frac{3}{6}=\frac{2}{4}=\frac{1}{2}\) है; संपाती होने के लिए (k=14) चाहिए। (k=7) होने पर रेखाएं समांतर अलग-अलग होंगी।
Dividing (6x-4y=20) by (2) gives (3x-2y=10). Same left side with different constants gives distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. (6x-4y=20). Dividing (6x-4y=20) by (2) gives (3x-2y=10). Same left side with different constants gives distinct parallel lines.
Step 3
Exam Tip
(6x-4y=20) को (2) से भाग देने पर (3x-2y=10) मिलता है। समान बाएँ पक्ष और अलग नियतांक अलग समांतर रेखाएँ देते हैं।
Dividing (4x-6y=18) by (2) gives (2x-3y=9). Same left side with different constants gives distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. (4x-6y=18). Dividing (4x-6y=18) by (2) gives (2x-3y=9). Same left side with different constants gives distinct parallel lines.
Step 3
Exam Tip
(4x-6y=18) को (2) से भाग देने पर (2x-3y=9) मिलता है। समान बाएँ पक्ष और अलग नियतांक अलग समांतर रेखाएँ देते हैं।
Dividing (2x+6y=30) by (2) gives (x+3y=15). Same left side with different constants gives distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. (2x+6y=30). Dividing (2x+6y=30) by (2) gives (x+3y=15). Same left side with different constants gives distinct parallel lines.
Step 3
Exam Tip
(2x+6y=30) को (2) से भाग देने पर (x+3y=15) मिलता है। समान बाएँ पक्ष और अलग नियतांक समांतर अलग रेखाएँ देते हैं।
A. \(\theta<0\) या \(\theta>3\)/\(\theta<0\) or \(\theta>3\)
Step 1
Concept
Here (D=4\theta-2-12\theta=4\theta\(\theta-3\)). From (D>0), \(\theta<0\) or \(\theta>3\).
Step 2
Why this answer is correct
The correct answer is A. \(\theta<0\) या \(\theta>3\) / \(\theta<0\) or \(\theta>3\). Here (D=4\theta-2-12\theta=4\theta\(\theta-3\)). From (D>0), \(\theta<0\) or \(\theta>3\).
Step 3
Exam Tip
यहाँ (D=4\theta-2-12\theta=4\theta\(\theta-3\)) है। (D>0) से \(\theta<0\) या \(\theta>3\)।
A. \(\lambda<0\) या \(\lambda>1\)/\(\lambda<0\) or \(\lambda>1\)
Step 1
Concept
Here (D=4\lambda-2-4\lambda=4\lambda\(\lambda-1\)). For distinct real roots (D>0), so \(\lambda<0\) or \(\lambda>1\).
Step 2
Why this answer is correct
The correct answer is A. \(\lambda<0\) या \(\lambda>1\) / \(\lambda<0\) or \(\lambda>1\). Here (D=4\lambda-2-4\lambda=4\lambda\(\lambda-1\)). For distinct real roots (D>0), so \(\lambda<0\) or \(\lambda>1\).
Step 3
Exam Tip
यहाँ (D=4\lambda-2-4\lambda=4\lambda\(\lambda-1\)) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए \(\lambda<0\) या \(\lambda>1\)।
A. \(k<2-4\sqrt{3}\) या \(k>2+4\sqrt{3}\)/\(k<2-4\sqrt{3}\) or \(k>2+4\sqrt{3}\)
Step 1
Concept
Here (D=(k-2)2-48). For distinct real roots (D>0), so ((k-2)2>48).
Step 2
Why this answer is correct
The correct answer is A. \(k<2-4\sqrt{3}\) या \(k>2+4\sqrt{3}\) / \(k<2-4\sqrt{3}\) or \(k>2+4\sqrt{3}\). Here (D=(k-2)2-48). For distinct real roots (D>0), so ((k-2)2>48).
Step 3
Exam Tip
यहाँ (D=(k-2)2-48) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए ((k-2)2>48)।
A. \(k<-1-2\sqrt{6}\) या \(k>-1+2\sqrt{6}\)/\(k<-1-2\sqrt{6}\) or \(k>-1+2\sqrt{6}\)
Step 1
Concept
Here (D=(k+1)2-24). For distinct real roots (D>0), so ((k+1)2>24).
Step 2
Why this answer is correct
The correct answer is A. \(k<-1-2\sqrt{6}\) या \(k>-1+2\sqrt{6}\) / \(k<-1-2\sqrt{6}\) or \(k>-1+2\sqrt{6}\). Here (D=(k+1)2-24). For distinct real roots (D>0), so ((k+1)2>24).
Step 3
Exam Tip
यहाँ (D=(k+1)2-24) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए ((k+1)2>24)।
In the first equation, (D=100-92=8>0), and (8) is not a perfect square. So the roots are real, irrational and distinct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+23=0\). In the first equation, (D=100-92=8>0), and (8) is not a perfect square. So the roots are real, irrational and distinct.
Step 3
Exam Tip
पहले समीकरण में (D=100-92=8>0) है और (8) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न हैं।
A. \(k^2<9\) और \(k\neq0\)/\(k^2<9\) and \(k\neq0\)
Step 1
Concept
Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).
Step 2
Why this answer is correct
The correct answer is A. \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\). Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).
Step 3
Exam Tip
यहाँ \(D=36-4k^2\) है। वास्तविक और भिन्न मूलों के लिए (D>0) और \(k\neq0\), अतः \(k^2<9\)।
For both roots to be negative, the sum (-12) and product \(\lambda>0\) are needed. For real distinct roots, \(144-4\lambda>0\), so \(0<\lambda<36\).
Step 2
Why this answer is correct
The correct answer is A. \(0<\lambda<36\). For both roots to be negative, the sum (-12) and product \(\lambda>0\) are needed. For real distinct roots, \(144-4\lambda>0\), so \(0<\lambda<36\).
Step 3
Exam Tip
दोनों ऋणात्मक जड़ों के लिए योग (-12) और गुणनफल \(\lambda>0\) चाहिए। वास्तविक भिन्न जड़ों के लिए \(144-4\lambda>0\), इसलिए \(0<\lambda<36\)।
For both roots to be negative, the sum (-10) and product \(\lambda>0\) are needed. For real distinct roots, \(100-4\lambda>0\), hence \(0<\lambda<25\).
Step 2
Why this answer is correct
The correct answer is B. \(0<\lambda<25\). For both roots to be negative, the sum (-10) and product \(\lambda>0\) are needed. For real distinct roots, \(100-4\lambda>0\), hence \(0<\lambda<25\).
Step 3
Exam Tip
दोनों ऋणात्मक जड़ों के लिए योग (-10) और गुणनफल \(\lambda>0\) चाहिए। वास्तविक भिन्न जड़ों के लिए \(100-4\lambda>0\), इसलिए \(0<\lambda<25\)।
For both roots to be negative, the sum (-2) and product \(\lambda>0\) are needed. For real distinct roots, \(4-4\lambda>0\), hence \(0<\lambda<1\).
Step 2
Why this answer is correct
The correct answer is A. \(0<\lambda<1\). For both roots to be negative, the sum (-2) and product \(\lambda>0\) are needed. For real distinct roots, \(4-4\lambda>0\), hence \(0<\lambda<1\).
Step 3
Exam Tip
दोनों ऋणात्मक जड़ों के लिए योग (-2) और गुणनफल \(\lambda>0\) चाहिए। वास्तविक भिन्न जड़ों के लिए \(4-4\lambda>0\), इसलिए \(0<\lambda<1\)।
A. दो भिन्न वास्तविक शून्यक/Two distinct real zeroes
Step 1
Concept
Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो भिन्न वास्तविक शून्यक / Two distinct real zeroes. Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.
Step 3
Exam Tip
दो अलग कटान दो अलग वास्तविक शून्यक देते हैं। ग्राफ में अलग (x)-प्रतिच्छेद अलग शून्यक होते हैं।
The vertex lies on the (x)-axis, so the parabola touches at ((-14,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((-14,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((-14,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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।
For eight distinct real zeroes, the degree must be at least (8). Tip: the number of distinct zeroes cannot exceed the degree.
Step 2
Why this answer is correct
The correct answer is C. (8). For eight distinct real zeroes, the degree must be at least (8). Tip: the number of distinct zeroes cannot exceed the degree.
Step 3
Exam Tip
आठ अलग वास्तविक शून्यकों के लिए घात कम से कम (8) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।
Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-11) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (c) और (-d) / (c) and (-d). From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.
Step 3
Exam Tip
(x-c=0) से (c) और (x+d=0) से (-d) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।
There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 2
Why this answer is correct
The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 3
Exam Tip
दो अलग शून्यक (-2) और (5) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।
The vertex lies on the (x)-axis, so the parabola touches at ((12,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((12,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((12,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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।
For seven distinct real zeroes, the degree must be at least (7). Tip: the number of distinct zeroes cannot exceed the degree.
Step 2
Why this answer is correct
The correct answer is C. (7). For seven distinct real zeroes, the degree must be at least (7). Tip: the number of distinct zeroes cannot exceed the degree.
Step 3
Exam Tip
सात अलग वास्तविक शून्यकों के लिए घात कम से कम (7) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।
Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-7) और (2) हैं। टिप: समान (x)-मान को एक बार गिनें।
From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-a) और (b) / (-a) and (b). From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.
Step 3
Exam Tip
(x+a=0) से (-a) और (x-b=0) से (b) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।
