100 results found for "distinct chairs" in Class 10.
एक विद्यालय में पहली पंक्ति में (12) कुर्सियाँ हैं और हर अगली पंक्ति में (3) कुर्सियाँ अधिक हैं। (15)वीं पंक्ति में कितनी कुर्सियाँ होंगी?
In a school hall, the first row has (12) chairs and each next row has (3) more chairs. How many chairs will be in the (15)th row?
#ap word problem
#nth term
#chairs
A (51)
B (54)
C (57)
D (54) से कम / Less than (54)
Explanation opens after your attempt
Step 1
Concept
Here (a=12), (d=3), so \(a_{15}=12+14\times3=54\). In word problems, treat rows as terms.
Step 2
Why this answer is correct
The correct answer is B. (54). Here (a=12), (d=3), so \(a_{15}=12+14\times3=54\). In word problems, treat rows as terms.
Step 3
Exam Tip
यहाँ (a=12), (d=3) है, इसलिए \(a_{15}=12+14\times3=54\)। शब्द प्रश्न में पंक्तियों को पद मानें।
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एक हॉल की पहली पंक्ति में (16) कुर्सियां हैं और हर अगली पंक्ति में (3) कुर्सियां अधिक हैं। यदि कुल (425) कुर्सियां हैं तो पंक्तियों की संख्या कितनी है?
The first row of a hall has (16) chairs and each next row has (3) more chairs. If there are (425) chairs in total then how many rows are there?
#ap
#word-problem
#find-n
A (10)
B (12)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
Putting \(S_n=425\) in the sum formula gives (n=10). Exam tip: when total sum is given, form an equation for (n).
Step 2
Why this answer is correct
The correct answer is A. (10). Putting \(S_n=425\) in the sum formula gives (n=10). Exam tip: when total sum is given, form an equation for (n).
Step 3
Exam Tip
योग सूत्र में \(S_n=425\) रखने पर (n=10) मिलता है। परीक्षा में कुल योग दिया हो तो (n) के लिए समीकरण बनाएं।
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एक हॉल की पहली पंक्ति में (14) कुर्सियां हैं और हर अगली पंक्ति में (2) कुर्सियां अधिक हैं। यदि कुल (360) कुर्सियां हैं तो पंक्तियों की संख्या कितनी है?
The first row of a hall has (14) chairs and each next row has (2) more chairs. If there are (360) chairs in total then how many rows are there?
#ap
#word-problem
#find-n
A (14)
B (15)
C (16)
D (18)
Explanation opens after your attempt
Step 1
Concept
Putting \(S_n=360\) gives (n=15). Exam tip: when total sum is given, form an equation for (n).
Step 2
Why this answer is correct
The correct answer is B. (15). Putting \(S_n=360\) gives (n=15). Exam tip: when total sum is given, form an equation for (n).
Step 3
Exam Tip
योग सूत्र में \(S_n=360\) रखने पर (n=15) मिलता है। परीक्षा में कुल योग दिया हो तो (n) के लिए समीकरण बनाएं।
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एक कुर्सी व्यवस्था में पहली पंक्ति में (9) कुर्सियां हैं और हर अगली पंक्ति में (3) कुर्सियां अधिक हैं। यदि कुल (306) कुर्सियां हैं तो पंक्तियां कितनी हैं?
In a chair arrangement the first row has (9) chairs and each next row has (3) more chairs. If there are (306) chairs in total then how many rows are there?
#ap
#word-problem
#arrangement
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Putting \(S_n=306\) in the sum formula gives (n=12). Exam tip: you can also check options in the sum formula.
Step 2
Why this answer is correct
The correct answer is C. (12). Putting \(S_n=306\) in the sum formula gives (n=12). Exam tip: you can also check options in the sum formula.
Step 3
Exam Tip
योग सूत्र में \(S_n=306\) रखने पर (n=12) मिलता है। परीक्षा में विकल्पों को योग सूत्र में रखकर भी जांच सकते हैं।
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एक हॉल की पहली पंक्ति में (12) कुर्सियां हैं और हर अगली पंक्ति में (2) कुर्सियां अधिक हैं। यदि कुल (432) कुर्सियां हैं तो पंक्तियों की संख्या कितनी है?
The first row of a hall has (12) chairs and each next row has (2) more chairs. If there are (432) chairs in total then how many rows are there?
#ap
#word-problem
#find-n
A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
Putting \(S_n=432\) gives (n=16). Exam tip: when total sum is given, form an equation for (n).
Step 2
Why this answer is correct
The correct answer is C. (16). Putting \(S_n=432\) gives (n=16). Exam tip: when total sum is given, form an equation for (n).
Step 3
Exam Tip
यहां \(S_n=432\) रखने पर (n=16) मिलता है। परीक्षा में कुल योग दिया हो तो (n) के लिए समीकरण बनाएं।
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एक मैदान में कुर्सियों की पंक्तियाँ \(80,115,150,\ldots\) के क्रम में हैं। पहले (10) पंक्तियों में कुल कितनी कुर्सियाँ होंगी?
In a ground, rows of chairs follow \(80,115,150,\ldots\). How many chairs will there be in the first (10) rows?
#word_problem
#chairs
#ap_sum
A (2325)
B (2350)
C (2375)
D (2400)
Explanation opens after your attempt
Step 1
Concept
The tenth row has (395) chairs, so the total is (S_{10}=\frac{10}{2}(80+395)=2375). Treat rows as the number of terms.
Step 2
Why this answer is correct
The correct answer is C. (2375). The tenth row has (395) chairs, so the total is (S_{10}=\frac{10}{2}(80+395)=2375). Treat rows as the number of terms.
Step 3
Exam Tip
दसवीं पंक्ति में (395) कुर्सियाँ हैं, इसलिए कुल (S_{10}=\frac{10}{2}(80+395)=2375) है। पंक्तियों को पदों की संख्या मानें।
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एक पंक्ति में कुर्सियों की संख्या \(8,11,14,\ldots\) के क्रम में बढ़ती है। पहले (10) पंक्तियों में कुल कितनी कुर्सियाँ होंगी?
The number of chairs in rows increases as \(8,11,14,\ldots\). How many chairs will there be in the first (10) rows?
#word_problem
#chairs
#ap_sum
A (205)
B (210)
C (215)
D (220)
Explanation opens after your attempt
Step 1
Concept
This is an arithmetic progression with (a=8), (d=3), and (n=10), so there will be (215) chairs. In word problems, convert the pattern into a progression.
Step 2
Why this answer is correct
The correct answer is C. (215). This is an arithmetic progression with (a=8), (d=3), and (n=10), so there will be (215) chairs. In word problems, convert the pattern into a progression.
Step 3
Exam Tip
यह समांतर श्रेढ़ी है जिसमें (a=8), (d=3), (n=10), इसलिए कुल (215) कुर्सियाँ होंगी। शब्द-प्रश्न में क्रम को श्रेढ़ी में बदलें।
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एक सभागार की पहली पंक्ति में (24) कुर्सियां हैं और हर अगली पंक्ति में (3) कुर्सियां अधिक हैं। (16)वीं पंक्ति में कितनी कुर्सियां होंगी?
An auditorium has (24) chairs in the first row and each next row has (3) more chairs. How many chairs are in the (16)th row?
#ap
#word-problem
#seating
#nth-term
A (66)
B (69)
C (72)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(a_{16}=24+15\times3=69\). Up to the (16)th row, the difference is added (15) times.
Step 2
Why this answer is correct
The correct answer is B. (69). \(a_{16}=24+15\times3=69\). Up to the (16)th row, the difference is added (15) times.
Step 3
Exam Tip
\(a_{16}=24+15\times3=69\)। (16)वीं पंक्ति तक अंतर (15) बार जुड़ता है।
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एक सभा में (x) पंक्तियाँ हैं और हर पंक्ति में (x+30) कुर्सियाँ हैं। कुल (2275) कुर्सियाँ हैं। पंक्तियाँ कितनी हैं?
In an assembly, there are (x) rows and (x+30) chairs in each row. There are (2275) chairs in total. How many rows are there?
#quadratic equations
#arrangement
#chairs
A (25)
B (30)
C (35)
D (65)
Explanation opens after your attempt
Step 1
Concept
Total chairs are (x(x+30)=2275). This gives (x=35).
Step 2
Why this answer is correct
The correct answer is C. (35). Total chairs are (x(x+30)=2275). This gives (x=35).
Step 3
Exam Tip
कुल कुर्सियाँ (x(x+30)=2275) हैं। इससे (x=35) मिलता है।
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एक सभा में (x) पंक्तियाँ हैं और हर पंक्ति में (x+23) कुर्सियाँ हैं। कुल (1748) कुर्सियाँ हैं। पंक्तियाँ कितनी हैं?
In an assembly, there are (x) rows and (x+23) chairs in each row. There are (1748) chairs in total. How many rows are there?
#quadratic equations
#arrangement
#chairs
A (28)
B (31)
C (34)
D (46)
Explanation opens after your attempt
Step 1
Concept
Total chairs are (x(x+23)=1748). This gives (x=31).
Step 2
Why this answer is correct
The correct answer is B. (31). Total chairs are (x(x+23)=1748). This gives (x=31).
Step 3
Exam Tip
कुल कुर्सियाँ (x(x+23)=1748) हैं। इससे (x=31) मिलता है।
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एक सभा में (x) पंक्तियाँ हैं और हर पंक्ति में (x+17) कुर्सियाँ हैं। कुल (1248) कुर्सियाँ हैं। पंक्तियाँ कितनी हैं?
In an assembly, there are (x) rows and (x+17) chairs in each row. There are (1248) chairs in total. How many rows are there?
#quadratic equations
#arrangement
#chairs
A (24)
B (26)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
Total chairs are (x(x+17)=1248). This gives (x=32).
Step 2
Why this answer is correct
The correct answer is D. (32). Total chairs are (x(x+17)=1248). This gives (x=32).
Step 3
Exam Tip
कुल कुर्सियाँ (x(x+17)=1248) हैं। इससे (x=32) मिलता है।
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एक सभा में (x) पंक्तियाँ हैं और हर पंक्ति में (x+15) कुर्सियाँ हैं। कुल (850) कुर्सियाँ हैं। पंक्तियाँ कितनी हैं?
In an assembly, there are (x) rows and (x+15) chairs in each row. There are (850) chairs in total. How many rows are there?
#quadratic equations
#arrangement
#chairs
A (20)
B (25)
C (30)
D (34)
Explanation opens after your attempt
Step 1
Concept
Total chairs are (x(x+15)=850). This gives (x=25).
Step 2
Why this answer is correct
The correct answer is B. (25). Total chairs are (x(x+15)=850). This gives (x=25).
Step 3
Exam Tip
कुल कुर्सियाँ (x(x+15)=850) हैं। इससे (x=25) मिलता है।
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एक सभा में (x) पंक्तियाँ हैं और हर पंक्ति में (x+12) कुर्सियाँ हैं। कुल (640) कुर्सियाँ हैं। पंक्तियों की संख्या क्या है?
In an assembly, there are (x) rows and each row has (x+12) chairs. There are (640) chairs in total. What is the number of rows?
#quadratic equations
#arrangement
#chairs
A (16)
B (20)
C (24)
D (28)
Explanation opens after your attempt
Step 1
Concept
(x(x+12)=640) gives (x=20). For total objects, multiply groups and objects per group.
Step 2
Why this answer is correct
The correct answer is B. (20). (x(x+12)=640) gives (x=20). For total objects, multiply groups and objects per group.
Step 3
Exam Tip
(x(x+12)=640) से (x=20) मिलता है। कुल वस्तुओं के लिए समूहों और प्रति समूह वस्तुओं को गुणा करें।
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एक सभा में (x) पंक्तियाँ हैं और प्रत्येक पंक्ति में (x+10) कुर्सियाँ हैं। कुल (416) कुर्सियाँ हैं। पंक्तियों की संख्या क्या है?
In an assembly, there are (x) rows and each row has (x+10) chairs. There are (416) chairs in total. What is the number of rows?
#quadratic equations
#arrangement
#chairs
A (13)
B (16)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
(x(x+10)=416) gives (x=16). Use multiplication to find total objects.
Step 2
Why this answer is correct
The correct answer is B. (16). (x(x+10)=416) gives (x=16). Use multiplication to find total objects.
Step 3
Exam Tip
(x(x+10)=416) से (x=16) मिलता है। कुल वस्तुएँ निकालने में गुणा का प्रयोग करें।
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एक सभा में (x) पंक्तियाँ हैं और प्रत्येक पंक्ति में (x+3) कुर्सियाँ हैं। कुल (154) कुर्सियाँ हैं। पंक्तियों की संख्या क्या है?
In an assembly, there are (x) rows and (x+3) chairs in each row. There are (154) chairs in total. What is the number of rows?
#quadratic equations
#arrangement
#chairs
A (9)
B (11)
C (14)
D (17)
Explanation opens after your attempt
Step 1
Concept
(x(x+3)=154) gives (x=11). In a word problem, clearly writing what the variable means is the first step.
Step 2
Why this answer is correct
The correct answer is B. (11). (x(x+3)=154) gives (x=11). In a word problem, clearly writing what the variable means is the first step.
Step 3
Exam Tip
(x(x+3)=154) से (x=11) मिलता है। शब्द समस्या में चर का अर्थ साफ लिखना सबसे पहला कदम है।
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तीन कुर्सियों और दो मेजों की कीमत (4900) रुपये है। दो कुर्सियों और तीन मेजों की कीमत (5600) रुपये है। एक मेज की कीमत क्या है?
Three chairs and two tables cost (4900) rupees. Two chairs and three tables cost (5600) rupees. What is the price of one table?
#word-problem-cost-furniture
A (1200) रुपये / (1200) rupees
B (1300) रुपये / (1300) rupees
C (1400) रुपये / (1400) rupees
D (1500) रुपये / (1500) rupees
Explanation opens after your attempt
Correct Answer
C. (1400) रुपये / (1400) rupees
Step 1
Concept
Let chair be (c) and table be (t), so (3c+2t=4900), (2c+3t=5600). Elimination gives (t=1400).
Step 2
Why this answer is correct
The correct answer is C. (1400) रुपये / (1400) rupees. Let chair be (c) and table be (t), so (3c+2t=4900), (2c+3t=5600). Elimination gives (t=1400).
Step 3
Exam Tip
यदि कुर्सी (c) और मेज (t) हो तो (3c+2t=4900), (2c+3t=5600)। विलोपन से (t=1400) मिलता है।
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किसी बहुपद के लिए (p(1)=0), (p(2)=0), (p(3)=0) है। यदि ये तीनों अलग शून्यक हैं, तो ग्राफ (x)-अक्ष से कितने अलग बिंदुओं पर मिलेगा?
For a polynomial (p(1)=0), (p(2)=0), (p(3)=0). If these are three distinct zeroes, at how many distinct points will the graph meet the (x)-axis?
#distinct zeroes
#graph
#count
A एक / One
B दो / Two
C तीन / Three
D छह / Six
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
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।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर छूता और काटता है, तो अलग वास्तविक शून्यक कितने होंगे?
If the graph of a cubic polynomial touches or crosses the (x)-axis at two distinct points, how many distinct real zeroes will it have?
#cubic
#distinct zeroes
#graph reading
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
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।
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किस मान पर (5x+9y=45) और (10x+18y=k) की रेखाएं समांतर अलग-अलग होंगी?
For which value will (5x+9y=45) and (10x+18y=k) be distinct parallel lines?
#graphical method
#parameter
#parallel distinct
#no solution
A (k=90)
B (k=88)
C (k=45)
D (k=0)
Explanation opens after your attempt
Step 1
Concept
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।
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किस मान पर (3x+ay=15) और (9x+12y=47) की रेखाएं समांतर अलग-अलग होंगी?
For which value will the lines (3x+ay=15) and (9x+12y=47) be distinct and parallel?
#graphical method
#parameter
#parallel distinct
#no solution
A (a=2)
B (a=3)
C (a=4)
D (a=5)
Explanation opens after your attempt
Step 1
Concept
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।
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किस मान पर (3x+7y=21) और (6x+14y=k) की रेखाएं समांतर अलग-अलग होंगी?
For which value will (3x+7y=21) and (6x+14y=k) be distinct parallel lines?
#graphical method
#parameter
#parallel distinct
#no solution
A (k=42)
B (k=40)
C (k=21)
D (k=0)
Explanation opens after your attempt
Step 1
Concept
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।
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किस मान पर (4x+ay=16) और (8x+10y=35) की रेखाएं समांतर अलग-अलग होंगी?
For which value will the lines (4x+ay=16) and (8x+10y=35) be distinct and parallel?
#graphical method
#parameter
#parallel distinct
#no solution
A (a=4)
B (a=5)
C (a=6)
D (a=8)
Explanation opens after your attempt
Step 1
Concept
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।
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किस मान पर (x+4y=12) और (2x+8y=k) की रेखाएं समांतर अलग-अलग होंगी?
For which value will (x+4y=12) and (2x+8y=k) be distinct parallel lines?
#graphical method
#parameter
#parallel distinct
#no solution
A (k=24)
B (k=20)
C (k=12)
D (k=0)
Explanation opens after your attempt
Step 1
Concept
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।
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किस मान पर (2x+ay=10) और (6x+9y=31) की रेखाएं समांतर अलग-अलग होंगी?
For which value will (2x+ay=10) and (6x+9y=31) be distinct parallel lines?
#graphical method
#parameter
#parallel distinct
#no solution
A (a=2)
B (a=3)
C (a=4)
D (a=5)
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (3x+2y=7) और (6x+4y=k) की रेखाएं समांतर अलग-अलग हों, तो (k) के लिए कौन सा विकल्प सही है?
If the lines (3x+2y=7) and (6x+4y=k) are parallel and distinct, which option is correct for (k)?
#linear equations
#graphical method
#parameter
#parallel distinct
A (14)
B (7)
C (0)
D (-14)
Explanation opens after your attempt
Step 1
Concept
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।
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कौन-सी रेखा (3x-2y=7) के समांतर और अलग होगी?
Which line will be parallel and distinct to (3x-2y=7)?
#parallel line
#distinct line
#ratio test
A (6x-4y=14)
B (3x-2y=7)
C (6x-4y=20)
D (x-2y=7)
Explanation opens after your attempt
Correct Answer
C. (6x-4y=20)
Step 1
Concept
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।
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कौन-सी रेखा (2x-3y=6) के समांतर और अलग होगी?
Which line will be parallel and distinct to (2x-3y=6)?
#parallel line
#distinct line
#ratio test
A (4x-6y=12)
B (2x-3y=6)
C (4x-6y=18)
D (x-3y=6)
Explanation opens after your attempt
Correct Answer
C. (4x-6y=18)
Step 1
Concept
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।
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कौन-सी रेखा (x+3y=11) के समांतर और अलग होगी?
Which line will be parallel and distinct to (x+3y=11)?
#parallel lines
#distinct lines
#ratio test
A (2x+6y=22)
B (x+3y=11)
C (2x+6y=30)
D (x+y=11)
Explanation opens after your attempt
Correct Answer
C. (2x+6y=30)
Step 1
Concept
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।
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कौन-सी रेखा (x+2y=7) के समांतर और अलग होगी?
Which line will be parallel and distinct to (x+2y=7)?
#parallel lines
#distinct lines
#ratio test
A (2x+4y=14)
B (x+2y=7)
C (2x+4y=18)
D (x+y=7)
Explanation opens after your attempt
Correct Answer
C. (2x+4y=18)
Step 1
Concept
Dividing (2x+4y=18) by (2) gives (x+2y=9). Same left side with different constants gives distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. (2x+4y=18). Dividing (2x+4y=18) by (2) gives (x+2y=9). Same left side with different constants gives distinct parallel lines.
Step 3
Exam Tip
(2x+4y=18) को (2) से भाग देने पर (x+2y=9) मिलता है। समान बाएँ पक्ष और अलग नियतांक अलग समांतर रेखाएँ देते हैं।
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यदि (p(x)=x-3 -9x), तो इसके कितने भिन्न वास्तविक शून्यक हैं?
If (p(x)=x-3 -9x), how many distinct real zeroes does it have?
#distinct-zeroes
#cubic
#factorisation
A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
(x-3 -9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (3). (x-3 -9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
Step 3
Exam Tip
(x-3 -9x=x(x-3)(x+3)), इसलिए शून्यक (-3,0,3) हैं। अतः भिन्न वास्तविक शून्यक (3) हैं।
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एक संख्या समस्या से समीकरण (n-2 -2pn+\(p^2-11p\)=0) बनता है। दो वास्तविक और असमान (n) के लिए (p) पर कौन सी शर्त है?
A number problem gives (n-2 -2pn+\(p^2-11p\)=0). What condition on (p) gives two real and distinct values of (n)?
#quadratic-equations
#application
#distinct-roots
A (p>0)
B (p=0)
C (p<0)
D हर (p) / Every (p)
Explanation opens after your attempt
Step 1
Concept
Here (D=4p-2 -4\(p^2-11p\)=44p). For two distinct real values (D>0), so (p>0).
Step 2
Why this answer is correct
The correct answer is A. (p>0). Here (D=4p-2 -4\(p^2-11p\)=44p). For two distinct real values (D>0), so (p>0).
Step 3
Exam Tip
यहाँ (D=4p-2 -4\(p^2-11p\)=44p) है। दो असमान वास्तविक मानों के लिए (D>0), इसलिए (p>0)।
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यदि किसी द्विघात का विविक्तकर (D=20n-80) है, तो दो वास्तविक और असमान मूलों के लिए (n) पर कौन सी शर्त होगी?
If a quadratic has discriminant (D=20n-80), what condition on (n) gives two real and distinct roots?
#quadratic-equations
#discriminant-inequality
#distinct-roots
A (n>4)
B (n=4)
C (n<4)
D हर (n) / Every (n)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots (D>0) is needed. (20n-80>0) gives (n>4).
Step 2
Why this answer is correct
The correct answer is A. (n>4). For two distinct real roots (D>0) is needed. (20n-80>0) gives (n>4).
Step 3
Exam Tip
दो असमान वास्तविक मूलों के लिए (D>0) चाहिए। (20n-80>0) से (n>4)।
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यदि \(x^2-2\theta x+3\theta=0\) के दो वास्तविक और असमान मूल हों, तो \(\theta\) पर कौन सी शर्त सही है?
If \(x^2-2\theta x+3\theta=0\) has two real and distinct roots, which condition on \(\theta\) is correct?
#quadratic-equations
#parameter-inequality
#distinct-roots
A \(\theta<0\) या \(\theta>3\) / \(\theta<0\) or \(\theta>3\)
B \(0<\theta<3\)
C \(\theta=0\) या \(\theta=3\) / \(\theta=0\) or \(\theta=3\)
D हर \(\theta\) / Every \(\theta\)
Explanation opens after your attempt
Correct Answer
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 \(\theta>3\)।
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समीकरण (x-2 -(t+7)x+7t=0) के दो वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?
Which condition is correct for two real and distinct roots of (x-2 -(t+7)x+7t=0)?
#quadratic-equations
#parameter
#distinct-roots
A \(t\neq7\)
B (t=7)
C (t>7) मात्र / Only (t>7)
D (t<7) मात्र / Only (t<7)
Explanation opens after your attempt
Correct Answer
A. \(t\neq7\)
Step 1
Concept
Here (D=(t+7)2 -28t=(t-7)2 ). For two distinct roots (D>0), so \(t\neq7\).
Step 2
Why this answer is correct
The correct answer is A. \(t\neq7\). Here (D=(t+7)2 -28t=(t-7)2 ). For two distinct roots (D>0), so \(t\neq7\).
Step 3
Exam Tip
यहाँ (D=(t+7)2 -28t=(t-7)2 ) है। दो असमान मूलों के लिए (D>0), इसलिए \(t\neq7\)।
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एक संख्या समस्या से समीकरण (n-2 -2pn+\(p^2-7p\)=0) बनता है। दो वास्तविक और असमान (n) के लिए (p) पर कौन सी शर्त है?
A number problem gives (n-2 -2pn+\(p^2-7p\)=0). What condition on (p) gives two real and distinct values of (n)?
#quadratic-equations
#application
#distinct-roots
A (p>0)
B (p=0)
C (p<0)
D हर (p) / Every (p)
Explanation opens after your attempt
Step 1
Concept
Here (D=4p-2 -4\(p^2-7p\)=28p). For two distinct real values (D>0), so (p>0).
Step 2
Why this answer is correct
The correct answer is A. (p>0). Here (D=4p-2 -4\(p^2-7p\)=28p). For two distinct real values (D>0), so (p>0).
Step 3
Exam Tip
यहाँ (D=4p-2 -4\(p^2-7p\)=28p) है। दो असमान वास्तविक मानों के लिए (D>0), इसलिए (p>0)।
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यदि किसी द्विघात का विविक्तकर (D=12n-36) है, तो दो वास्तविक और असमान मूलों के लिए (n) पर कौन सी शर्त होगी?
If a quadratic has discriminant (D=12n-36), what condition on (n) gives two real and distinct roots?
#quadratic-equations
#discriminant-inequality
#distinct-roots
A (n>3)
B (n=3)
C (n<3)
D हर (n) / Every (n)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots (D>0) is needed. (12n-36>0) gives (n>3).
Step 2
Why this answer is correct
The correct answer is A. (n>3). For two distinct real roots (D>0) is needed. (12n-36>0) gives (n>3).
Step 3
Exam Tip
दो असमान वास्तविक मूलों के लिए (D>0) चाहिए। (12n-36>0) से (n>3) मिलता है।
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यदि \(x^2-2\mu x+2\mu=0\) के दो वास्तविक और असमान मूल हों, तो \(\mu\) पर कौन सी शर्त सही है?
If \(x^2-2\mu x+2\mu=0\) has two real and distinct roots, which condition on \(\mu\) is correct?
#quadratic-equations
#parameter-inequality
#distinct-roots
A \(\mu<0\) या \(\mu>2\) / \(\mu<0\) or \(\mu>2\)
B \(0<\mu<2\)
C \(\mu=0\) या \(\mu=2\) / \(\mu=0\) or \(\mu=2\)
D हर \(\mu\) / Every \(\mu\)
Explanation opens after your attempt
Correct Answer
A. \(\mu<0\) या \(\mu>2\) / \(\mu<0\) or \(\mu>2\)
Step 1
Concept
Here (D=4\mu-2 -8\mu=4\mu\(\mu-2\)). From (D>0), \(\mu<0\) or \(\mu>2\).
Step 2
Why this answer is correct
The correct answer is A. \(\mu<0\) या \(\mu>2\) / \(\mu<0\) or \(\mu>2\). Here (D=4\mu-2 -8\mu=4\mu\(\mu-2\)). From (D>0), \(\mu<0\) or \(\mu>2\).
Step 3
Exam Tip
यहाँ (D=4\mu-2 -8\mu=4\mu\(\mu-2\)) है। (D>0) से \(\mu<0\) या \(\mu>2\)।
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समीकरण (x-2 -(r+5)x+5r=0) के दो वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?
Which condition is correct for two real and distinct roots of (x-2 -(r+5)x+5r=0)?
#quadratic-equations
#parameter
#distinct-roots
A \(r\neq5\)
B (r=5)
C (r>5) मात्र / Only (r>5)
D (r<5) मात्र / Only (r<5)
Explanation opens after your attempt
Correct Answer
A. \(r\neq5\)
Step 1
Concept
Here (D=(r+5)2 -20r=(r-5)2 ). For two distinct roots (D>0), so \(r\neq5\).
Step 2
Why this answer is correct
The correct answer is A. \(r\neq5\). Here (D=(r+5)2 -20r=(r-5)2 ). For two distinct roots (D>0), so \(r\neq5\).
Step 3
Exam Tip
यहाँ (D=(r+5)2 -20r=(r-5)2 ) है। दो असमान मूलों के लिए (D>0), इसलिए \(r\neq5\)।
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एक संख्या पहेली से समीकरण (n-2 -2pn+\(p^2-5p\)=0) बनता है। दो वास्तविक और असमान (n) के लिए (p) पर कौन सी शर्त है?
A number puzzle gives (n-2 -2pn+\(p^2-5p\)=0). What condition on (p) gives two real and distinct values of (n)?
#quadratic-equations
#application
#distinct-roots
A (p>0)
B (p=0)
C (p<0)
D हर (p) / Every (p)
Explanation opens after your attempt
Step 1
Concept
Here (D=4p-2 -4\(p^2-5p\)=20p). For two distinct real values (D>0), so (p>0).
Step 2
Why this answer is correct
The correct answer is A. (p>0). Here (D=4p-2 -4\(p^2-5p\)=20p). For two distinct real values (D>0), so (p>0).
Step 3
Exam Tip
यहाँ (D=4p-2 -4\(p^2-5p\)=20p) है। दो असमान वास्तविक मानों के लिए (D>0), इसलिए (p>0)।
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समीकरण (3x-2 -2(2k+1)x+(k+1)2 =0) के दो असमान वास्तविक मूलों के लिए कौन सी शर्त सही है?
Which condition is correct for two distinct real roots of (3x-2 -2(2k+1)x+(k+1)2 =0)?
#quadratic-equations
#distinct-roots
#parameter-interval
A (k<-2) या (k>1) / (k<-2) or (k>1)
B (-2<k<1)
C (k=-2) या (k=1) / (k=-2) or (k=1)
D हर (k) / Every (k)
Explanation opens after your attempt
Correct Answer
A. (k<-2) या (k>1) / (k<-2) or (k>1)
Step 1
Concept
Here (D=4(k-1)(k+2)). From (D>0), we get (k<-2) or (k>1).
Step 2
Why this answer is correct
The correct answer is A. (k<-2) या (k>1) / (k<-2) or (k>1). Here (D=4(k-1)(k+2)). From (D>0), we get (k<-2) or (k>1).
Step 3
Exam Tip
यहाँ (D=4(k-1)(k+2)) है। (D>0) से (k<-2) या (k>1) मिलता है।
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यदि \(x^2-2\lambda x+\lambda=0\) के दो वास्तविक और असमान मूल हों, तो \(\lambda\) पर कौन सी शर्त सही है?
If \(x^2-2\lambda x+\lambda=0\) has two real and distinct roots, which condition on \(\lambda\) is correct?
#quadratic-equations
#parameter-inequality
#distinct-roots
A \(\lambda<0\) या \(\lambda>1\) / \(\lambda<0\) or \(\lambda>1\)
B \(0<\lambda<1\)
C \(\lambda=0\) या \(\lambda=1\) / \(\lambda=0\) or \(\lambda=1\)
D हर वास्तविक \(\lambda\) / Every real \(\lambda\)
Explanation opens after your attempt
Correct Answer
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 \(\lambda>1\)।
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यदि (x-2 -2(a+b)x+(a-b)2 =0) के मूल वास्तविक और असमान हों, तो (a) और (b) के लिए सही शर्त क्या है?
If (x-2 -2(a+b)x+(a-b)2 =0) has real and distinct roots, what is the correct condition for (a) and (b)?
#quadratic-equations
#algebraic-parameter
#distinct-roots
A (ab>0)
B (ab=0)
C (ab<0)
D (a=b)
Explanation opens after your attempt
Step 1
Concept
Here (D=4(a+b)2 -4(a-b)2 =16ab). For distinct real roots (D>0), so (ab>0).
Step 2
Why this answer is correct
The correct answer is A. (ab>0). Here (D=4(a+b)2 -4(a-b)2 =16ab). For distinct real roots (D>0), so (ab>0).
Step 3
Exam Tip
यहाँ (D=4(a+b)2 -4(a-b)2 =16ab) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए (ab>0)।
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समीकरण (x-2 -(m+3)x+3m=0) के दो वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?
Which condition is correct for two real and distinct roots of (x-2 -(m+3)x+3m=0)?
#quadratic-equations
#parameter
#distinct-roots
A \(m\neq3\)
B (m=3)
C (m>3) मात्र / Only (m>3)
D (m<3) मात्र / Only (m<3)
Explanation opens after your attempt
Correct Answer
A. \(m\neq3\)
Step 1
Concept
Here (D=(m+3)2 -12m=(m-3 )2 ). For two distinct roots (D>0), so \(m\neq3\).
Step 2
Why this answer is correct
The correct answer is A. \(m\neq3\). Here (D=(m+3)2 -12m=(m-3 )2 ). For two distinct roots (D>0), so \(m\neq3\).
Step 3
Exam Tip
यहाँ (D=(m+3)2 -12m=(m-3 )2 ) है। दो असमान मूलों के लिए (D>0), इसलिए \(m\neq3\)।
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यदि (3x-2 +(k-2)x+4=0) के दो असमान वास्तविक मूल हों, तो (k) पर कौन सी शर्त सही है?
If (3x-2 +(k-2)x+4=0) has two distinct real roots, which condition on (k) is correct?
#quadratic-equations
#distinct-roots
#parameter-interval
A \(k<2-4\sqrt{3}\) या \(k>2+4\sqrt{3}\) / \(k<2-4\sqrt{3}\) or \(k>2+4\sqrt{3}\)
B \(2-4\sqrt{3}<k<2+4\sqrt{3}\)
C (k=2) मात्र / Only (k=2)
D \(k=4\sqrt{3}\) मात्र / Only \(k=4\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
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)।
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समीकरण \(x^2-16x+k=0\) के दो वास्तविक और असमान मूलों के लिए (k) पर कौन सी शर्त सही है?
Which condition on (k) is correct for two real and distinct roots of \(x^2-16x+k=0\)?
#quadratic-equations
#distinct-roots
#parameter
A (k<64)
B (k=64)
C (k>64)
D (k=16)
Explanation opens after your attempt
Step 1
Concept
Here (D=256-4k). For two distinct real roots (D>0), so (k<64).
Step 2
Why this answer is correct
The correct answer is A. (k<64). Here (D=256-4k). For two distinct real roots (D>0), so (k<64).
Step 3
Exam Tip
यहाँ (D=256-4k) है। दो असमान वास्तविक मूलों के लिए (D>0), इसलिए (k<64)।
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समीकरण (3x-2 -2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक और भिन्न मूल कब होंगे?
When will (3x-2 -2(2a+1)x+\(a^2+a+1\)=0) have real and distinct roots?
#quadratic equations
#real distinct
#interval
A (a<-2) या (a>1) / (a<-2) or (a>1)
B (-2<a<1)
C (a=-2) या (a=1) / (a=-2) or (a=1)
D सभी वास्तविक (a) / All real (a)
Explanation opens after your attempt
Correct Answer
A. (a<-2) या (a>1) / (a<-2) or (a>1)
Step 1
Concept
For real and distinct roots, (D>0) is needed. From \(a^2+a-2>0\), we get (a<-2) or (a>1).
Step 2
Why this answer is correct
The correct answer is A. (a<-2) या (a>1) / (a<-2) or (a>1). For real and distinct roots, (D>0) is needed. From \(a^2+a-2>0\), we get (a<-2) or (a>1).
Step 3
Exam Tip
वास्तविक और भिन्न मूलों के लिए (D>0) चाहिए। \(a^2+a-2>0\) से (a<-2) या (a>1) मिलता है।
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यदि \(x^2-2hx+h^2+8h=0\) के मूल वास्तविक और भिन्न हैं, तो (h) पर सही शर्त क्या है?
If \(x^2-2hx+h^2+8h=0\) has real and distinct roots, what is the correct condition on (h)?
#quadratic equations
#parameter inequality
#real distinct
A (h<0)
B (h>0)
C (h=0)
D \(h\ge0\)
Explanation opens after your attempt
Step 1
Concept
Here (D=4h-2 -4\(h^2+8h\)=-32h). For (D>0), (h<0) is required.
Step 2
Why this answer is correct
The correct answer is A. (h<0). Here (D=4h-2 -4\(h^2+8h\)=-32h). For (D>0), (h<0) is required.
Step 3
Exam Tip
यहाँ (D=4h-2 -4\(h^2+8h\)=-32h) है। (D>0) के लिए (h<0) चाहिए।
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समीकरण (x-2 -2(m-4 )x+m-2 -16=0) के मूल वास्तविक और भिन्न कब होंगे?
When will the roots of (x-2 -2(m-4 )x+m-2 -16=0) be real and distinct?
#quadratic equations
#parameter
#real distinct roots
A (m<4)
B (m>4)
C (m=4)
D \(m\le -4\)
Explanation opens after your attempt
Step 1
Concept
Here (D=32(4-m)). For real and distinct roots (D>0), so (m<4).
Step 2
Why this answer is correct
The correct answer is A. (m<4). Here (D=32(4-m)). For real and distinct roots (D>0), so (m<4).
Step 3
Exam Tip
यहाँ (D=32(4-m)) है। वास्तविक और भिन्न मूलों के लिए (D>0), इसलिए (m<4)।
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निम्न में से किस समीकरण के दो वास्तविक और असमान मूल हैं?
Which of the following equations has two real and distinct roots?
#quadratic-equations
#choose-equation
#real-distinct-roots
A \(x^2-11x+18=0\)
B \(x^2+4x+4=0\)
C \(x^2+2x+6=0\)
D \(x^2-8x+16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-11x+18=0\)
Step 1
Concept
In option (A), (D=(-11)2 -4(1)(18)=49). When (D>0), two distinct real roots exist.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-11x+18=0\). In option (A), (D=(-11)2 -4(1)(18)=49). When (D>0), two distinct real roots exist.
Step 3
Exam Tip
विकल्प (A) में (D=(-11)2 -4(1)(18)=49) है। (D>0) होने पर दो असमान वास्तविक मूल मिलते हैं।
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यदि (2x-2 +(k+1)x+3=0) के दो असमान वास्तविक मूल हों, तो (k) पर कौन सी शर्त सही है?
If (2x-2 +(k+1)x+3=0) has two distinct real roots, which condition on (k) is correct?
#quadratic-equations
#distinct-roots
#parameter-interval
A \(k<-1-2\sqrt{6}\) या \(k>-1+2\sqrt{6}\) / \(k<-1-2\sqrt{6}\) or \(k>-1+2\sqrt{6}\)
B \(-1-2\sqrt{6}<k<-1+2\sqrt{6}\)
C (k=-1) मात्र / Only (k=-1)
D \(k=2\sqrt{6}\) मात्र / Only \(k=2\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
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)।
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समीकरण \(x^2-12x+k=0\) के दो वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?
Which condition is correct for two real and distinct roots of \(x^2-12x+k=0\)?
#quadratic-equations
#distinct-roots
#parameter
A (k<36)
B (k=36)
C (k>36)
D (k=12)
Explanation opens after your attempt
Step 1
Concept
Here (D=144-4k). For two distinct real roots (D>0), so (k<36).
Step 2
Why this answer is correct
The correct answer is A. (k<36). Here (D=144-4k). For two distinct real roots (D>0), so (k<36).
Step 3
Exam Tip
यहाँ (D=144-4k) है। दो असमान वास्तविक मूलों के लिए (D>0), इसलिए (k<36)।
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समीकरण \(x^2-2mx+3m=0\) के वास्तविक और भिन्न मूलों के लिए (m) पर क्या शर्त है?
What condition on (m) gives real and distinct roots for \(x^2-2mx+3m=0\)?
#quadratic equations
#real distinct roots
#interval
A (m<0) या (m>3) / (m<0) or (m>3)
B (0<m<3)
C (m=0) या (m=3) / (m=0) or (m=3)
D (m>0)
Explanation opens after your attempt
Correct Answer
A. (m<0) या (m>3) / (m<0) or (m>3)
Step 1
Concept
Here (D=4m(m-3 )). From (D>0), (m<0) or (m>3).
Step 2
Why this answer is correct
The correct answer is A. (m<0) या (m>3) / (m<0) or (m>3). Here (D=4m(m-3 )). From (D>0), (m<0) or (m>3).
Step 3
Exam Tip
यहाँ (D=4m(m-3 )) है। (D>0) से (m<0) या (m>3) मिलता है।
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कौन सा समीकरण वास्तविक, अपरिमेय और भिन्न मूल देता है?
Which equation gives real, irrational and distinct roots?
#quadratic equations
#irrational distinct roots
#choose equation
A \(x^2-10x+23=0\)
B \(x^2-10x+24=0\)
C \(x^2-10x+25=0\)
D \(x^2+10x+26=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+23=0\)
Step 1
Concept
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।
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यदि (x-2 -2\(\alpha+2\)x+\alpha-2 =0) के मूल वास्तविक और भिन्न हैं, तो \(\alpha\) पर शर्त क्या है?
If (x-2 -2\(\alpha+2\)x+\alpha-2 =0) has real and distinct roots, what is the condition on \(\alpha\)?
#quadratic equations
#alpha
#real distinct roots
A \(\alpha>-1\)
B \(\alpha<-1\)
C \(\alpha=-1\)
D \(\alpha>2\) केवल / \(\alpha>2\) only
Explanation opens after your attempt
Correct Answer
A. \(\alpha>-1\)
Step 1
Concept
(D=4\(\alpha+2\)2 -4\alpha-2 =16\(\alpha+1\)). From (D>0), \(\alpha>-1\).
Step 2
Why this answer is correct
The correct answer is A. \(\alpha>-1\). (D=4\(\alpha+2\)2 -4\alpha-2 =16\(\alpha+1\)). From (D>0), \(\alpha>-1\).
Step 3
Exam Tip
(D=4\(\alpha+2\)2 -4\alpha-2 =16\(\alpha+1\)) है। (D>0) से \(\alpha>-1\) मिलता है।
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किस शर्त पर \(x^2-2sx+s+2=0\) के मूल वास्तविक और भिन्न होंगे?
Under which condition will \(x^2-2sx+s+2=0\) have real and distinct roots?
#quadratic equations
#interval condition
#real distinct roots
A (s<-1) या (s>2) / (s<-1) or (s>2)
B (-1<s<2)
C (s=-1) या (s=2) / (s=-1) or (s=2)
D (0<s<1)
Explanation opens after your attempt
Correct Answer
A. (s<-1) या (s>2) / (s<-1) or (s>2)
Step 1
Concept
Here (D=4s-2 -4(s+2)=4(s-2 )(s+1)). From (D>0), (s<-1) or (s>2).
Step 2
Why this answer is correct
The correct answer is A. (s<-1) या (s>2) / (s<-1) or (s>2). Here (D=4s-2 -4(s+2)=4(s-2 )(s+1)). From (D>0), (s<-1) or (s>2).
Step 3
Exam Tip
यहाँ (D=4s-2 -4(s+2)=4(s-2 )(s+1)) है। (D>0) से (s<-1) या (s>2) मिलता है।
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समीकरण \(kx^2-6x+k=0\) के वास्तविक और भिन्न मूलों के लिए सही शर्त क्या है?
What is the correct condition for real and distinct roots of \(kx^2-6x+k=0\)?
#quadratic equations
#real distinct roots
#leading coefficient
A \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\)
B \(k^2>9\)
C \(k^2=9\)
D (k=0)
Explanation opens after your attempt
Correct Answer
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 \(k^2<9\)।
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समीकरण (x-2 -2(k+1)x+k-2 =0) के मूल वास्तविक और भिन्न कब होंगे?
When will the roots of (x-2 -2(k+1)x+k-2 =0) be real and distinct?
#quadratic equations
#real distinct roots
#inequality
A \(k>-\frac{1}{2}\)
B \(k<-\frac{1}{2}\)
C \(k=-\frac{1}{2}\)
D (k=0)
Explanation opens after your attempt
Correct Answer
A. \(k>-\frac{1}{2}\)
Step 1
Concept
Here (D=4(k+1)2 -4k-2 =4(2k+1)). For distinct real roots (D>0), so \(k>-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(k>-\frac{1}{2}\). Here (D=4(k+1)2 -4k-2 =4(2k+1)). For distinct real roots (D>0), so \(k>-\frac{1}{2}\).
Step 3
Exam Tip
यहाँ (D=4(k+1)2 -4k-2 =4(2k+1)) है। भिन्न वास्तविक मूलों के लिए (D>0), इसलिए \(k>-\frac{1}{2}\)।
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समीकरण (x-2 +2(k+1)x+k-2 =0) के दो असमान वास्तविक मूलों के लिए सही शर्त चुनिए।
Choose the correct condition for two distinct real roots of (x-2 +2(k+1)x+k-2 =0).
#quadratic-equations
#distinct-roots
#parameter
A \(k>-\frac{1}{2}\)
B \(k=-\frac{1}{2}\)
C \(k<-\frac{1}{2}\)
D (k=0) मात्र / Only (k=0)
Explanation opens after your attempt
Correct Answer
A. \(k>-\frac{1}{2}\)
Step 1
Concept
Here (D=4(k+1)2 -4k-2 =4(2k+1)). For distinct real roots (D>0), so \(k>-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(k>-\frac{1}{2}\). Here (D=4(k+1)2 -4k-2 =4(2k+1)). For distinct real roots (D>0), so \(k>-\frac{1}{2}\).
Step 3
Exam Tip
यहाँ (D=4(k+1)2 -4k-2 =4(2k+1)) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए \(k>-\frac{1}{2}\)।
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यदि \(x^2+px+6=0\) के मूल वास्तविक और भिन्न हैं तो (p) के लिए कौन सी शर्त सही है?
If the roots of \(x^2+px+6=0\) are real and distinct, which condition is correct for (p)?
#quadratic equations
#parameter
#real distinct roots
A \(p^2>24\)
B \(p^2=24\)
C \(p^2<24\)
D \(p^2=6\)
Explanation opens after your attempt
Correct Answer
A. \(p^2>24\)
Step 1
Concept
For real and distinct roots (D>0). So \(p^2-24>0\), that is \(p^2>24\).
Step 2
Why this answer is correct
The correct answer is A. \(p^2>24\). For real and distinct roots (D>0). So \(p^2-24>0\), that is \(p^2>24\).
Step 3
Exam Tip
वास्तविक और भिन्न मूलों के लिए (D>0) होता है। इसलिए \(p^2-24>0\), अर्थात \(p^2>24\)।
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यदि \(x^2+px+4=0\) के मूल वास्तविक और भिन्न हैं तो (p) के लिए सही शर्त क्या है?
If the roots of \(x^2+px+4=0\) are real and distinct, what is the correct condition for (p)?
#quadratic equations
#parameter
#real distinct roots
A \(p^2>16\)
B \(p^2=16\)
C \(p^2<16\)
D \(p^2=4\)
Explanation opens after your attempt
Correct Answer
A. \(p^2>16\)
Step 1
Concept
For real and distinct roots (D>0), so \(p^2-16>0\). Therefore \(p^2>16\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(p^2>16\). For real and distinct roots (D>0), so \(p^2-16>0\). Therefore \(p^2>16\) is correct.
Step 3
Exam Tip
वास्तविक और भिन्न मूलों के लिए (D>0) होता है इसलिए \(p^2-16>0\)। अतः \(p^2>16\) सही है।
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यदि किसी द्विघात समीकरण के दो असमान वास्तविक मूल हैं, तो (D) कैसा होगा?
If a quadratic equation has two distinct real roots, how will (D) be?
#quadratic equations
#concept
#distinct roots
A (D>0)
B (D=0)
C (D<0)
D \(D\leq0\)
Explanation opens after your attempt
Step 1
Concept
For distinct real roots, (D>0). Do not add the equality sign by mistake.
Step 2
Why this answer is correct
The correct answer is A. (D>0). For distinct real roots, (D>0). Do not add the equality sign by mistake.
Step 3
Exam Tip
असमान वास्तविक मूलों के लिए (D>0) होता है। बराबर का चिन्ह गलती से न लगाएं।
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समीकरण \(2x^2+3x+\lambda=0\) के वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?
For \(2x^2+3x+\lambda=0\) to have real and distinct roots, which condition is correct?
#quadratic equations
#parameter
#distinct roots
#fraction
A \(\lambda<\frac{9}{8}\)
B \(\lambda=\frac{9}{8}\)
C \(\lambda>\frac{9}{8}\)
D \(\lambda=\frac{8}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\lambda<\frac{9}{8}\)
Step 1
Concept
(D=32 -4(2)\lambda=9-8\lambda). From (D>0), we get \(\lambda<\frac{9}{8}\).
Step 2
Why this answer is correct
The correct answer is A. \(\lambda<\frac{9}{8}\). (D=32 -4(2)\lambda=9-8\lambda). From (D>0), we get \(\lambda<\frac{9}{8}\).
Step 3
Exam Tip
(D=32 -4(2)\lambda=9-8\lambda) है। (D>0) से \(\lambda<\frac{9}{8}\) मिलता है।
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समीकरण \(x^2-2x+n=0\) के दो वास्तविक और असमान मूल होने के लिए कौन सी शर्त सही है?
For \(x^2-2x+n=0\) to have two real and distinct roots, which condition is correct?
#quadratic equations
#parameter
#distinct roots
#inequality
A (n<1)
B (n=1)
C (n>1)
D (n=2)
Explanation opens after your attempt
Step 1
Concept
For distinct real roots (D>0), so ((-2)2 -4n>0) gives (n<1). Use a strict inequality for distinct roots.
Step 2
Why this answer is correct
The correct answer is A. (n<1). For distinct real roots (D>0), so ((-2)2 -4n>0) gives (n<1). Use a strict inequality for distinct roots.
Step 3
Exam Tip
असमान वास्तविक मूलों के लिए (D>0), इसलिए ((-2)2 -4n>0) से (n<1)। असमान के लिए कड़ाई वाली असमता लगती है।
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यदि (D=0) और \(a\neq0\) हो तो द्विघात समीकरण में कितने अलग-अलग वास्तविक मूल होंगे?
If (D=0) and \(a\neq0\), how many distinct real roots will the quadratic equation have?
#quadratic equations
#equal roots
#distinct count
A (1)
B (2)
C (0)
D (3)
Explanation opens after your attempt
Step 1
Concept
At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.
Step 2
Why this answer is correct
The correct answer is A. (1). At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.
Step 3
Exam Tip
(D=0) पर दोनों मूल समान होते हैं, इसलिए अलग-अलग वास्तविक मूलों की संख्या (1) है। ध्यान रखें मूल दो बार दोहरता है।
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किस समीकरण के दो वास्तविक और असमान मूल होंगे?
Which equation will have two real and distinct roots?
#quadratic equations
#choose equation
#distinct roots
A \(x^2-7x+10=0\)
B \(x^2+2x+1=0\)
C \(x^2+4x+8=0\)
D \(4x^2+4x+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+10=0\)
Step 1
Concept
For the first equation, (D=(-7)2 -4(1)(10)=9>0). Hence its roots are real and distinct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-7x+10=0\). For the first equation, (D=(-7)2 -4(1)(10)=9>0). Hence its roots are real and distinct.
Step 3
Exam Tip
पहले समीकरण में (D=(-7)2 -4(1)(10)=9>0) है। इसलिए उसके मूल वास्तविक और असमान हैं।
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यदि \(x^2-16x+n=0\) के दो अलग वास्तविक मूल हैं, तो (n) के लिए कौनसी शर्त सही है?
If \(x^2-16x+n=0\) has two distinct real roots, which condition on (n) is correct?
#quadratic
#discriminant
#distinct-roots
A (n<64)
B (n>64)
C (n=64)
D \(n\ge64\)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots, (D>0), so (256-4n>0) and (n<64). In exams, connect (D>0) with distinct real roots.
Step 2
Why this answer is correct
The correct answer is A. (n<64). For two distinct real roots, (D>0), so (256-4n>0) and (n<64). In exams, connect (D>0) with distinct real roots.
Step 3
Exam Tip
दो अलग वास्तविक मूलों के लिए (D>0), इसलिए (256-4n>0) और (n<64) है। परीक्षा में (D>0) को अलग वास्तविक मूल से जोड़ें।
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यदि \(x^2-14x+n=0\) के दो अलग वास्तविक मूल हैं, तो (n) के लिए कौनसी शर्त सही है?
If \(x^2-14x+n=0\) has two distinct real roots, which condition on (n) is correct?
#quadratic
#discriminant
#distinct-roots
A (n<49)
B (n>49)
C (n=49)
D \(n\ge49\)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots, (D>0), so (196-4n>0) and (n<49). In exams, connect (D>0) with distinct real roots.
Step 2
Why this answer is correct
The correct answer is A. (n<49). For two distinct real roots, (D>0), so (196-4n>0) and (n<49). In exams, connect (D>0) with distinct real roots.
Step 3
Exam Tip
दो अलग वास्तविक मूलों के लिए (D>0), इसलिए (196-4n>0) और (n<49) है। परीक्षा में (D>0) को अलग वास्तविक मूल से जोड़ें।
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यदि \(x^2-12x+n=0\) के दो अलग वास्तविक मूल हैं, तो (n) के लिए कौनसी शर्त सही है?
If \(x^2-12x+n=0\) has two distinct real roots, which condition on (n) is correct?
#quadratic
#discriminant
#distinct-roots
A (n<36)
B (n>36)
C (n=36)
D \(n\ge36\)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots, (D>0), so (144-4n>0) and (n<36). In exams, connect (D>0) with distinct real roots.
Step 2
Why this answer is correct
The correct answer is A. (n<36). For two distinct real roots, (D>0), so (144-4n>0) and (n<36). In exams, connect (D>0) with distinct real roots.
Step 3
Exam Tip
दो अलग वास्तविक मूलों के लिए (D>0), इसलिए (144-4n>0) और (n<36) है। परीक्षा में (D>0) को अलग वास्तविक मूल से जोड़ें।
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यदि \(x^2-10x+n=0\) के दो अलग वास्तविक मूल हैं, तो (n) के लिए कौनसी शर्त सही है?
If \(x^2-10x+n=0\) has two distinct real roots, which condition on (n) is correct?
#quadratic
#discriminant
#distinct-roots
A (n<25)
B (n>25)
C (n=25)
D \(n\ge25\)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots, (D>0), so (100-4n>0) and (n<25). In exams, connect (D>0) with distinct real roots.
Step 2
Why this answer is correct
The correct answer is A. (n<25). For two distinct real roots, (D>0), so (100-4n>0) and (n<25). In exams, connect (D>0) with distinct real roots.
Step 3
Exam Tip
दो अलग वास्तविक मूलों के लिए (D>0), इसलिए (100-4n>0) और (n<25) है। परीक्षा में (D>0) को अलग वास्तविक मूल से जोड़ें।
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यदि \(x^2-8x+n=0\) के दो अलग वास्तविक मूल हैं, तो (n) के लिए कौनसी शर्त सही है?
If \(x^2-8x+n=0\) has two distinct real roots, which condition on (n) is correct?
#quadratic
#discriminant
#distinct-roots
A (n<16)
B (n>16)
C (n=16)
D \(n\ge16\)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots, (D>0), so (64-4n>0) and (n<16). In exams, connect (D>0) with distinct real roots.
Step 2
Why this answer is correct
The correct answer is A. (n<16). For two distinct real roots, (D>0), so (64-4n>0) and (n<16). In exams, connect (D>0) with distinct real roots.
Step 3
Exam Tip
दो अलग वास्तविक मूलों के लिए (D>0), इसलिए (64-4n>0) और (n<16) है। परीक्षा में (D>0) को अलग वास्तविक मूल से जोड़ें।
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यदि \(x^2-4x+n=0\) के दो अलग वास्तविक मूल हैं, तो (n) के लिए कौनसी शर्त सही है?
If \(x^2-4x+n=0\) has two distinct real roots, which condition on (n) is correct?
#quadratic
#discriminant
#distinct-roots
A (n<4)
B (n>4)
C (n=4)
D \(n\ge4\)
Explanation opens after your attempt
Step 1
Concept
For two distinct real roots, (D>0), so (16-4n>0) and (n<4). In exams, connect (D>0) with distinct roots.
Step 2
Why this answer is correct
The correct answer is A. (n<4). For two distinct real roots, (D>0), so (16-4n>0) and (n<4). In exams, connect (D>0) with distinct roots.
Step 3
Exam Tip
दो अलग वास्तविक मूलों के लिए (D>0), इसलिए (16-4n>0) और (n<4) है। परीक्षा में (D>0) को distinct roots से जोड़ें।
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\(x^2+12x+\lambda=0\) की जड़ें वास्तविक भिन्न और दोनों ऋणात्मक हों, तो \(\lambda\) पर सही शर्त क्या है?
For \(x^2+12x+\lambda=0\) to have real distinct roots and both negative roots, what is the correct condition on \(\lambda\)?
#quadratic-roots
#negative-distinct-roots
#condition
A \(0<\lambda<36\)
B \(\lambda=36\)
C \(\lambda>36\)
D \(\lambda<0\)
Explanation opens after your attempt
Correct Answer
A. \(0<\lambda<36\)
Step 1
Concept
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 \(0<\lambda<36\)।
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\(x^2+10x+\lambda=0\) की जड़ें वास्तविक भिन्न और दोनों ऋणात्मक हों, तो \(\lambda\) पर सही शर्त क्या है?
For \(x^2+10x+\lambda=0\) to have real distinct roots and both negative roots, what is the correct condition on \(\lambda\)?
#quadratic-roots
#negative-distinct-roots
#condition
A \(\lambda<0\)
B \(0<\lambda<25\)
C \(\lambda=25\)
D \(\lambda>25\)
Explanation opens after your attempt
Correct Answer
B. \(0<\lambda<25\)
Step 1
Concept
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 \(0<\lambda<25\)।
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\(x^2+2x+\lambda=0\) की जड़ें वास्तविक और भिन्न हों तथा दोनों ऋणात्मक हों, तो \(\lambda\) पर सही शर्त क्या है?
For \(x^2+2x+\lambda=0\) to have real distinct roots and both negative roots, what is the correct condition on \(\lambda\)?
#quadratic-roots
#negative-distinct-roots
#condition
A \(0<\lambda<1\)
B \(\lambda>1\)
C \(\lambda<0\)
D \(\lambda=1\)
Explanation opens after your attempt
Correct Answer
A. \(0<\lambda<1\)
Step 1
Concept
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 \(0<\lambda<1\)।
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(x-2 -2(k+1)x+k-2 =0) की जड़ें वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
For (x-2 -2(k+1)x+k-2 =0) to have real and distinct roots, what is the correct condition on (k)?
#quadratic-roots
#distinct-roots
#discriminant
A \(k>-\frac{1}{2}\)
B \(k\ge-\frac{1}{2}\)
C \(k<-\frac{1}{2}\)
D \(k\le-\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(k>-\frac{1}{2}\)
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (D=4(2k+1)), so \(k>-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(k>-\frac{1}{2}\). For real and distinct roots, (D>0) is needed. Here (D=4(2k+1)), so \(k>-\frac{1}{2}\).
Step 3
Exam Tip
वास्तविक और भिन्न जड़ों के लिए (D>0) चाहिए। यहाँ (D=4(2k+1)), इसलिए \(k>-\frac{1}{2}\)।
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समीकरण \(x^2-20x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-20x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<100)
B (k=100)
C (k>100)
D \(k\leq100\)
Explanation opens after your attempt
Correct Answer
A. (k<100)
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 2
Why this answer is correct
The correct answer is A. (k<100). For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (400-4k>0), इसलिए (k<100)।
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समीकरण \(x^2-16x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-16x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<64)
B (k=64)
C (k>64)
D \(k\leq64\)
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
Step 2
Why this answer is correct
The correct answer is A. (k<64). For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (256-4k>0), इसलिए (k<64)।
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समीकरण \(x^2-12x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-12x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<36)
B (k=36)
C (k>36)
D \(k\leq36\)
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).
Step 2
Why this answer is correct
The correct answer is A. (k<36). For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (144-4k>0), इसलिए (k<36)।
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समीकरण \(x^2-8x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-8x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#hard
A (k<16)
B (k=16)
C (k>16)
D \(k\leq16\)
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (64-4k>0), so (k<16).
Step 2
Why this answer is correct
The correct answer is A. (k<16). For real and distinct roots, (D>0) is needed. Here (64-4k>0), so (k<16).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (64-4k>0), इसलिए (k<16)।
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समीकरण \(x^2-6x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-6x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#hard
A (k<9)
B (k=9)
C (k>9)
D \(k\leq9\)
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (36-4k>0), so (k<9).
Step 2
Why this answer is correct
The correct answer is A. (k<9). For real and distinct roots, (D>0) is needed. Here (36-4k>0), so (k<9).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (36-4k>0), इसलिए (k<9)।
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यदि बहुपद (p(x)=5(x+1)(x-2)(x-4)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=5(x+1)(x-2)(x-4)), at how many distinct points will the graph cut the (x)-axis?
#cubic
#factor-form
#distinct-intercepts
A तीन / Three
B दो / Two
C एक / One
D पाँच / Five
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 3
Exam Tip
गुणनखंडों से शून्यक (-1), (2), और (4) हैं। तीन अलग शून्यक तीन अलग (x)-प्रतिच्छेद देते हैं।
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यदि द्विघात ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटता है तो उसके वास्तविक शून्यक कैसे होंगे?
If a quadratic graph cuts the (x)-axis at two distinct points, what kind of real zeroes does it have?
#quadratic
#distinct-real-zeroes
#graph
A दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
B दो समान वास्तविक शून्यक / Two equal real zeroes
C कोई वास्तविक शून्यक नहीं / No real zero
D एक ही शून्यक और एक काल्पनिक शून्यक / One zero and one imaginary zero
Explanation opens after your attempt
Correct Answer
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।
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यदि किसी परवलय का शीर्ष ((-14,0)) है और वह नीचे की ओर खुलता है, तो अलग वास्तविक शून्यक कितने हैं?
If the vertex of a parabola is ((-14,0)) and it opens downward, how many distinct real zeroes are there?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (p(x)=11(x+5)2 (x-14)) है, तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?
If (p(x)=11(x+5)2 (x-14)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?
#multiplicity
#distinct points
#touching
A दो बिंदु, (x=-5) पर स्पर्श / Two points, touching at (x=-5)
B दो बिंदु, (x=14) पर स्पर्श / Two points, touching at (x=14)
C तीन बिंदु, (x=-5) पर स्पर्श / Three points, touching at (x=-5)
D एक बिंदु, (x=14) पर स्पर्श / One point, touching at (x=14)
Explanation opens after your attempt
Correct Answer
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।
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यदि कोई बहुपद (x)-अक्ष को आठ अलग बिंदुओं पर काटता है, तो न्यूनतम संभावित घात क्या होगी?
If a polynomial cuts the (x)-axis at eight distinct points, what is the minimum possible degree?
#minimum degree
#distinct zeroes
#graph
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (x)-अक्ष से मिलने वाले बिंदु ((-11,0)), ((-11,0)), ((4,0)), ((4,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-11,0)), ((-11,0)), ((4,0)), ((4,0)), how many distinct real zeroes are there?
#repeated points
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (p(x)=(x-c)5 (x+d)2 ), जहाँ \(c\neq -d\), तो अलग शून्यक कौन से हैं?
If (p(x)=(x-c)5 (x+d)2 ), where \(c\neq -d\), what are the distinct zeroes?
#symbolic factors
#distinct zeroes
#multiplicity
A (c) और (-d) / (c) and (-d)
B (-c) और (d) / (-c) and (d)
C (c), (-d), (-d)
D केवल (c) / Only (c)
Explanation opens after your attempt
Correct Answer
A. (c) और (-d) / (c) and (-d)
Step 1
Concept
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।
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यदि (p(x)=(x+2)6 (x-5)2 ) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?
If (p(x)=(x+2)6 (x-5)2 ), what are the number of distinct real zeroes and graph behavior?
#even multiplicity
#distinct zeroes
#tangent
A दो, दोनों पर स्पर्श / Two, touches at both
B दो, दोनों पर कटान / Two, crosses at both
C आठ, सभी पर स्पर्श / Eight, touches at all
D एक, केवल (x=-2) पर स्पर्श / One, touches only at (x=-2)
Explanation opens after your attempt
Correct Answer
A. दो, दोनों पर स्पर्श / Two, touches at both
Step 1
Concept
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।
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यदि किसी परवलय का शीर्ष ((12,0)) है और वह ऊपर की ओर खुलता है, तो अलग वास्तविक शून्यक कितने हैं?
If the vertex of a parabola is ((12,0)) and it opens upward, how many distinct real zeroes are there?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (p(x)=9(x+4)2 (x-12)) है, तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?
If (p(x)=9(x+4)2 (x-12)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?
#multiplicity
#distinct points
#touching
A दो बिंदु, (x=-4) पर स्पर्श / Two points, touching at (x=-4)
B दो बिंदु, (x=12) पर स्पर्श / Two points, touching at (x=12)
C तीन बिंदु, (x=-4) पर स्पर्श / Three points, touching at (x=-4)
D एक बिंदु, (x=12) पर स्पर्श / One point, touching at (x=12)
Explanation opens after your attempt
Correct Answer
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।
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यदि कोई बहुपद (x)-अक्ष को सात अलग बिंदुओं पर काटता है, तो न्यूनतम संभावित घात क्या होगी?
If a polynomial cuts the (x)-axis at seven distinct points, what is the minimum possible degree?
#minimum degree
#distinct zeroes
#graph
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (x)-अक्ष से मिलने वाले बिंदु ((-7,0)), ((-7,0)), ((2,0)), ((2,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-7,0)), ((-7,0)), ((2,0)), ((2,0)), how many distinct real zeroes are there?
#repeated points
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
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।
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यदि (p(x)=(x+a)3 (x-b)2 ), जहाँ \(a\neq -b\), तो अलग शून्यक कौन से हैं?
If (p(x)=(x+a)3 (x-b)2 ), where \(a\neq -b\), what are the distinct zeroes?
#symbolic factors
#distinct zeroes
#multiplicity
A (-a) और (b) / (-a) and (b)
B (a) और (-b) / (a) and (-b)
C (-a), (b), (b)
D केवल (b) / Only (b)
Explanation opens after your attempt
Correct Answer
A. (-a) और (b) / (-a) and (b)
Step 1
Concept
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।
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यदि (p(x)=(x-1)2 (x+4)4 ) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?
If (p(x)=(x-1)2 (x+4)4 ), what are the number of distinct real zeroes and graph behavior?
#even multiplicity
#distinct zeroes
#tangent
A दो, दोनों पर स्पर्श / Two, touches at both
B दो, दोनों पर कटान / Two, crosses at both
C छह, सभी पर स्पर्श / Six, touches at all
D एक, केवल (x=1) पर स्पर्श / One, touches only at (x=1)
Explanation opens after your attempt
Correct Answer
A. दो, दोनों पर स्पर्श / Two, touches at both
Step 1
Concept
There are two distinct zeroes (1) and (-4), 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 (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 3
Exam Tip
दो अलग शून्यक (1) और (-4) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।
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यदि किसी परवलय का शीर्ष ((-5,0)) है तो वास्तविक शून्यकों की अलग संख्या क्या होगी?
If the vertex of a parabola is ((-5,0)), what will be the distinct number of real zeroes?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The vertex lies on the (x)-axis, so the parabola touches at ((-5,0)). 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 ((-5,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है इसलिए परवलय ((-5,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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यदि (p(x)=7(x+3)2 (x-10)) है तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?
If (p(x)=7(x+3)2 (x-10)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?
#multiplicity
#distinct points
#touching
A दो बिंदु, (x=-3) पर स्पर्श / Two points, touching at (x=-3)
B दो बिंदु, (x=10) पर स्पर्श / Two points, touching at (x=10)
C तीन बिंदु, (x=-3) पर स्पर्श / Three points, touching at (x=-3)
D एक बिंदु, (x=10) पर स्पर्श / One point, touching at (x=10)
Explanation opens after your attempt
Correct Answer
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।
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यदि कोई बहुपद (x)-अक्ष को छह अलग बिंदुओं पर काटता है तो न्यूनतम संभावित घात क्या होगी?
If a polynomial cuts the (x)-axis at six distinct points, what is the minimum possible degree?
#minimum degree
#distinct zeroes
#graph
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For six distinct real zeroes, the degree must be at least (6). Tip: the number of distinct zeroes cannot exceed the degree.
Step 2
Why this answer is correct
The correct answer is C. (6). For six distinct real zeroes, the degree must be at least (6). Tip: the number of distinct zeroes cannot exceed the degree.
Step 3
Exam Tip
छह अलग वास्तविक शून्यकों के लिए घात कम से कम (6) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।
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यदि (x)-अक्ष से मिलने वाले बिंदु ((-5,0)), ((-5,0)), ((4,0)) लिखे हैं तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-5,0)), ((-5,0)), ((4,0)), how many distinct real zeroes are there?
#repeated point
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. ((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
((-5,0)) दोहराया गया है इसलिए अलग शून्यक (-5) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
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यदि (p(x)=(x-4)(x+7)3 ) है तो अलग शून्यक कौन से हैं?
If (p(x)=(x-4)(x+7)3 ), what are the distinct zeroes?
#distinct zeroes
#repeated factor
#graph
A (4) और (-7) / (4) and (-7)
B (-4) और (7) / (-4) and (7)
C (4), (-7), (-7), (-7)
D केवल (-7) / Only (-7)
Explanation opens after your attempt
Correct Answer
A. (4) और (-7) / (4) and (-7)
Step 1
Concept
The zeroes are (4) and (-7), but (-7) is repeated. Tip: count repetition once for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (4) और (-7) / (4) and (-7). The zeroes are (4) and (-7), but (-7) is repeated. Tip: count repetition once for distinct zeroes.
Step 3
Exam Tip
शून्यक (4) और (-7) हैं पर (-7) दोहराया गया है। टिप: अलग शून्यक में दोहराव को एक बार गिनें।
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यदि (p(x)=x-3 -25x) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=x-3 -25x), at how many distinct points will the graph cut the (x)-axis?
#cubic
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
(x-3 -25x=x(x-5)(x+5)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -25x=x(x-5)(x+5)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 3
Exam Tip
(x-3 -25x=x(x-5)(x+5)) है इसलिए तीन अलग शून्यक हैं। टिप: पहले सामान्य गुणनखंड निकालें।
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