एक वर्ग की भुजा \(a+b\) है। उसके क्षेत्रफल का दृश्य मॉडल किस सर्वसमिका को दिखाता है?
A square has side \(a+b\). Which identity is shown by its area model?
#algebraic identities
#area model
#square
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A \(a^2+2ab+b^2\)
B \(a^2-b^2\)
C \(a^2+ab+b^2\)
D \(2a+2b\)
Explanation opens after your attempt
Correct Answer
A. \(a^2+2ab+b^2\)
Step 1
Concept
The area of the square is \((a+b)^2\) and its parts give \(a^2+2ab+b^2\). Exam tip: split the big square into smaller parts.
Step 2
Why this answer is correct
The correct answer is A. \(a^2+2ab+b^2\). The area of the square is \((a+b)^2\) and its parts give \(a^2+2ab+b^2\). Exam tip: split the big square into smaller parts.
Step 3
Exam Tip
वर्ग का क्षेत्रफल \((a+b)^2\) होता है और चार भाग मिलकर \(a^2+2ab+b^2\) देते हैं। परीक्षा में बड़े वर्ग को छोटे भागों में बांटकर देखें।
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चित्र में \(a\) और \(b\) भुजाओं से बने दो छोटे वर्ग और दो बराबर आयत हैं। कुल क्षेत्रफल क्या होगा?
A diagram has two small squares with sides \(a\) and \(b\) and two equal rectangles. What is the total area?
#visual model
#rectangle
#square
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A \(a^2+b^2\)
B \(a^2+2ab+b^2\)
C \(a^2-ab+b^2\)
D \(2a^2+2b^2\)
Explanation opens after your attempt
Correct Answer
B. \(a^2+2ab+b^2\)
Step 1
Concept
The two equal rectangles have area \(ab+ab=2ab\). So the total area is \(a^2+2ab+b^2\).
Step 2
Why this answer is correct
The correct answer is B. \(a^2+2ab+b^2\). The two equal rectangles have area \(ab+ab=2ab\). So the total area is \(a^2+2ab+b^2\).
Step 3
Exam Tip
दो बराबर आयतों का क्षेत्रफल \(ab+ab=2ab\) है। इसलिए कुल क्षेत्रफल \(a^2+2ab+b^2\) होगा।
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यदि बड़े वर्ग की भुजा \(x+3\) है तो उसका क्षेत्रफल किस रूप में लिखा जाएगा?
If the side of a big square is \(x+3\), how will its area be written?
#square identity
#area
#visual identities
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A \(x^2+3x+9\)
B \(x^2+6x+3\)
C \(x^2+6x+9\)
D \(x^2-6x+9\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+6x+9\)
Step 1
Concept
The area is \((x+3)^2\) and \((a+b)^2\) gives \(x^2+6x+9\). Exam tip: do not miss the middle term \(2ab\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+6x+9\). The area is \((x+3)^2\) and \((a+b)^2\) gives \(x^2+6x+9\). Exam tip: do not miss the middle term \(2ab\).
Step 3
Exam Tip
क्षेत्रफल \((x+3)^2\) है और \((a+b)^2\) से \(x^2+6x+9\) मिलता है। परीक्षा में \(2ab\) वाला मध्य पद न भूलें।
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एक वर्ग की भुजा \(a\) है। उसमें से कोने का \(b \times b\) वर्ग हटाया गया है। बचा हुआ क्षेत्रफल किससे संबंधित है?
A square has side \(a\). A corner square of \(b \times b\) is removed. The remaining area is related to which expression?
#difference of squares
#visual model
#area
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A \(a^2+b^2\)
B \(2ab\)
C \((a+b)^2\)
D \(a^2-b^2\)
Explanation opens after your attempt
Correct Answer
D. \(a^2-b^2\)
Step 1
Concept
The smaller square is subtracted from the larger square so we get \(a^2-b^2\). Exam tip: remember to subtract the removed part.
Step 2
Why this answer is correct
The correct answer is D. \(a^2-b^2\). The smaller square is subtracted from the larger square so we get \(a^2-b^2\). Exam tip: remember to subtract the removed part.
Step 3
Exam Tip
बड़े वर्ग से छोटे वर्ग का क्षेत्रफल घटता है इसलिए \(a^2-b^2\) मिलता है। परीक्षा में हटाए गए भाग को घटाना याद रखें।
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दृश्य मॉडल में \(a^2-b^2\) को दो आयतों में फिर से सजाया गया है। यह किस गुणनखंड को दिखाता है?
In a visual model \(a^2-b^2\) is rearranged into two rectangles. Which factorisation does it show?
#factorisation
#area model
#difference of squares
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A \((a-b)(a+b)\)
B \((a+b)^2\)
C \((a-b)^2\)
D \(a(a+b)\)
Explanation opens after your attempt
Correct Answer
A. \((a-b)(a+b)\)
Step 1
Concept
The difference of squares model shows \(a^2-b^2=(a-b)(a+b)\). Exam tip: look for both difference and sum factors.
Step 2
Why this answer is correct
The correct answer is A. \((a-b)(a+b)\). The difference of squares model shows \(a^2-b^2=(a-b)(a+b)\). Exam tip: look for both difference and sum factors.
Step 3
Exam Tip
अंतर के वर्ग का मॉडल \(a^2-b^2=(a-b)(a+b)\) दिखाता है। परीक्षा में अंतर और योग दोनों कारक देखें।
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भुजा \(a-b\) वाले वर्ग का क्षेत्रफल कौन सा होगा?
What is the area of a square with side \(a-b\)?
#minus identity
#square model
#area
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A \(a^2-b^2\)
B \(a^2-2ab+b^2\)
C \(a^2+2ab+b^2\)
D \(a^2+ab-b^2\)
Explanation opens after your attempt
Correct Answer
B. \(a^2-2ab+b^2\)
Step 1
Concept
The area of the square is \((a-b)^2\). Expanding it gives \(a^2-2ab+b^2\).
Step 2
Why this answer is correct
The correct answer is B. \(a^2-2ab+b^2\). The area of the square is \((a-b)^2\). Expanding it gives \(a^2-2ab+b^2\).
Step 3
Exam Tip
वर्ग का क्षेत्रफल \((a-b)^2\) होता है। इसे फैलाने पर \(a^2-2ab+b^2\) मिलता है।
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चित्र में बड़े \(a \times a\) वर्ग से दो \(a \times b\) आयत घटते हैं और \(b \times b\) वर्ग दोबारा जुड़ता है। कौन सी सर्वसमिका बनती है?
In a diagram two \(a \times b\) rectangles are subtracted from a big \(a \times a\) square and a \(b \times b\) square is added back. Which identity is formed?
#visual subtraction
#identity
#area
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A \((a+b)^2=a^2+2ab+b^2\)
B \(a^2-b^2=(a-b)(a+b)\)
C \((a-b)^2=a^2-2ab+b^2\)
D \(ab+bc+ca\)
Explanation opens after your attempt
Correct Answer
C. \((a-b)^2=a^2-2ab+b^2\)
Step 1
Concept
Two \(ab\) areas are subtracted and \(b^2\) is added back once. So \((a-b)^2=a^2-2ab+b^2\).
Step 2
Why this answer is correct
The correct answer is C. \((a-b)^2=a^2-2ab+b^2\). Two \(ab\) areas are subtracted and \(b^2\) is added back once. So \((a-b)^2=a^2-2ab+b^2\).
Step 3
Exam Tip
दो \(ab\) क्षेत्र घटते हैं और \(b^2\) एक बार वापस जुड़ता है। इसलिए \((a-b)^2=a^2-2ab+b^2\) है।
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लंबाई \(x+2\) और चौड़ाई \(x+5\) वाले आयत का क्षेत्रफल दृश्य रूप में क्या है?
What is the area of a rectangle with length \(x+2\) and breadth \(x+5\) in visual form?
#rectangle model
#product identity
#area
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A \(x^2+7x+7\)
B \(x^2+10x+7\)
C \(x^2+3x+10\)
D \(x^2+7x+10\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+7x+10\)
Step 1
Concept
The rectangle area is \((x+2)(x+5)\). Its parts give \(x^2+5x+2x+10=x^2+7x+10\).
Step 2
Why this answer is correct
The correct answer is D. \(x^2+7x+10\). The rectangle area is \((x+2)(x+5)\). Its parts give \(x^2+5x+2x+10=x^2+7x+10\).
Step 3
Exam Tip
आयत का क्षेत्रफल \((x+2)(x+5)\) है। भागों से \(x^2+5x+2x+10=x^2+7x+10\) मिलता है।
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टाइल मॉडल में \(x^2\) टाइल एक है और \(x\) टाइल \(8\) हैं। यदि स्थिर टाइल \(16\) हैं तो पूरा वर्ग किसका मॉडल है?
In a tile model there is one \(x^2\) tile and \(8\) \(x\)-tiles. If there are \(16\) constant tiles then the complete square models what?
#algebra tiles
#complete square
#visual model
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A \((x+4)^2\)
B \((x+8)^2\)
C \((x-4)^2\)
D \(x^2+16\)
Explanation opens after your attempt
Correct Answer
A. \((x+4)^2\)
Step 1
Concept
\(x^2+8x+16\) is written as \((x+4)^2\). Exam tip: identify it using \(2 \times 4=8\).
Step 2
Why this answer is correct
The correct answer is A. \((x+4)^2\). \(x^2+8x+16\) is written as \((x+4)^2\). Exam tip: identify it using \(2 \times 4=8\).
Step 3
Exam Tip
\(x^2+8x+16\) को \((x+4)^2\) लिखा जाता है। परीक्षा में \(2 \times 4=8\) देखकर पहचानें।
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यदि वर्ग मॉडल में बीच के दो आयतों का कुल क्षेत्रफल \(10x\) और छोटे वर्ग का क्षेत्रफल \(25\) है तो भुजा क्या होगी?
If in a square model the total area of the two middle rectangles is \(10x\) and the small square area is \(25\), what is the side?
#complete square
#side
#area model
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A \(x+10\)
B \(x+5\)
C \(x-5\)
D \(x+25\)
Explanation opens after your attempt
Correct Answer
B. \(x+5\)
Step 1
Concept
The small square has side \(5\) and \(2 \times 5x=10x\). So the big side is \(x+5\).
Step 2
Why this answer is correct
The correct answer is B. \(x+5\). The small square has side \(5\) and \(2 \times 5x=10x\). So the big side is \(x+5\).
Step 3
Exam Tip
छोटे वर्ग की भुजा \(5\) है और \(2 \times 5x=10x\) है। इसलिए बड़ी भुजा \(x+5\) होगी।
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दृश्य मॉडल में \((p+q)^2\) के लिए कितने \(pq\) आयत मिलते हैं?
In the visual model of \((p+q)^2\), how many \(pq\) rectangles are formed?
#square expansion
#visual model
#middle term
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A \(1\)
B \(3\)
C \(2\)
D \(4\)
Explanation opens after your attempt
Step 1
Concept
In \((p+q)^2\), there are two equal rectangles \(pq\) and \(pq\). Exam tip: remember the middle term \(2pq\).
Step 2
Why this answer is correct
The correct answer is C. \(2\). In \((p+q)^2\), there are two equal rectangles \(pq\) and \(pq\). Exam tip: remember the middle term \(2pq\).
Step 3
Exam Tip
\((p+q)^2\) में दो बराबर आयत \(pq\) और \(pq\) होते हैं। परीक्षा में मध्य पद \(2pq\) याद रखें।
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भुजाएं \(m+n\) और \(m+n\) वाले वर्ग को चार भागों में बांटने पर कौन सा भाग नहीं बनता?
A square with sides \(m+n\) and \(m+n\) is split into four parts. Which part is not formed?
#area partition
#visual identity
#square
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A \(m^2\)
B \(mn\)
C \(n^2\)
D \(m^2-n^2\)
Explanation opens after your attempt
Correct Answer
D. \(m^2-n^2\)
Step 1
Concept
The four parts are \(m^2\), \(mn\), \(mn\), and \(n^2\). \(m^2-n^2\) belongs to another identity.
Step 2
Why this answer is correct
The correct answer is D. \(m^2-n^2\). The four parts are \(m^2\), \(mn\), \(mn\), and \(n^2\). \(m^2-n^2\) belongs to another identity.
Step 3
Exam Tip
चार भाग \(m^2\), \(mn\), \(mn\) और \(n^2\) होते हैं। \(m^2-n^2\) अलग सर्वसमिका से जुड़ा है।
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एक आयत की लंबाई \(a+b\) और चौड़ाई \(a-b\) है। उसका क्षेत्रफल किसके बराबर है?
A rectangle has length \(a+b\) and breadth \(a-b\). Its area is equal to what?
#rectangle area
#difference of squares
#identity
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A \(a^2-b^2\)
B \(a^2+2ab+b^2\)
C \(a^2-2ab+b^2\)
D \(2a+2b\)
Explanation opens after your attempt
Correct Answer
A. \(a^2-b^2\)
Step 1
Concept
The area is \((a+b)(a-b)\). It equals \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-b^2\). The area is \((a+b)(a-b)\). It equals \(a^2-b^2\).
Step 3
Exam Tip
आयत का क्षेत्रफल \((a+b)(a-b)\) है। यह \(a^2-b^2\) के बराबर होता है।
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यदि \(7 \times 9\) को दृश्य मॉडल में \((8-1)(8+1)\) की तरह देखें तो मान क्या होगा?
If \(7 \times 9\) is viewed as \((8-1)(8+1)\) in a visual model, what is its value?
#numeric model
#difference of squares
#visual multiplication
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A \(62\)
B \(63\)
C \(64\)
D \(65\)
Explanation opens after your attempt
Step 1
Concept
\((8-1)(8+1)=8^2-1^2=64-1=63\). Exam tip: use a nearby perfect square.
Step 2
Why this answer is correct
The correct answer is B. \(63\). \((8-1)(8+1)=8^2-1^2=64-1=63\). Exam tip: use a nearby perfect square.
Step 3
Exam Tip
\((8-1)(8+1)=8^2-1^2=64-1=63\) है। परीक्षा में पास के पूर्ण वर्ग का उपयोग करें।
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भुजा \(10+2\) वाले वर्ग का क्षेत्रफल दृश्य मॉडल से कितना होगा?
Using a visual model, what is the area of a square with side \(10+2\)?
#numeric square
#area model
#identity
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A \(104\)
B \(120\)
C \(144\)
D \(124\)
Explanation opens after your attempt
Correct Answer
C. \(144\)
Step 1
Concept
\((10+2)^2=10^2+2 \times 10 \times 2+2^2=144\). Exam tip: add all four parts.
Step 2
Why this answer is correct
The correct answer is C. \(144\). \((10+2)^2=10^2+2 \times 10 \times 2+2^2=144\). Exam tip: add all four parts.
Step 3
Exam Tip
\((10+2)^2=10^2+2 \times 10 \times 2+2^2=144\) है। परीक्षा में चारों भागों का योग करें।
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एक वर्ग मॉडल में \(6^2\), दो \(6 \times 4\) आयत और \(4^2\) वर्ग हैं। कुल क्षेत्रफल क्या है?
A square model contains \(6^2\), two \(6 \times 4\) rectangles and a \(4^2\) square. What is the total area?
#numeric area
#square identity
#visual model
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A \(76\)
B \(84\)
C \(96\)
D \(100\)
Explanation opens after your attempt
Correct Answer
D. \(100\)
Step 1
Concept
The total area is \(36+24+24+16=100\). This is the visual model of \((6+4)^2\).
Step 2
Why this answer is correct
The correct answer is D. \(100\). The total area is \(36+24+24+16=100\). This is the visual model of \((6+4)^2\).
Step 3
Exam Tip
कुल क्षेत्रफल \(36+24+24+16=100\) है। यह \((6+4)^2\) का दृश्य मॉडल है।
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यदि \(99^2\) को \((100-1)^2\) के मॉडल से निकालें तो सही मान क्या है?
If \(99^2\) is found using the model of \((100-1)^2\), what is the correct value?
#near hundred
#square model
#minus identity
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A \(9801\)
B \(9901\)
C \(9999\)
D \(10001\)
Explanation opens after your attempt
Correct Answer
A. \(9801\)
Step 1
Concept
\((100-1)^2=10000-200+1=9801\). Exam tip: in a subtraction square \(2ab\) is subtracted.
Step 2
Why this answer is correct
The correct answer is A. \(9801\). \((100-1)^2=10000-200+1=9801\). Exam tip: in a subtraction square \(2ab\) is subtracted.
Step 3
Exam Tip
\((100-1)^2=10000-200+1=9801\) है। परीक्षा में घटाव वाले वर्ग में \(2ab\) घटता है।
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दृश्य मॉडल में \(x^2+12x+36\) को किस पूर्ण वर्ग के रूप में देखा जा सकता है?
In a visual model, \(x^2+12x+36\) can be seen as which perfect square?
#perfect square
#algebra tiles
#visual identity
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A \((x+12)^2\)
B \((x+6)^2\)
C \((x-6)^2\)
D \((x+3)^2\)
Explanation opens after your attempt
Correct Answer
B. \((x+6)^2\)
Step 1
Concept
Here \(36=6^2\) and \(12x=2 \times 6x\). So it is \((x+6)^2\).
Step 2
Why this answer is correct
The correct answer is B. \((x+6)^2\). Here \(36=6^2\) and \(12x=2 \times 6x\). So it is \((x+6)^2\).
Step 3
Exam Tip
\(36=6^2\) और \(12x=2 \times 6x\) है। इसलिए यह \((x+6)^2\) है।
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चार भागों \(y^2\), \(4y\), \(4y\) और \(16\) से बना वर्ग किस अभिव्यक्ति को दिखाता है?
A square made of four parts \(y^2\), \(4y\), \(4y\), and \(16\) shows which expression?
#area parts
#perfect square
#visual model
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A \((y+8)^2\)
B \((y-4)^2\)
C \((y+4)^2\)
D \(y^2+4\)
Explanation opens after your attempt
Correct Answer
C. \((y+4)^2\)
Step 1
Concept
The sum of the parts is \(y^2+8y+16\). It equals \((y+4)^2\).
Step 2
Why this answer is correct
The correct answer is C. \((y+4)^2\). The sum of the parts is \(y^2+8y+16\). It equals \((y+4)^2\).
Step 3
Exam Tip
भागों का योग \(y^2+8y+16\) है। यह \((y+4)^2\) के बराबर है।
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यदि वर्ग की भुजा \(r+s\) है तो उसके मॉडल में \(s^2\) किस भाग को दिखाता है?
If the side of a square is \(r+s\), what does \(s^2\) show in its model?
#area parts
#square model
#identity
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A दो आयतों का कुल क्षेत्रफल / Total area of two rectangles
B बड़े \(r\) वाले वर्ग का क्षेत्रफल / Area of the large \(r\)-square
C छोटे \(s\) वाले वर्ग का क्षेत्रफल / Area of the small \(s\)-square
D पूरे वर्ग की परिमिति / Perimeter of the whole square
Explanation opens after your attempt
Correct Answer
C. छोटे \(s\) वाले वर्ग का क्षेत्रफल / Area of the small \(s\)-square
Step 1
Concept
\(s^2\) is the area of the small square whose side is \(s\). Exam tip: identify each part from its two sides.
Step 2
Why this answer is correct
The correct answer is C. छोटे \(s\) वाले वर्ग का क्षेत्रफल / Area of the small \(s\)-square. \(s^2\) is the area of the small square whose side is \(s\). Exam tip: identify each part from its two sides.
Step 3
Exam Tip
\(s^2\) उस छोटे वर्ग का क्षेत्रफल है जिसकी भुजा \(s\) है। परीक्षा में हर भाग को उसकी दोनों भुजाओं से पहचानें।
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भुजा \(x-2\) वाले वर्ग के दृश्य मॉडल में कौन सा पद धनात्मक रहता है?
In the visual model of a square with side \(x-2\), which term remains positive?
#minus square
#signs
#visual model
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A \(-4x\)
B \(x^2\) और \(4\) / \(x^2\) and \(4\)
C \(-x^2\)
D \(-4\)
Explanation opens after your attempt
Correct Answer
B. \(x^2\) और \(4\) / \(x^2\) and \(4\)
Step 1
Concept
In \((x-2)^2=x^2-4x+4\), \(x^2\) and \(4\) are positive. Exam tip: square terms are positive.
Step 2
Why this answer is correct
The correct answer is B. \(x^2\) और \(4\) / \(x^2\) and \(4\). In \((x-2)^2=x^2-4x+4\), \(x^2\) and \(4\) are positive. Exam tip: square terms are positive.
Step 3
Exam Tip
\((x-2)^2=x^2-4x+4\) में \(x^2\) और \(4\) धनात्मक हैं। परीक्षा में वर्ग पद हमेशा धनात्मक देखें।
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किस दृश्य मॉडल में दो बराबर आयतों के क्षेत्रफल जोड़कर \(2ab\) बनता है?
In which visual model do two equal rectangle areas combine to form \(2ab\)?
#middle term
#rectangle
#area model
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A \((a+b)^2\)
B \(a^2-b^2\)
C \((a-b)(a+b)\)
D \(a+b\)
Explanation opens after your attempt
Correct Answer
A. \((a+b)^2\)
Step 1
Concept
The model of \((a+b)^2\) has two \(ab\) rectangles. Their sum forms \(2ab\).
Step 2
Why this answer is correct
The correct answer is A. \((a+b)^2\). The model of \((a+b)^2\) has two \(ab\) rectangles. Their sum forms \(2ab\).
Step 3
Exam Tip
\((a+b)^2\) के मॉडल में दो \(ab\) आयत होते हैं। इनका योग \(2ab\) बनाता है।
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आयत मॉडल में \((x+1)(x+4)\) को कितने भागों में बांटना सबसे सरल है?
In a rectangle model, into how many parts is \((x+1)(x+4)\) most simply divided?
#grid model
#rectangle product
#visual algebra
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A \(2\)
B \(4\)
C \(6\)
D \(8\)
Explanation opens after your attempt
Step 1
Concept
Two parts in length and two parts in breadth make \(2 \times 2=4\) parts. Exam tip: drawing a grid model is easy.
Step 2
Why this answer is correct
The correct answer is B. \(4\). Two parts in length and two parts in breadth make \(2 \times 2=4\) parts. Exam tip: drawing a grid model is easy.
Step 3
Exam Tip
दो भाग लंबाई में और दो भाग चौड़ाई में लेने से \(2 \times 2=4\) भाग बनते हैं। परीक्षा में ग्रिड मॉडल बनाना आसान तरीका है।
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\((x+1)(x+4)\) के आयत मॉडल में \(x\)-पदों का कुल योग क्या होगा?
In the rectangle model of \((x+1)(x+4)\), what is the total of the \(x\)-terms?
#rectangle product
#x terms
#visual model
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A \(4x\)
B \(x\)
C \(5x\)
D \(6x\)
Explanation opens after your attempt
Step 1
Concept
The parts are \(x^2\), \(4x\), \(x\), and \(4\). The sum of the \(x\)-terms is \(5x\).
Step 2
Why this answer is correct
The correct answer is C. \(5x\). The parts are \(x^2\), \(4x\), \(x\), and \(4\). The sum of the \(x\)-terms is \(5x\).
Step 3
Exam Tip
भागों से \(x^2\), \(4x\), \(x\) और \(4\) मिलते हैं। \(x\)-पदों का योग \(5x\) है।
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यदि एक आयत का क्षेत्रफल मॉडल \((a+3)(a+2)\) है तो स्थिर भाग का क्षेत्रफल क्या होगा?
If the area model of a rectangle is \((a+3)(a+2)\), what is the area of the constant part?
#constant term
#rectangle model
#identity
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A \(3a\)
B \(2a\)
C \(5a\)
D \(6\)
Explanation opens after your attempt
Step 1
Concept
The constant part comes from \(3 \times 2=6\). Exam tip: multiply the number parts separately.
Step 2
Why this answer is correct
The correct answer is D. \(6\). The constant part comes from \(3 \times 2=6\). Exam tip: multiply the number parts separately.
Step 3
Exam Tip
स्थिर भाग \(3 \times 2=6\) से मिलता है। परीक्षा में संख्या वाले भागों का गुणन अलग से करें।
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दृश्य मॉडल में \((a+b+c)^2\) बनाते समय कौन सा पद दो बार आता है?
While making the visual model of \((a+b+c)^2\), which term appears twice?
#three terms
#square model
#visual identity
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A \(ab\)
B \(a^2\)
C \(b^2\)
D \(c^2\)
Explanation opens after your attempt
Step 1
Concept
In the square grid, \(ab\) and \(ba\) are two equal parts. So their sum becomes \(2ab\).
Step 2
Why this answer is correct
The correct answer is A. \(ab\). In the square grid, \(ab\) and \(ba\) are two equal parts. So their sum becomes \(2ab\).
Step 3
Exam Tip
वर्ग ग्रिड में \(ab\) और \(ba\) दो समान भाग होते हैं। इसलिए उनका योग \(2ab\) बनता है।
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\((a+b+c)^2\) के क्षेत्र मॉडल में कितने वर्ग पद होते हैं?
How many square terms are there in the area model of \((a+b+c)^2\)?
#three terms
#area model
#square terms
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A \(2\)
B \(3\)
C \(4\)
D \(6\)
Explanation opens after your attempt
Step 1
Concept
There are three square terms \(a^2\), \(b^2\), and \(c^2\). Exam tip: identify square terms and rectangle terms separately.
Step 2
Why this answer is correct
The correct answer is B. \(3\). There are three square terms \(a^2\), \(b^2\), and \(c^2\). Exam tip: identify square terms and rectangle terms separately.
Step 3
Exam Tip
तीन वर्ग पद \(a^2\), \(b^2\) और \(c^2\) होते हैं। परीक्षा में वर्ग पद और आयत पद अलग पहचानें।
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यदि \(a+b+c\) भुजा वाले वर्ग को \(3\) भागों में प्रत्येक दिशा में बांटा जाए तो कुल छोटे खंड कितने होंगे?
If a square of side \(a+b+c\) is split into \(3\) parts in each direction, how many small sections are formed?
#grid sections
#three terms
#visual model
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A \(3\)
B \(6\)
C \(9\)
D \(12\)
Explanation opens after your attempt
Step 1
Concept
There are \(3\) parts in each direction so \(3 \times 3=9\) sections form. Exam tip: multiply rows and columns.
Step 2
Why this answer is correct
The correct answer is C. \(9\). There are \(3\) parts in each direction so \(3 \times 3=9\) sections form. Exam tip: multiply rows and columns.
Step 3
Exam Tip
हर दिशा में \(3\) भाग हैं इसलिए कुल \(3 \times 3=9\) खंड बनेंगे। परीक्षा में पंक्ति और स्तंभ का गुणन करें।
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किस मॉडल में \(a^2+2ab+b^2\) को एक पूर्ण वर्ग के रूप में दिखाया जाता है?
Which model shows \(a^2+2ab+b^2\) as a complete square?
#complete square
#area model
#identity
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A भुजा \(a-b\) का वर्ग / Square of side \(a-b\)
B भुजा \(a\) और \(b\) के दो अलग वर्ग / Two separate squares of sides \(a\) and \(b\)
C भुजा \(a+b\) का वर्ग / Square of side \(a+b\)
D लंबाई \(a+b\) और चौड़ाई \(a-b\) का आयत / Rectangle of length \(a+b\) and breadth \(a-b\)
Explanation opens after your attempt
Correct Answer
C. भुजा \(a+b\) का वर्ग / Square of side \(a+b\)
Step 1
Concept
This is the expansion of \((a+b)^2\). So the square with side \(a+b\) is the correct model.
Step 2
Why this answer is correct
The correct answer is C. भुजा \(a+b\) का वर्ग / Square of side \(a+b\). This is the expansion of \((a+b)^2\). So the square with side \(a+b\) is the correct model.
Step 3
Exam Tip
यह \((a+b)^2\) का विस्तार है। इसलिए भुजा \(a+b\) वाला वर्ग सही मॉडल है।
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किस मॉडल में \(a^2-2ab+b^2\) को देखा जा सकता है?
In which model can \(a^2-2ab+b^2\) be seen?
#minus identity
#complete square
#visual model
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A भुजा \(a+b\) का वर्ग / Square of side \(a+b\)
B भुजा \(a-b\) का वर्ग / Square of side \(a-b\)
C भुजा \(ab\) का वर्ग / Square of side \(ab\)
D भुजा \(a+b^2\) का वर्ग / Square of side \(a+b^2\)
Explanation opens after your attempt
Correct Answer
B. भुजा \(a-b\) का वर्ग / Square of side \(a-b\)
Step 1
Concept
The form \(a^2-2ab+b^2\) is \((a-b)^2\). Exam tip: identify the subtraction square from the negative sign.
Step 2
Why this answer is correct
The correct answer is B. भुजा \(a-b\) का वर्ग / Square of side \(a-b\). The form \(a^2-2ab+b^2\) is \((a-b)^2\). Exam tip: identify the subtraction square from the negative sign.
Step 3
Exam Tip
\(a^2-2ab+b^2\) का रूप \((a-b)^2\) है। परीक्षा में ऋण चिह्न देखकर घटाव वाला वर्ग पहचानें।
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यदि \(13^2\) को \((10+3)^2\) के दृश्य मॉडल से समझें तो \(2ab\) वाला भाग कितना होगा?
If \(13^2\) is understood using the visual model of \((10+3)^2\), what is the \(2ab\) part?
#numeric square
#middle term
#area model
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A \(30\)
B \(60\)
C \(90\)
D \(100\)
Explanation opens after your attempt
Step 1
Concept
Here \(2ab=2 \times 10 \times 3=60\). Exam tip: the middle part comes from two equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(60\). Here \(2ab=2 \times 10 \times 3=60\). Exam tip: the middle part comes from two equal rectangles.
Step 3
Exam Tip
यहां \(2ab=2 \times 10 \times 3=60\) है। परीक्षा में मध्य भाग दो बराबर आयतों से आता है।
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दृश्य मॉडल में \(15^2\) को \((10+5)^2\) से निकालने पर छोटे वर्ग का क्षेत्रफल कितना है?
In the visual model of \(15^2\) using \((10+5)^2\), what is the area of the small square?
#numeric model
#small square
#area
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A \(10\)
B \(25\)
C \(50\)
D \(100\)
Explanation opens after your attempt
Step 1
Concept
The small square has side \(5\), so its area is \(5^2=25\). Exam tip: identify the small square separately.
Step 2
Why this answer is correct
The correct answer is B. \(25\). The small square has side \(5\), so its area is \(5^2=25\). Exam tip: identify the small square separately.
Step 3
Exam Tip
छोटे वर्ग की भुजा \(5\) है इसलिए क्षेत्रफल \(5^2=25\) होगा। परीक्षा में छोटे वर्ग को अलग पहचानें।
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यदि \(18^2\) को \((20-2)^2\) के मॉडल से देखें तो कौन सा पद घटेगा?
If \(18^2\) is seen using the model \((20-2)^2\), which term will be subtracted?
#subtraction model
#numeric identity
#visual square
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A \(2 \times 20 \times 2\)
B \(20^2\)
C \(2^2\)
D \(18^2\)
Explanation opens after your attempt
Correct Answer
A. \(2 \times 20 \times 2\)
Step 1
Concept
In \((a-b)^2\), \(2ab\) is subtracted. Here the subtracted term is \(2 \times 20 \times 2\).
Step 2
Why this answer is correct
The correct answer is A. \(2 \times 20 \times 2\). In \((a-b)^2\), \(2ab\) is subtracted. Here the subtracted term is \(2 \times 20 \times 2\).
Step 3
Exam Tip
\((a-b)^2\) में \(2ab\) घटता है। यहां घटने वाला पद \(2 \times 20 \times 2\) है।
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क्षेत्र मॉडल में \(x^2+9x+18\) किस गुणनफल से मिल सकता है?
In an area model, \(x^2+9x+18\) can come from which product?
#factor model
#rectangle area
#visual identity
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A \((x+2)(x+7)\)
B \((x+3)(x+6)\)
C \((x+9)(x+18)\)
D \((x+1)(x+18)\)
Explanation opens after your attempt
Correct Answer
B. \((x+3)(x+6)\)
Step 1
Concept
\((x+3)(x+6)=x^2+6x+3x+18=x^2+9x+18\). Exam tip: check the factors of the constant term.
Step 2
Why this answer is correct
The correct answer is B. \((x+3)(x+6)\). \((x+3)(x+6)=x^2+6x+3x+18=x^2+9x+18\). Exam tip: check the factors of the constant term.
Step 3
Exam Tip
\((x+3)(x+6)=x^2+6x+3x+18=x^2+9x+18\) है। परीक्षा में स्थिर पद के कारक देखें।
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आयत मॉडल में \((x+4)(x+4)\) और वर्ग मॉडल में \((x+4)^2\) का संबंध क्या है?
What is the relation between the rectangle model \((x+4)(x+4)\) and the square model \((x+4)^2\)?
#same model
#square
#rectangle
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A दोनों अलग क्षेत्रफल देते हैं / Both give different areas
B दोनों समान क्षेत्रफल देते हैं / Both give the same area
C पहला केवल परिमिति है / The first is only perimeter
D दूसरा केवल रेखा खंड है / The second is only a line segment
Explanation opens after your attempt
Correct Answer
B. दोनों समान क्षेत्रफल देते हैं / Both give the same area
Step 1
Concept
\((x+4)(x+4)\) is the same as \((x+4)^2\). So both show the same area.
Step 2
Why this answer is correct
The correct answer is B. दोनों समान क्षेत्रफल देते हैं / Both give the same area. \((x+4)(x+4)\) is the same as \((x+4)^2\). So both show the same area.
Step 3
Exam Tip
\((x+4)(x+4)\) ही \((x+4)^2\) है। इसलिए दोनों एक ही क्षेत्रफल दिखाते हैं।
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यदि \(a^2-b^2\) को दृश्य रूप में समझाना हो तो कौन सा तरीका सही है?
Which method is correct to explain \(a^2-b^2\) visually?
#visual explanation
#difference of squares
#area
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A बड़े \(a\) वर्ग से छोटे \(b\) वर्ग को हटाना / Removing the smaller \(b\)-square from the larger \(a\)-square
B दो \(a\) वर्ग जोड़ना / Adding two \(a\)-squares
C चार \(b\) वर्ग जोड़ना / Adding four \(b\)-squares
D केवल \(a+b\) की रेखा खींचना / Drawing only the line \(a+b\)
Explanation opens after your attempt
Correct Answer
A. बड़े \(a\) वर्ग से छोटे \(b\) वर्ग को हटाना / Removing the smaller \(b\)-square from the larger \(a\)-square
Step 1
Concept
In \(a^2-b^2\), the smaller square area is subtracted from the larger square. Exam tip: distinguish square of difference and difference of squares.
Step 2
Why this answer is correct
The correct answer is A. बड़े \(a\) वर्ग से छोटे \(b\) वर्ग को हटाना / Removing the smaller \(b\)-square from the larger \(a\)-square. In \(a^2-b^2\), the smaller square area is subtracted from the larger square. Exam tip: distinguish square of difference and difference of squares.
Step 3
Exam Tip
\(a^2-b^2\) में छोटे वर्ग का क्षेत्रफल बड़े वर्ग से घटता है। परीक्षा में अंतर के वर्ग और वर्गों के अंतर में फर्क रखें।
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किस पहचान को मॉडल करने के लिए \(a+b\) और \(a-b\) भुजाओं वाला आयत बनाया जाता है?
Which identity is modeled by drawing a rectangle with sides \(a+b\) and \(a-b\)?
#rectangle model
#identity
#difference of squares
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A \((a+b)^2\)
B \(a^2-b^2\)
C \((a-b)^2\)
D \(a^2+b^2\)
Explanation opens after your attempt
Correct Answer
B. \(a^2-b^2\)
Step 1
Concept
The area of such a rectangle is \((a+b)(a-b)\). It equals \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is B. \(a^2-b^2\). The area of such a rectangle is \((a+b)(a-b)\). It equals \(a^2-b^2\).
Step 3
Exam Tip
ऐसे आयत का क्षेत्रफल \((a+b)(a-b)\) होता है। यह \(a^2-b^2\) के बराबर है।
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वर्ग मॉडल में \(x^2+2xy+y^2\) किस भुजा के वर्ग का क्षेत्रफल है?
In a square model, \(x^2+2xy+y^2\) is the area of a square with which side?
#square model
#identity
#area
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A \(x-y\)
B \(xy\)
C \(x+y\)
D \(x^2+y^2\)
Explanation opens after your attempt
Correct Answer
C. \(x+y\)
Step 1
Concept
This is the expansion of \((x+y)^2\). So the side of the square is \(x+y\).
Step 2
Why this answer is correct
The correct answer is C. \(x+y\). This is the expansion of \((x+y)^2\). So the side of the square is \(x+y\).
Step 3
Exam Tip
यह \((x+y)^2\) का विस्तार है। इसलिए वर्ग की भुजा \(x+y\) होगी।
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दृश्य मॉडल में \(x^2-6x+9\) को किस भुजा वाले वर्ग से दिखाया जा सकता है?
In a visual model, \(x^2-6x+9\) can be shown by a square of which side?
#minus square
#visual identity
#complete square
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A \(x+3\)
B \(x-6\)
C \(x+9\)
D \(x-3\)
Explanation opens after your attempt
Correct Answer
D. \(x-3\)
Step 1
Concept
Here \(9=3^2\) and \(-6x=-2 \times 3x\). So it is \((x-3)^2\).
Step 2
Why this answer is correct
The correct answer is D. \(x-3\). Here \(9=3^2\) and \(-6x=-2 \times 3x\). So it is \((x-3)^2\).
Step 3
Exam Tip
\(9=3^2\) और \(-6x=-2 \times 3x\) है। इसलिए यह \((x-3)^2\) है।
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यदि \(21 \times 19\) को \((20+1)(20-1)\) की तरह देखें तो कौन सी सर्वसमिका प्रयोग होगी?
If \(21 \times 19\) is seen as \((20+1)(20-1)\), which identity is used?
#numeric identity
#visual multiplication
#difference of squares
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A \((a+b)(a-b)=a^2-b^2\)
B \((a+b)^2=a^2+2ab+b^2\)
C \((a-b)^2=a^2-2ab+b^2\)
D \(a(b+c)=ab+ac\)
Explanation opens after your attempt
Correct Answer
A. \((a+b)(a-b)=a^2-b^2\)
Step 1
Concept
This is a product of sum and difference. So \((a+b)(a-b)=a^2-b^2\) applies.
Step 2
Why this answer is correct
The correct answer is A. \((a+b)(a-b)=a^2-b^2\). This is a product of sum and difference. So \((a+b)(a-b)=a^2-b^2\) applies.
Step 3
Exam Tip
यह योग और अंतर का गुणन है। इसलिए \((a+b)(a-b)=a^2-b^2\) लागू होगा।
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एक \(x+7\) भुजा वाले वर्ग में छोटे कोने का वर्ग \(7^2\) है। उस छोटे वर्ग का क्षेत्रफल कितना है?
In a square of side \(x+7\), the small corner square is \(7^2\). What is its area?
#constant square
#area model
#visual identity
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A \(7\)
B \(14\)
C \(49\)
D \(x+49\)
Explanation opens after your attempt
Step 1
Concept
The small square has side \(7\), so its area is \(7^2=49\). Exam tip: treat the square of the number as the constant term.
Step 2
Why this answer is correct
The correct answer is C. \(49\). The small square has side \(7\), so its area is \(7^2=49\). Exam tip: treat the square of the number as the constant term.
Step 3
Exam Tip
छोटे वर्ग की भुजा \(7\) है इसलिए क्षेत्रफल \(7^2=49\) होगा। परीक्षा में संख्या के वर्ग को स्थिर पद समझें।
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यदि एक वर्ग के क्षेत्र मॉडल में \(x^2\), \(5x\), \(5x\) और \(25\) भाग हैं तो पूरा क्षेत्रफल क्या है?
If a square area model has parts \(x^2\), \(5x\), \(5x\), and \(25\), what is the whole area?
#area sum
#complete square
#visual model
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A \(x^2+5x+25\)
B \(x^2+10x+25\)
C \(x^2+25x+10\)
D \(x^2+10x+5\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+10x+25\)
Step 1
Concept
The two \(5x\) parts combine to form \(10x\). So the total is \(x^2+10x+25\).
Step 2
Why this answer is correct
The correct answer is B. \(x^2+10x+25\). The two \(5x\) parts combine to form \(10x\). So the total is \(x^2+10x+25\).
Step 3
Exam Tip
दोनों \(5x\) भाग मिलकर \(10x\) बनाते हैं। इसलिए कुल \(x^2+10x+25\) है।
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किस विकल्प में \((x+2)^2\) का दृश्य क्षेत्रफल सही लिखा है?
Which option correctly writes the visual area of \((x+2)^2\)?
#square expansion
#middle term
#area model
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A \(x^2+4\)
B \(x^2+2x+4\)
C \(x^2+4x+4\)
D \(x^2-4x+4\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+4x+4\)
Step 1
Concept
In \((x+2)^2\), there are two \(2x\) rectangles. So the middle term is \(4x\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+4x+4\). In \((x+2)^2\), there are two \(2x\) rectangles. So the middle term is \(4x\).
Step 3
Exam Tip
\((x+2)^2\) में दो \(2x\) आयत होते हैं। इसलिए मध्य पद \(4x\) बनता है।
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किस विकल्प में \((x-4)^2\) का दृश्य क्षेत्रफल सही है?
Which option correctly gives the visual area of \((x-4)^2\)?
#minus square
#area model
#visual identity
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A \(x^2-8x+16\)
B \(x^2+8x+16\)
C \(x^2-4x+16\)
D \(x^2-16\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+16\)
Step 1
Concept
\((x-4)^2=x^2-2 \times x \times 4+16=x^2-8x+16\). Exam tip: take care of the negative middle term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+16\). \((x-4)^2=x^2-2 \times x \times 4+16=x^2-8x+16\). Exam tip: take care of the negative middle term.
Step 3
Exam Tip
\((x-4)^2=x^2-2 \times x \times 4+16=x^2-8x+16\) है। परीक्षा में घटाव वाले मध्य पद का ध्यान रखें।
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यदि \(52^2\) को \((50+2)^2\) के क्षेत्र मॉडल से हल करें तो \(50^2\) वाला बड़ा भाग कितना है?
If \(52^2\) is solved using the area model of \((50+2)^2\), what is the large part \(50^2\)?
#numeric square
#big square
#area model
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A \(100\)
B \(2500\)
C \(2600\)
D \(2704\)
Explanation opens after your attempt
Correct Answer
B. \(2500\)
Step 1
Concept
The big square has side \(50\), so its area is \(50^2=2500\). Exam tip: start with the large square.
Step 2
Why this answer is correct
The correct answer is B. \(2500\). The big square has side \(50\), so its area is \(50^2=2500\). Exam tip: start with the large square.
Step 3
Exam Tip
बड़े वर्ग की भुजा \(50\) है इसलिए उसका क्षेत्रफल \(50^2=2500\) है। परीक्षा में बड़े वर्ग से शुरुआत करें।
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\(49^2\) के दृश्य मॉडल में \((50-1)^2\) लेने पर छोटा वर्ग कौन सा है?
In the visual model of \(49^2\), using \((50-1)^2\), which is the small square?
#near fifty
#minus model
#small square
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A \(50^2\)
B \(49^2\)
C \(1^2\)
D \(2 \times 50 \times 1\)
Explanation opens after your attempt
Correct Answer
C. \(1^2\)
Step 1
Concept
In \((50-1)^2\), the small square is \(1^2\). Exam tip: identify the small subtracted part.
Step 2
Why this answer is correct
The correct answer is C. \(1^2\). In \((50-1)^2\), the small square is \(1^2\). Exam tip: identify the small subtracted part.
Step 3
Exam Tip
\((50-1)^2\) में छोटा वर्ग \(1^2\) है। परीक्षा में घटाए गए छोटे भाग को पहचानें।
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क्षेत्र मॉडल में \((x+3)(x+3)\) को जोड़ने पर कौन सा विस्तार मिलता है?
In an area model, what expansion is obtained by adding the parts of \((x+3)(x+3)\)?
#rectangle grid
#square expansion
#visual model
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A \(x^2+3x+9\)
B \(x^2+9x+9\)
C \(x^2+6x+9\)
D \(x^2+6x+3\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+6x+9\)
Step 1
Concept
The parts are \(x^2\), \(3x\), \(3x\), and \(9\). Their sum is \(x^2+6x+9\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+6x+9\). The parts are \(x^2\), \(3x\), \(3x\), and \(9\). Their sum is \(x^2+6x+9\).
Step 3
Exam Tip
भाग \(x^2\), \(3x\), \(3x\) और \(9\) हैं। इनका योग \(x^2+6x+9\) है।
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किस मॉडल में केवल क्षेत्रफलों को जोड़कर सर्वसमिका समझाई जाती है?
In which model is an identity explained by only adding areas?
#area model
#visual identity
#basic concept
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A क्षेत्र मॉडल / Area model
B संख्या रेखा मॉडल / Number line model
C घड़ी मॉडल / Clock model
D केवल मौखिक मॉडल / Only verbal model
Explanation opens after your attempt
Correct Answer
A. क्षेत्र मॉडल / Area model
Step 1
Concept
In an area model, areas of smaller parts are added to get total area. Exam tip: add the parts in such questions.
Step 2
Why this answer is correct
The correct answer is A. क्षेत्र मॉडल / Area model. In an area model, areas of smaller parts are added to get total area. Exam tip: add the parts in such questions.
Step 3
Exam Tip
क्षेत्र मॉडल में छोटे भागों के क्षेत्रफल जोड़कर कुल क्षेत्रफल मिलता है। परीक्षा में ऐसे प्रश्नों में भागों का योग करें।
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वर्ग मॉडल में \((a+b)^2\) और \((a-b)^2\) के बीच मुख्य दृश्य अंतर क्या है?
What is the main visual difference between \((a+b)^2\) and \((a-b)^2\) in square models?
#plus minus models
#visual difference
#identity
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A पहले में भाग जोड़े जाते हैं और दूसरे में कुछ भाग घटाए जाते हैं / In the first parts are added and in the second some parts are subtracted
B दोनों में कोई क्षेत्रफल नहीं होता / Both have no area
C पहले में केवल रेखा होती है / The first has only a line
D दूसरे में हमेशा \(a+b\) भुजा होती है / The second always has side \(a+b\)
Explanation opens after your attempt
Correct Answer
A. पहले में भाग जोड़े जाते हैं और दूसरे में कुछ भाग घटाए जाते हैं / In the first parts are added and in the second some parts are subtracted
Step 1
Concept
\((a+b)^2\) is an addition model while \((a-b)^2\) is a subtraction model. Exam tip: identify the model from the sign.
Step 2
Why this answer is correct
The correct answer is A. पहले में भाग जोड़े जाते हैं और दूसरे में कुछ भाग घटाए जाते हैं / In the first parts are added and in the second some parts are subtracted. \((a+b)^2\) is an addition model while \((a-b)^2\) is a subtraction model. Exam tip: identify the model from the sign.
Step 3
Exam Tip
\((a+b)^2\) जोड़ का मॉडल है जबकि \((a-b)^2\) घटाव का मॉडल है। परीक्षा में संकेत से मॉडल पहचानें।
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यदि किसी दृश्य मॉडल में कुल क्षेत्रफल \(p^2+2pq+q^2\) है तो पूरे वर्ग की भुजा क्या होगी?
If a visual model has total area \(p^2+2pq+q^2\), what is the side of the whole square?
#side identification
#complete square
#visual model
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A \(p-q\)
B \(p+q\)
C \(pq\)
D \(p^2+q^2\)
Explanation opens after your attempt
Correct Answer
B. \(p+q\)
Step 1
Concept
This is the area of \((p+q)^2\). So the side of the whole square is \(p+q\).
Step 2
Why this answer is correct
The correct answer is B. \(p+q\). This is the area of \((p+q)^2\). So the side of the whole square is \(p+q\).
Step 3
Exam Tip
यह \((p+q)^2\) का क्षेत्रफल है। इसलिए पूरे वर्ग की भुजा \(p+q\) होगी।
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