एक वर्ग मॉडल में भुजा (x+1) है। इसका क्षेत्रफल किसके बराबर होगा?
In a square model, the side is (x+1). What will its area be equal to?
#square model
#area identity
#visual algebra
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A \(x^2+1\)
B \(x^2+2x+1\)
C \(x^2+x+1\)
D (2x+1)
Explanation opens after your attempt
Correct Answer
B. \(x^2+2x+1\)
Step 1
Concept
The area is ((x+1)2 ), and the expansion is \(x^2+2x+1\). Exam tip: remember to add the two (x)-rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+2x+1\). The area is ((x+1)2 ), and the expansion is \(x^2+2x+1\). Exam tip: remember to add the two (x)-rectangles.
Step 3
Exam Tip
वर्ग का क्षेत्रफल ((x+1)2 ) है और विस्तार \(x^2+2x+1\) मिलता है। परीक्षा में दो (x) आयतों को जोड़ना याद रखें।
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भुजा (a+2) वाले वर्ग में छोटे कोने वाले वर्ग का क्षेत्रफल क्या होगा?
In a square with side (a+2), what is the area of the small corner square?
#small square
#area model
#constant term
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A (2)
B (2a)
C (4)
D \(a^2\)
Explanation opens after your attempt
Step 1
Concept
The small square has side (2), so its area is \(2^2=4\). Exam tip: connect the constant term with the small square.
Step 2
Why this answer is correct
The correct answer is C. (4). The small square has side (2), so its area is \(2^2=4\). Exam tip: connect the constant term with the small square.
Step 3
Exam Tip
छोटे वर्ग की भुजा (2) है इसलिए क्षेत्रफल \(2^2=4\) होगा। परीक्षा में स्थिर पद को छोटे वर्ग से जोड़ें।
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यदि आयत की लंबाई (x+3) और चौड़ाई (x+1) है तो क्षेत्र मॉडल से कुल क्षेत्रफल क्या होगा?
If a rectangle has length (x+3) and breadth (x+1), what is the total area from the area model?
#rectangle model
#area parts
#product identity
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A \(x^2+4x+3\)
B \(x^2+3x+1\)
C \(x^2+2x+3\)
D \(x^2+4x+4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+3\)
Step 1
Concept
The parts are \(x^2\), (3x), (x), and (3). Their sum is \(x^2+4x+3\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+3\). The parts are \(x^2\), (3x), (x), and (3). Their sum is \(x^2+4x+3\).
Step 3
Exam Tip
भाग \(x^2\), (3x), (x) और (3) हैं। उनका योग \(x^2+4x+3\) है।
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दृश्य मॉडल में ((y+4)2 ) के लिए दो समान आयतों का कुल क्षेत्रफल कितना है?
In the visual model of ((y+4)2 ), what is the total area of the two equal rectangles?
#middle term
#visual square
#area model
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A (4y)
B (8y)
C (16y)
D \(y^2\)
Explanation opens after your attempt
Step 1
Concept
Each of the two rectangles has area (4y). So their total area is (8y).
Step 2
Why this answer is correct
The correct answer is B. (8y). Each of the two rectangles has area (4y). So their total area is (8y).
Step 3
Exam Tip
दो आयतों में प्रत्येक का क्षेत्रफल (4y) है। इसलिए कुल क्षेत्रफल (8y) होगा।
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भुजा (m+n) वाले वर्ग को चार भागों में बांटने पर कौन सा पद दो बार आता है?
When a square of side (m+n) is divided into four parts, which term appears twice?
#area partition
#middle term
#square identity
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A \(m^2\)
B \(n^2\)
C (mn)
D (m+n)
Explanation opens after your attempt
Step 1
Concept
Two rectangles (mn) and (mn) are formed. Therefore the middle term is (2mn).
Step 2
Why this answer is correct
The correct answer is C. (mn). Two rectangles (mn) and (mn) are formed. Therefore the middle term is (2mn).
Step 3
Exam Tip
दो आयत (mn) और (mn) बनते हैं। इसलिए मध्य पद (2mn) होता है।
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यदि बड़े वर्ग की भुजा (p+5) है तो पूरा क्षेत्रफल कौन सा होगा?
If the side of a big square is (p+5), what will be the whole area?
#square expansion
#visual model
#identity
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A \(p^2+5p+25\)
B \(p^2+10p+5\)
C \(p^2+25p+10\)
D \(p^2+10p+25\)
Explanation opens after your attempt
Correct Answer
D. \(p^2+10p+25\)
Step 1
Concept
In ((p+5)2 ), there are two (5p) rectangles and a small square (25). So the area is \(p^2+10p+25\).
Step 2
Why this answer is correct
The correct answer is D. \(p^2+10p+25\). In ((p+5)2 ), there are two (5p) rectangles and a small square (25). So the area is \(p^2+10p+25\).
Step 3
Exam Tip
((p+5)2 ) में दो (5p) आयत और (25) छोटा वर्ग होता है। इसलिए क्षेत्रफल \(p^2+10p+25\) है।
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एक वर्ग की भुजा (a-b) है। उसका क्षेत्रफल किस रूप में लिखा जाएगा?
A square has side (a-b). How will its area be written?
#minus square
#area model
#algebraic identity
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A \(a^2-2ab+b^2\)
B \(a^2+2ab+b^2\)
C \(a^2-b^2\)
D \(a^2+ab-b^2\)
Explanation opens after your attempt
Correct Answer
A. \(a^2-2ab+b^2\)
Step 1
Concept
The area of the square is ((a-b)2 ). On expanding, it gives \(a^2-2ab+b^2\).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-2ab+b^2\). The area of the square is ((a-b)2 ). On expanding, it gives \(a^2-2ab+b^2\).
Step 3
Exam Tip
वर्ग का क्षेत्रफल ((a-b)2 ) होता है। विस्तार करने पर \(a^2-2ab+b^2\) मिलता है।
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दृश्य मॉडल में बड़े \(x^2\) वर्ग से दो (3x) आयत हटाए जाते हैं और (9) जोड़ा जाता है। कौन सा वर्ग बनता है?
In a visual model, two (3x) rectangles are removed from the big \(x^2\) square and (9) is added. Which square is formed?
#subtraction model
#visual square
#complete square
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A ((x+3)2 )
B ((x-3)2 )
C \(x^2-9\)
D \(x^2+9\)
Explanation opens after your attempt
Correct Answer
B. ((x-3)2 )
Step 1
Concept
This is a subtraction square model. Therefore (x-2 -6x+9=(x-3)2 ) is formed.
Step 2
Why this answer is correct
The correct answer is B. ((x-3)2 ). This is a subtraction square model. Therefore (x-2 -6x+9=(x-3)2 ) is formed.
Step 3
Exam Tip
यह घटाव वाला वर्ग मॉडल है। इसलिए (x-2 -6x+9=(x-3)2 ) बनता है।
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यदि \(a^2-b^2\) का क्षेत्र मॉडल बनाना हो तो कौन सा भाग हटाया जाता है?
If an area model of \(a^2-b^2\) is to be made, which part is removed?
#difference of squares
#removed area
#visual model
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A \(a^2\) वाला वर्ग / Square of \(a^2\)
B \(b^2\) वाला वर्ग / Square of \(b^2\)
C (ab) वाला आयत / Rectangle of (ab)
D (2ab) वाला भाग / Part of (2ab)
Explanation opens after your attempt
Correct Answer
B. \(b^2\) वाला वर्ग / Square of \(b^2\)
Step 1
Concept
In \(a^2-b^2\), the smaller \(b^2\) square is removed from the larger \(a^2\) square. Exam tip: identify the removed square.
Step 2
Why this answer is correct
The correct answer is B. \(b^2\) वाला वर्ग / Square of \(b^2\). In \(a^2-b^2\), the smaller \(b^2\) square is removed from the larger \(a^2\) square. Exam tip: identify the removed square.
Step 3
Exam Tip
\(a^2-b^2\) में बड़े \(a^2\) वर्ग से छोटा \(b^2\) वर्ग हटता है। परीक्षा में घटाए गए वर्ग को पहचानें।
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लंबाई (r+s) और चौड़ाई (r-s) वाले आयत का क्षेत्रफल किसके बराबर है?
The area of a rectangle with length (r+s) and breadth (r-s) is equal to what?
#rectangle model
#sum difference
#difference of squares
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A \(r^2+s^2\)
B \(r^2-2rs+s^2\)
C \(r^2-s^2\)
D \(r^2+2rs+s^2\)
Explanation opens after your attempt
Correct Answer
C. \(r^2-s^2\)
Step 1
Concept
The area is ((r+s)(r-s)). It is equal to \(r^2-s^2\).
Step 2
Why this answer is correct
The correct answer is C. \(r^2-s^2\). The area is ((r+s)(r-s)). It is equal to \(r^2-s^2\).
Step 3
Exam Tip
आयत का क्षेत्रफल ((r+s)(r-s)) है। यह \(r^2-s^2\) के बराबर होता है।
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यदि \(11^2\) को ((10+1)2 ) के क्षेत्र मॉडल से देखें तो दो आयतों का कुल क्षेत्रफल कितना है?
If \(11^2\) is seen using the area model of ((10+1)2 ), what is the total area of the two rectangles?
#numeric square
#area model
#middle area
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A (20)
B (10)
C (1)
D (100)
Explanation opens after your attempt
Step 1
Concept
The total area of the two rectangles is \(2\cdot10\cdot1=20\). Exam tip: link the middle part with two equal rectangles.
Step 2
Why this answer is correct
The correct answer is A. (20). The total area of the two rectangles is \(2\cdot10\cdot1=20\). Exam tip: link the middle part with two equal rectangles.
Step 3
Exam Tip
दो आयतों का कुल क्षेत्रफल \(2\cdot10\cdot1=20\) है। परीक्षा में मध्य भाग को दो बराबर आयतों से जोड़ें।
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भुजा (20-1) वाले वर्ग का क्षेत्र मॉडल किस संख्या का वर्ग दिखाता है?
The area model of a square with side (20-1) shows the square of which number?
#numeric model
#minus square
#visual identity
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A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
(20-1=19). So this is the area model of \(19^2\).
Step 2
Why this answer is correct
The correct answer is B. (19). (20-1=19). So this is the area model of \(19^2\).
Step 3
Exam Tip
(20-1=19) है। इसलिए यह \(19^2\) का क्षेत्र मॉडल है।
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((x+6)2 ) के वर्ग मॉडल में छोटे वर्ग का क्षेत्रफल क्या होगा?
In the square model of ((x+6)2 ), what will be the area of the small square?
#small square
#constant area
#visual identity
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A (6x)
B (12x)
C (36)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
The side of the small square is (6). Its area will be \(6^2=36\).
Step 2
Why this answer is correct
The correct answer is C. (36). The side of the small square is (6). Its area will be \(6^2=36\).
Step 3
Exam Tip
छोटे वर्ग की भुजा (6) है। उसका क्षेत्रफल \(6^2=36\) होगा।
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यदि क्षेत्र मॉडल में \(x^2+8x+16\) दिखता है तो यह किसका पूर्ण वर्ग है?
If an area model shows \(x^2+8x+16\), whose perfect square is it?
#perfect square
#area model
#visual algebra
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A ((x+2)2 )
B ((x+4)2 )
C ((x+8)2 )
D ((x-4)2 )
Explanation opens after your attempt
Correct Answer
B. ((x+4)2 )
Step 1
Concept
\(16=4^2\) and \(8x=2\cdot4x\). Therefore it is ((x+4)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((x+4)2 ). \(16=4^2\) and \(8x=2\cdot4x\). Therefore it is ((x+4)2 ).
Step 3
Exam Tip
\(16=4^2\) और \(8x=2\cdot4x\) है। इसलिए यह ((x+4)2 ) है।
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आयत मॉडल में ((x+2)(x+4)) के स्थिर भाग का क्षेत्रफल कितना है?
In the rectangle model of ((x+2)(x+4)), what is the area of the constant part?
#constant term
#rectangle model
#area product
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The constant part comes from \(2\cdot4=8\). Exam tip: multiply the number parts separately.
Step 2
Why this answer is correct
The correct answer is D. (8). The constant part comes from \(2\cdot4=8\). Exam tip: multiply the number parts separately.
Step 3
Exam Tip
स्थिर भाग \(2\cdot4=8\) से मिलता है। परीक्षा में संख्या वाले भागों का गुणन अलग से करें।
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किस मॉडल में \(x^2+7x+12\) का क्षेत्रफल मिल सकता है?
Which model can give an area of \(x^2+7x+12\)?
#rectangle area
#factor model
#visual identity
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A लंबाई (x+3) और चौड़ाई (x+4) / Length (x+3) and breadth (x+4)
B लंबाई (x+2) और चौड़ाई (x+5) / Length (x+2) and breadth (x+5)
C लंबाई (x+1) और चौड़ाई (x+12) / Length (x+1) and breadth (x+12)
D लंबाई (x+6) और चौड़ाई (x+6) / Length (x+6) and breadth (x+6)
Explanation opens after your attempt
Correct Answer
A. लंबाई (x+3) और चौड़ाई (x+4) / Length (x+3) and breadth (x+4)
Step 1
Concept
((x+3)(x+4)=x-2 +4x+3x+12=x-2 +7x+12). Exam tip: add both (x)-parts for the middle term.
Step 2
Why this answer is correct
The correct answer is A. लंबाई (x+3) और चौड़ाई (x+4) / Length (x+3) and breadth (x+4). ((x+3)(x+4)=x-2 +4x+3x+12=x-2 +7x+12). Exam tip: add both (x)-parts for the middle term.
Step 3
Exam Tip
((x+3)(x+4)=x-2 +4x+3x+12=x-2 +7x+12) है। परीक्षा में मध्य पद के लिए दोनों (x)-भाग जोड़ें।
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वर्ग मॉडल में ((2x+1)2 ) के बड़े वर्ग का क्षेत्रफल क्या होगा?
In the square model of ((2x+1)2 ), what will be the area of the larger square?
#coefficient square
#area model
#visual expansion
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A \(2x^2\)
B \(4x^2\)
C \(x^2\)
D (2x)
Explanation opens after your attempt
Correct Answer
B. \(4x^2\)
Step 1
Concept
The larger square has side (2x). Its area will be ((2x)2 =4x-2 ).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2\). The larger square has side (2x). Its area will be ((2x)2 =4x-2 ).
Step 3
Exam Tip
बड़े वर्ग की भुजा (2x) है। उसका क्षेत्रफल ((2x)2 =4x-2 ) होगा।
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यदि ((3x+2)2 ) का दृश्य मॉडल बनता है तो स्थिर छोटा वर्ग कौन सा होगा?
If the visual model of ((3x+2)2 ) is made, which will be the constant small square?
#constant square
#visual model
#binomial square
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A \(2^2\)
B (3x)
C (6x)
D \(9x^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^2\)
Step 1
Concept
The side of the constant small square is (2). Therefore its area is \(2^2=4\).
Step 2
Why this answer is correct
The correct answer is A. \(2^2\). The side of the constant small square is (2). Therefore its area is \(2^2=4\).
Step 3
Exam Tip
स्थिर छोटे वर्ग की भुजा (2) है। इसलिए उसका क्षेत्रफल \(2^2=4\) होगा।
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किस दृश्य मॉडल में (2ab) को दो समान आयतों के रूप में दिखाया जाता है?
In which visual model is (2ab) shown as two equal rectangles?
#two rectangles
#middle term
#square model
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A \(a^2-b^2\)
B ((a+b)2 )
C (a+b)
D \(a^2+b^2\)
Explanation opens after your attempt
Correct Answer
B. ((a+b)2 )
Step 1
Concept
The model of ((a+b)2 ) has two rectangles (ab) and (ab). Their sum is (2ab).
Step 2
Why this answer is correct
The correct answer is B. ((a+b)2 ). The model of ((a+b)2 ) has two rectangles (ab) and (ab). Their sum is (2ab).
Step 3
Exam Tip
((a+b)2 ) के मॉडल में (ab) और (ab) दो आयत होते हैं। उनका योग (2ab) है।
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यदि \(15^2\) को ((10+5)2 ) से देखें तो बड़े वर्ग का क्षेत्रफल क्या होगा?
If \(15^2\) is seen as ((10+5)2 ), what is the area of the large square?
#numeric square
#large square
#area model
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A (25)
B (50)
C (100)
D (150)
Explanation opens after your attempt
Step 1
Concept
The large square has side (10), so its area is \(10^2=100\). Exam tip: identify large and small squares separately.
Step 2
Why this answer is correct
The correct answer is C. (100). The large square has side (10), so its area is \(10^2=100\). Exam tip: identify large and small squares separately.
Step 3
Exam Tip
बड़े वर्ग की भुजा (10) है इसलिए उसका क्षेत्रफल \(10^2=100\) है। परीक्षा में बड़े और छोटे वर्ग अलग पहचानें।
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भुजा (a+b+c) वाले वर्ग को (3) भागों में दोनों दिशाओं में बांटने पर कुल कितने छोटे क्षेत्र बनेंगे?
When a square of side (a+b+c) is divided into (3) parts in both directions, how many small regions are formed?
#three term square
#grid model
#visual identity
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A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Three rows and three columns make \(3\cdot3=9\) regions. Exam tip: multiply rows and columns.
Step 2
Why this answer is correct
The correct answer is C. (9). Three rows and three columns make \(3\cdot3=9\) regions. Exam tip: multiply rows and columns.
Step 3
Exam Tip
तीन पंक्तियां और तीन स्तंभ मिलकर \(3\cdot3=9\) क्षेत्र बनाते हैं। परीक्षा में पंक्तियों और स्तंभों को गुणा करें।
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((a+b+c)2 ) के ग्रिड मॉडल में \(a^2\), \(b^2\), और \(c^2\) किस प्रकार के भाग हैं?
In the grid model of ((a+b+c)2 ), what type of parts are \(a^2\), \(b^2\), and \(c^2\)?
#square terms
#three term model
#area grid
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A आयत भाग / Rectangular parts
B वर्ग भाग / Square parts
C रेखा भाग / Line parts
D परिमिति भाग / Perimeter parts
Explanation opens after your attempt
Correct Answer
B. वर्ग भाग / Square parts
Step 1
Concept
\(a^2\), \(b^2\), and \(c^2\) are areas of separate squares. Exam tip: identify square terms and rectangle terms separately.
Step 2
Why this answer is correct
The correct answer is B. वर्ग भाग / Square parts. \(a^2\), \(b^2\), and \(c^2\) are areas of separate squares. Exam tip: identify square terms and rectangle terms separately.
Step 3
Exam Tip
\(a^2\), \(b^2\), और \(c^2\) अलग-अलग वर्गों के क्षेत्रफल हैं। परीक्षा में वर्ग पद और आयत पद अलग पहचानें।
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यदि (a+b+c) मॉडल में (ab) एक आयत है तो (ba) कैसा क्षेत्रफल देगा?
If (ab) is one rectangle in the (a+b+c) model, what area will (ba) give?
#cross rectangles
#commutative property
#visual model
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A (ab) के बराबर / Equal to (ab)
B \(a^2\) के बराबर / Equal to \(a^2\)
C \(b^2\) के बराबर / Equal to \(b^2\)
D \(c^2\) के बराबर / Equal to \(c^2\)
Explanation opens after your attempt
Correct Answer
A. (ab) के बराबर / Equal to (ab)
Step 1
Concept
(ab) and (ba) are two rectangles with equal area. Exam tip: the order of multiplication does not change area.
Step 2
Why this answer is correct
The correct answer is A. (ab) के बराबर / Equal to (ab). (ab) and (ba) are two rectangles with equal area. Exam tip: the order of multiplication does not change area.
Step 3
Exam Tip
(ab) और (ba) बराबर क्षेत्रफल वाले दो आयत हैं। परीक्षा में गुणन के क्रम से क्षेत्रफल नहीं बदलता।
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कौन सा विकल्प ((u+v)2 ) के क्षेत्र मॉडल का सही विस्तार है?
Which option is the correct expansion of the area model of ((u+v)2 )?
#binomial square
#area model
#visual proof
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A \(u^2+v^2\)
B \(u^2+uv+v^2\)
C \(u^2+2uv+v^2\)
D (2u+2v)
Explanation opens after your attempt
Correct Answer
C. \(u^2+2uv+v^2\)
Step 1
Concept
The square model has two (uv) rectangles. Therefore the expansion is \(u^2+2uv+v^2\).
Step 2
Why this answer is correct
The correct answer is C. \(u^2+2uv+v^2\). The square model has two (uv) rectangles. Therefore the expansion is \(u^2+2uv+v^2\).
Step 3
Exam Tip
वर्ग मॉडल में दो (uv) आयत होते हैं। इसलिए विस्तार \(u^2+2uv+v^2\) है।
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यदि \(18^2\) को ((20-2)2 ) से निकालें तो अंत में जोड़ा जाने वाला छोटा वर्ग कितना है?
If \(18^2\) is found using ((20-2)2 ), what is the small square added at the end?
#minus square
#numeric model
#small area
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A (2)
B (4)
C (40)
D (80)
Explanation opens after your attempt
Step 1
Concept
In ((20-2)2 ), the small square is \(2^2=4\). Exam tip: after subtracting two rectangles, add the small square.
Step 2
Why this answer is correct
The correct answer is B. (4). In ((20-2)2 ), the small square is \(2^2=4\). Exam tip: after subtracting two rectangles, add the small square.
Step 3
Exam Tip
((20-2)2 ) में छोटा वर्ग \(2^2=4\) है। परीक्षा में दो आयत घटाने के बाद छोटा वर्ग जोड़ें।
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एक आयत मॉडल में लंबाई (x+5) और चौड़ाई (x+2) है। (x)-पदों का कुल योग क्या होगा?
In a rectangle model, length is (x+5) and breadth is (x+2). What will be the total of the (x)-terms?
#rectangle model
#x terms
#area parts
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A (2x)
B (5x)
C (7x)
D (10x)
Explanation opens after your attempt
Step 1
Concept
The two (x)-terms are (5x) and (2x). Their sum is (7x).
Step 2
Why this answer is correct
The correct answer is C. (7x). The two (x)-terms are (5x) and (2x). Their sum is (7x).
Step 3
Exam Tip
दो (x)-पद (5x) और (2x) हैं। उनका योग (7x) है।
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किस आयत मॉडल से \(x^2+6x+8\) मिलता है?
Which rectangle model gives \(x^2+6x+8\)?
#factor model
#rectangle area
#visual algebra
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A ((x+1)(x+8))
B ((x+2)(x+4))
C ((x+3)(x+3))
D ((x+6)(x+8))
Explanation opens after your attempt
Correct Answer
B. ((x+2)(x+4))
Step 1
Concept
((x+2)(x+4)=x-2 +4x+2x+8=x-2 +6x+8). Exam tip: look at the factors of the constant term.
Step 2
Why this answer is correct
The correct answer is B. ((x+2)(x+4)). ((x+2)(x+4)=x-2 +4x+2x+8=x-2 +6x+8). Exam tip: look at the factors of the constant term.
Step 3
Exam Tip
((x+2)(x+4)=x-2 +4x+2x+8=x-2 +6x+8) है। परीक्षा में स्थिर पद के कारक देखें।
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यदि \(x^2+12x+36\) एक पूर्ण वर्ग क्षेत्र मॉडल है तो पूरी भुजा क्या होगी?
If \(x^2+12x+36\) is a perfect square area model, what is the whole side?
#complete square
#side finding
#visual model
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A (x+12)
B (x+6)
C (x+3)
D (x-6)
Explanation opens after your attempt
Step 1
Concept
\(36=6^2\) and \(12x=2\cdot6x\). So the whole side is (x+6).
Step 2
Why this answer is correct
The correct answer is B. (x+6). \(36=6^2\) and \(12x=2\cdot6x\). So the whole side is (x+6).
Step 3
Exam Tip
\(36=6^2\) और \(12x=2\cdot6x\) है। इसलिए पूरी भुजा (x+6) होगी।
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दृश्य मॉडल में ((x-5)2 ) का विस्तार क्या होगा?
What is the expansion of ((x-5)2 ) in a visual model?
#subtraction square
#visual expansion
#area model
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A \(x^2-5x+25\)
B \(x^2+10x+25\)
C \(x^2-10x+25\)
D \(x^2-25\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-10x+25\)
Step 1
Concept
In ((x-5)2 ), two (5x) rectangles are subtracted and (25) is added. So \(x^2-10x+25\) is obtained.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-10x+25\). In ((x-5)2 ), two (5x) rectangles are subtracted and (25) is added. So \(x^2-10x+25\) is obtained.
Step 3
Exam Tip
((x-5)2 ) में दो (5x) आयत घटते हैं और (25) जुड़ता है। इसलिए \(x^2-10x+25\) मिलता है।
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यदि (x+7) भुजा वाले वर्ग में दो समान आयतों का कुल क्षेत्रफल (14x) है तो छोटे वर्ग की भुजा क्या है?
If in a square of side (x+7), the total area of two equal rectangles is (14x), what is the side of the small square?
#side identification
#middle term
#visual square
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A (7)
B (14)
C (49)
D (x)
Explanation opens after your attempt
Step 1
Concept
The total area of the two rectangles is \(2\cdot7x=14x\). So the side of the small square is (7).
Step 2
Why this answer is correct
The correct answer is A. (7). The total area of the two rectangles is \(2\cdot7x=14x\). So the side of the small square is (7).
Step 3
Exam Tip
दो आयतों का कुल क्षेत्रफल \(2\cdot7x=14x\) है। इसलिए छोटे वर्ग की भुजा (7) है।
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किस मॉडल में \(a^2-b^2\) को ((a-b)(a+b)) के रूप में दिखाया जाता है?
In which model is \(a^2-b^2\) shown as ((a-b)(a+b))?
#difference of squares
#rearrangement
#visual proof
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A वर्ग जोड़ मॉडल / Square addition model
B वर्ग हटाने और पुनर्व्यवस्था मॉडल / Square removal and rearrangement model
C तीन पदों का वर्ग मॉडल / Three-term square model
D केवल परिमिति मॉडल / Only perimeter model
Explanation opens after your attempt
Correct Answer
B. वर्ग हटाने और पुनर्व्यवस्था मॉडल / Square removal and rearrangement model
Step 1
Concept
The smaller square is removed from the larger square and the remaining area is arranged as a rectangle. This gives ((a-b)(a+b)).
Step 2
Why this answer is correct
The correct answer is B. वर्ग हटाने और पुनर्व्यवस्था मॉडल / Square removal and rearrangement model. The smaller square is removed from the larger square and the remaining area is arranged as a rectangle. This gives ((a-b)(a+b)).
Step 3
Exam Tip
बड़े वर्ग से छोटा वर्ग हटाकर बचे क्षेत्र को आयत में सजाया जाता है। इससे ((a-b)(a+b)) मिलता है।
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यदि \(24\cdot26\) को ((25-1)(25+1)) से देखें तो कौन सा परिणाम मिलेगा?
If \(24\cdot26\) is viewed as ((25-1)(25+1)), what result will be obtained?
#numeric identity
#difference of squares
#visual multiplication
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A (624)
B (625)
C (626)
D (650)
Explanation opens after your attempt
Step 1
Concept
((25-1)(25+1)=252 -12 =625-1=624). Exam tip: square the middle number and subtract (1).
Step 2
Why this answer is correct
The correct answer is A. (624). ((25-1)(25+1)=252 -12 =625-1=624). Exam tip: square the middle number and subtract (1).
Step 3
Exam Tip
((25-1)(25+1)=252 -12 =625-1=624) है। परीक्षा में मध्य संख्या का वर्ग लेकर (1) घटाएं।
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भुजा (2a+3) वाले वर्ग के क्षेत्र मॉडल में दो आयतों का कुल क्षेत्रफल क्या है?
In the area model of a square with side (2a+3), what is the total area of the two rectangles?
#coefficient
#binomial square
#area model
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A (6a)
B (12a)
C \(4a^2\)
D (9)
Explanation opens after your attempt
Step 1
Concept
The total area of the two rectangles is \(2\cdot2a\cdot3=12a\). Exam tip: take the side along with its coefficient.
Step 2
Why this answer is correct
The correct answer is B. (12a). The total area of the two rectangles is \(2\cdot2a\cdot3=12a\). Exam tip: take the side along with its coefficient.
Step 3
Exam Tip
दो आयतों का कुल क्षेत्रफल \(2\cdot2a\cdot3=12a\) है। परीक्षा में गुणांक सहित भुजा लें।
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यदि ((2x+3)2 ) को फैलाएं तो कौन सा क्षेत्रफल सही है?
If ((2x+3)2 ) is expanded, which area is correct?
#visual expansion
#area model
#binomial square
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A \(4x^2+12x+9\)
B \(2x^2+12x+9\)
C \(4x^2+6x+9\)
D \(4x^2+12x+3\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+12x+9\)
Step 1
Concept
The larger square area is \(4x^2\), the middle part is (12x), and the small square is (9). Exam tip: add all three parts.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+12x+9\). The larger square area is \(4x^2\), the middle part is (12x), and the small square is (9). Exam tip: add all three parts.
Step 3
Exam Tip
बड़े वर्ग का क्षेत्रफल \(4x^2\), मध्य भाग (12x), और छोटा वर्ग (9) है। परीक्षा में तीनों भाग जोड़ें।
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एक वर्ग मॉडल में \(4x^2+4x+1\) दिखता है। यह किस भुजा का वर्ग है?
A square model shows \(4x^2+4x+1\). It is the square of which side?
#perfect square
#side model
#visual identity
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A (4x+1)
B (2x+1)
C (2x+2)
D (x+1)
Explanation opens after your attempt
Step 1
Concept
(4x-2 =(2x)2 ) and \(1=1^2\), with middle term (4x). So the side is (2x+1).
Step 2
Why this answer is correct
The correct answer is B. (2x+1). (4x-2 =(2x)2 ) and \(1=1^2\), with middle term (4x). So the side is (2x+1).
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(1=1^2\), साथ में मध्य पद (4x) है। इसलिए भुजा (2x+1) है।
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यदि आयत की भुजाएं (3x+1) और (x+2) हैं तो क्षेत्र मॉडल का (x)-पद कुल कितना होगा?
If the rectangle sides are (3x+1) and (x+2), what will be the total (x)-term in the area model?
#cross terms
#rectangle model
#area multiplication
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A (2x)
B (3x)
C (7x)
D (6x)
Explanation opens after your attempt
Step 1
Concept
The cross parts are (6x) and (x). Their sum is (7x).
Step 2
Why this answer is correct
The correct answer is C. (7x). The cross parts are (6x) and (x). Their sum is (7x).
Step 3
Exam Tip
क्रॉस भाग (6x) और (x) हैं। उनका योग (7x) है।
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((a+1)(a+6)) के क्षेत्र मॉडल में स्थिर भाग क्या होगा?
What is the constant part in the area model of ((a+1)(a+6))?
#constant part
#rectangle grid
#product model
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A (1)
B (6)
C (7)
D (6a)
Explanation opens after your attempt
Step 1
Concept
The constant part is formed by \(1\cdot6=6\). Exam tip: observe the small number rectangle.
Step 2
Why this answer is correct
The correct answer is B. (6). The constant part is formed by \(1\cdot6=6\). Exam tip: observe the small number rectangle.
Step 3
Exam Tip
स्थिर भाग \(1\cdot6=6\) से बनता है। परीक्षा में संख्या वाले छोटे आयत को देखें।
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दृश्य मॉडल में \(x^2+5x+6\) किस आयत से बन सकता है?
In a visual model, \(x^2+5x+6\) can be formed by which rectangle?
#quadratic model
#rectangle factors
#visual algebra
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A ((x+1)(x+6))
B ((x+2)(x+3))
C ((x+5)(x+6))
D ((x+1)(x+5))
Explanation opens after your attempt
Correct Answer
B. ((x+2)(x+3))
Step 1
Concept
((x+2)(x+3)=x-2 +3x+2x+6=x-2 +5x+6). Exam tip: check that the two factors add to (5) and multiply to (6).
Step 2
Why this answer is correct
The correct answer is B. ((x+2)(x+3)). ((x+2)(x+3)=x-2 +3x+2x+6=x-2 +5x+6). Exam tip: check that the two factors add to (5) and multiply to (6).
Step 3
Exam Tip
((x+2)(x+3)=x-2 +3x+2x+6=x-2 +5x+6) है। परीक्षा में दो कारकों का योग (5) और गुणन (6) देखें।
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यदि बड़े वर्ग की भुजा (30+2) है तो पूरा क्षेत्रफल किस संख्या के बराबर है?
If the side of a big square is (30+2), the whole area is equal to which number?
#numeric square
#area model
#quick calculation
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A (900)
B (960)
C (1024)
D (1064)
Explanation opens after your attempt
Step 1
Concept
(30+2=32), and the area is \(32^2=1024\). Exam tip: you can also add the parts of the area model.
Step 2
Why this answer is correct
The correct answer is C. (1024). (30+2=32), and the area is \(32^2=1024\). Exam tip: you can also add the parts of the area model.
Step 3
Exam Tip
(30+2=32) और क्षेत्रफल \(32^2=1024\) है। परीक्षा में क्षेत्र मॉडल से भागों का योग भी कर सकते हैं।
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यदि ((50-3)2 ) का मॉडल बनता है तो कौन सा मध्य क्षेत्र घटेगा?
If the model of ((50-3)2 ) is made, which middle area will be subtracted?
#minus model
#middle area
#numeric identity
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A \(2\cdot50\cdot3\)
B \(50^2\)
C \(3^2\)
D (50-3)
Explanation opens after your attempt
Correct Answer
A. \(2\cdot50\cdot3\)
Step 1
Concept
In ((a-b)2 ), (2ab) is subtracted. Here the subtracted area is \(2\cdot50\cdot3\).
Step 2
Why this answer is correct
The correct answer is A. \(2\cdot50\cdot3\). In ((a-b)2 ), (2ab) is subtracted. Here the subtracted area is \(2\cdot50\cdot3\).
Step 3
Exam Tip
((a-b)2 ) में (2ab) घटता है। यहां घटने वाला क्षेत्र \(2\cdot50\cdot3\) है।
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किस दृश्य मॉडल में पूरा क्षेत्रफल \(x^2-4x+4\) मिलता है?
Which visual model gives the whole area \(x^2-4x+4\)?
#minus square
#visual identification
#area model
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A भुजा (x+2) का वर्ग / Square of side (x+2)
B भुजा (x-2) का वर्ग / Square of side (x-2)
C भुजा (x+4) का वर्ग / Square of side (x+4)
D लंबाई (x+2) और चौड़ाई (x-2) का आयत / Rectangle of length (x+2) and breadth (x-2)
Explanation opens after your attempt
Correct Answer
B. भुजा (x-2) का वर्ग / Square of side (x-2)
Step 1
Concept
(x-2 -4x+4=(x-2)2 ). Exam tip: identify the subtraction square from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. भुजा (x-2) का वर्ग / Square of side (x-2). (x-2 -4x+4=(x-2)2 ). Exam tip: identify the subtraction square from the negative middle term.
Step 3
Exam Tip
(x-2 -4x+4=(x-2)2 ) है। परीक्षा में ऋण मध्य पद देखकर घटाव वाला वर्ग पहचानें।
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यदि किसी क्षेत्र मॉडल में \(a^2+2ab+b^2\) दिखता है तो पूरी भुजा क्या होगी?
If an area model shows \(a^2+2ab+b^2\), what is the whole side?
#side recognition
#complete square
#visual model
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A (a-b)
B (a+b)
C (ab)
D \(a^2+b^2\)
Explanation opens after your attempt
Step 1
Concept
This is the area of ((a+b)2 ). Therefore the side of the whole square is (a+b).
Step 2
Why this answer is correct
The correct answer is B. (a+b). This is the area of ((a+b)2 ). Therefore the side of the whole square is (a+b).
Step 3
Exam Tip
यह ((a+b)2 ) का क्षेत्रफल है। इसलिए पूरे वर्ग की भुजा (a+b) होगी।
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भुजा (a-b) वाले वर्ग में अंतिम \(b^2\) भाग क्यों जोड़ा जाता है?
Why is the final \(b^2\) part added in a square with side (a-b)?
#subtraction model
#corner square
#visual explanation
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A क्योंकि कोना दो बार हट जाता है / Because the corner is removed twice
B क्योंकि क्षेत्रफल हमेशा बढ़ता है / Because area always increases
C क्योंकि \(a^2\) शून्य है / Because \(a^2\) is zero
D क्योंकि (ab) नहीं बनता / Because (ab) is not formed
Explanation opens after your attempt
Correct Answer
A. क्योंकि कोना दो बार हट जाता है / Because the corner is removed twice
Step 1
Concept
In the subtraction model, the \(b^2\) corner is removed twice. It is added back once for the correct area.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि कोना दो बार हट जाता है / Because the corner is removed twice. In the subtraction model, the \(b^2\) corner is removed twice. It is added back once for the correct area.
Step 3
Exam Tip
घटाव मॉडल में \(b^2\) कोना दो बार हट जाता है। सही क्षेत्र के लिए उसे एक बार वापस जोड़ा जाता है।
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यदि ((x+2)2 ) मॉडल में \(x^2\) और (4) दिखते हैं तो बीच के दो आयतों का कुल क्षेत्रफल क्या है?
If \(x^2\) and (4) are shown in the ((x+2)2 ) model, what is the total area of the two middle rectangles?
#middle rectangles
#area model
#binomial square
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A (2x)
B (4x)
C (x+4)
D (8x)
Explanation opens after your attempt
Step 1
Concept
Each of the two rectangles has area (2x). So the total is (4x).
Step 2
Why this answer is correct
The correct answer is B. (4x). Each of the two rectangles has area (2x). So the total is (4x).
Step 3
Exam Tip
दो आयतों में प्रत्येक का क्षेत्रफल (2x) है। इसलिए कुल (4x) होगा।
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एक ग्रिड में ऊपर (x) और (3), बगल में (x) और (2) लिखा है। कुल क्षेत्रफल क्या होगा?
In a grid, (x) and (3) are written on the top, and (x) and (2) on the side. What will be the total area?
#grid model
#rectangle area
#visual multiplication
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A \(x^2+5x+6\)
B \(x^2+6x+5\)
C \(x^2+3x+2\)
D \(x^2+2x+3\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x+6\)
Step 1
Concept
The grid shows ((x+3)(x+2)). Its area is \(x^2+2x+3x+6=x^2+5x+6\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x+6\). The grid shows ((x+3)(x+2)). Its area is \(x^2+2x+3x+6=x^2+5x+6\).
Step 3
Exam Tip
ग्रिड ((x+3)(x+2)) दिखाता है। इसका क्षेत्रफल \(x^2+2x+3x+6=x^2+5x+6\) है।
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कौन सा क्षेत्र मॉडल \(x^2-9\) को दिखाता है?
Which area model shows \(x^2-9\)?
#difference of squares
#removed square
#visual model
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A भुजा (x) वाले वर्ग से भुजा (3) वाला वर्ग हटाना / Removing a square of side (3) from a square of side (x)
B भुजा (x+3) वाला वर्ग बनाना / Making a square of side (x+3)
C भुजा (x-3) वाला वर्ग बनाना / Making a square of side (x-3)
D दो (3x) आयत जोड़ना / Adding two (3x) rectangles
Explanation opens after your attempt
Correct Answer
A. भुजा (x) वाले वर्ग से भुजा (3) वाला वर्ग हटाना / Removing a square of side (3) from a square of side (x)
Step 1
Concept
\(x^2-9=x^2-3^2\). Therefore removing a square of side (3) from a square of side (x) is correct.
Step 2
Why this answer is correct
The correct answer is A. भुजा (x) वाले वर्ग से भुजा (3) वाला वर्ग हटाना / Removing a square of side (3) from a square of side (x). \(x^2-9=x^2-3^2\). Therefore removing a square of side (3) from a square of side (x) is correct.
Step 3
Exam Tip
\(x^2-9=x^2-3^2\) है। इसलिए (x) वर्ग से (3) वर्ग हटाने का मॉडल सही है।
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यदि ((a+4)(a-4)) को आयत क्षेत्र मॉडल से देखें तो परिणाम क्या होगा?
If ((a+4)(a-4)) is seen through a rectangle area model, what will be the result?
#sum difference
#rectangle model
#identity
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A \(a^2+8a+16\)
B \(a^2-8a+16\)
C \(a^2-16\)
D \(a^2+16\)
Explanation opens after your attempt
Correct Answer
C. \(a^2-16\)
Step 1
Concept
This is a product of sum and difference. Therefore ((a+4)(a-4)=a-2 -16).
Step 2
Why this answer is correct
The correct answer is C. \(a^2-16\). This is a product of sum and difference. Therefore ((a+4)(a-4)=a-2 -16).
Step 3
Exam Tip
यह योग और अंतर का गुणन है। इसलिए ((a+4)(a-4)=a-2 -16) होगा।
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भुजा (3+2) वाले वर्ग के क्षेत्र मॉडल में दो आयतों का कुल क्षेत्रफल कितना होगा?
In the area model of a square with side (3+2), what will be the total area of the two rectangles?
#numeric square
#rectangle parts
#area model
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A (6)
B (12)
C (4)
D (25)
Explanation opens after your attempt
Step 1
Concept
The total area of the two rectangles is \(2\cdot3\cdot2=12\). Exam tip: treat the middle part as two equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. (12). The total area of the two rectangles is \(2\cdot3\cdot2=12\). Exam tip: treat the middle part as two equal rectangles.
Step 3
Exam Tip
दो आयतों का कुल क्षेत्रफल \(2\cdot3\cdot2=12\) है। परीक्षा में मध्य भाग को दो समान आयत मानें।
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यदि \(7^2\) को ((5+2)2 ) से दिखाएं तो पूरा क्षेत्रफल कितने भागों के योग से बनेगा?
If \(7^2\) is shown as ((5+2)2 ), the whole area will be formed by the sum of how many parts?
#numeric visual model
#four parts
#square identity
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The square model of ((5+2)2 ) gives four parts \(5^2\), \(5\cdot2\), \(5\cdot2\), and \(2^2\). Exam tip: add all four parts.
Step 2
Why this answer is correct
The correct answer is C. (4). The square model of ((5+2)2 ) gives four parts \(5^2\), \(5\cdot2\), \(5\cdot2\), and \(2^2\). Exam tip: add all four parts.
Step 3
Exam Tip
((5+2)2 ) का वर्ग मॉडल \(5^2\), \(5\cdot2\), \(5\cdot2\), और \(2^2\) चार भाग देता है। परीक्षा में चारों भाग जोड़ें।
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एक क्षेत्र मॉडल में \(x^2\), दो (9x) आयत और (81) छोटा वर्ग है। पूरी भुजा क्या होगी?
An area model has \(x^2\), two (9x) rectangles, and a small square (81). What will be the whole side?
#side finding
#complete square
#visual model
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A (x+9)
B (x+18)
C (x-9)
D (9x+1)
Explanation opens after your attempt
Step 1
Concept
\(81=9^2\), and the two (9x) rectangles give (18x). So the whole square is ((x+9)2 ).
Step 2
Why this answer is correct
The correct answer is A. (x+9). \(81=9^2\), and the two (9x) rectangles give (18x). So the whole square is ((x+9)2 ).
Step 3
Exam Tip
\(81=9^2\) और दो (9x) आयत मिलकर (18x) देते हैं। इसलिए पूरा वर्ग ((x+9)2 ) है।
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