एक आयत मॉडल \(2x^2+9x+10\) दिखाता है। सही भुजाएं कौन-सी हैं?
A rectangle model shows \(2x^2+9x+10\). Which sides are correct?
#rectangle grid
#factor model
#visual multiplication
A (2x+5) और (x+2) / correct factors
B (2x+2) और (x+5) / middle wrong
C (x+5) और (x+4) / leading term wrong
D (2x+10) और (x+1) / middle wrong
Explanation opens after your attempt
Correct Answer
A. (2x+5) और (x+2) / correct factors
Step 1
Concept
((2x+5)(x+2)=2x-2 +4x+5x+10). In exams the sum of cross strips should be (9x).
Step 2
Why this answer is correct
The correct answer is A. (2x+5) और (x+2) / correct factors. ((2x+5)(x+2)=2x-2 +4x+5x+10). In exams the sum of cross strips should be (9x).
Step 3
Exam Tip
((2x+5)(x+2)=2x-2 +4x+5x+10) है। परीक्षा में क्रॉस पट्टियों का योग (9x) होना चाहिए।
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एक ग्रिड मॉडल में पंक्तियां (x) और (5), स्तंभ (x) और (2) हैं। कुल क्षेत्रफल क्या होगा?
In a grid model, the rows are (x) and (5), and the columns are (x) and (2). What will be the total area?
#grid model
#rectangle area
#visual multiplication
A \(x^2+7x+10\) / correct total
B \(x^2+10x+7\) / swapped terms
C \(x^2+5x+2\) / corner missed
D \(x^2-7x+10\) / wrong sign
Explanation opens after your attempt
Correct Answer
A. \(x^2+7x+10\) / correct total
Step 1
Concept
The four cells are \(x^2\), (2x), (5x), and (10), whose sum is \(x^2+7x+10\). In exams multiply every cell.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+7x+10\) / correct total. The four cells are \(x^2\), (2x), (5x), and (10), whose sum is \(x^2+7x+10\). In exams multiply every cell.
Step 3
Exam Tip
चार खाने \(x^2\), (2x), (5x), और (10) हैं जिनका योग \(x^2+7x+10\) है। परीक्षा में हर खाने का गुणन करें।
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भुजाएँ (x+2) और (x+6) वाले आयत में छोटे कोने का क्षेत्रफल क्या होगा?
In a rectangle with sides (x+2) and (x+6), what will be the area of the small corner?
#small rectangle
#corner area
#visual multiplication
A (8)
B (12)
C (2x)
D (6x)
Explanation opens after your attempt
Step 1
Concept
The small corner area is \(2\cdot 6=12\). Exam tip: multiply the numerical parts.
Step 2
Why this answer is correct
The correct answer is B. (12). The small corner area is \(2\cdot 6=12\). Exam tip: multiply the numerical parts.
Step 3
Exam Tip
छोटे कोने का क्षेत्रफल \(2\cdot 6=12\) है। परीक्षा में संख्यात्मक भागों का गुणन करें।
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यदि एक आयत की लंबाई (2x+5) और चौड़ाई (x) है, तो क्षेत्र मॉडल क्या देगा?
If a rectangle has length (2x+5) and breadth (x), what will the area model give?
#distributive-area
#rectangle-model
#visual-multiplication
A \(2x^2+5x\)
B \(2x^2+5\)
C \(x^2+10x\)
D (2x+5x)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+5x\)
Step 1
Concept
Multiplying (x) by (2x) and (5) gives \(2x^2+5x\). Exam tip: multiply the breadth by both parts.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+5x\). Multiplying (x) by (2x) and (5) gives \(2x^2+5x\). Exam tip: multiply the breadth by both parts.
Step 3
Exam Tip
(x) को (2x) और (5) से गुणा करने पर \(2x^2+5x\) मिलता है। परीक्षा में चौड़ाई को दोनों भागों से गुणा करें।
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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
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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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
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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एक आयत के भाग \(6x^2\), (9x), (4x) और (6) हैं। कौन सा गुणनफल इस मॉडल को सही दिखाता है?
The parts of a rectangle are \(6x^2\), (9x), (4x), and (6). Which product correctly represents this model?
#area decomposition
#rectangle factors
#visual multiplication
A ((3x+2)(2x+3))
B ((6x+1)(x+6))
C ((2x+2)(3x+3))
D ((3x+6)(2x+1))
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(2x+3))
Step 1
Concept
((3x+2)(2x+3)) gives \(6x^2\), (9x), (4x), and (6). Exam tip: verify all four areas.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(2x+3)). ((3x+2)(2x+3)) gives \(6x^2\), (9x), (4x), and (6). Exam tip: verify all four areas.
Step 3
Exam Tip
((3x+2)(2x+3)) से \(6x^2\), (9x), (4x) और (6) मिलते हैं। परीक्षा में चारों क्षेत्रफल मिलाकर जाँचें।
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एक आयत मॉडल में ((2x+1)(2x+7)) है। कुल क्षेत्रफल में स्थिर कोना और (x) वाले संयुक्त पद कौन से होंगे?
A rectangle model represents ((2x+1)(2x+7)). What will be the constant corner and combined (x)-term in the total area?
#rectangle area
#combined terms
#visual multiplication
A (7) और (16x) / (7) and (16x)
B (14) और (8x) / (14) and (8x)
C (7) और (8x) / (7) and (8x)
D (1) और (14x) / (1) and (14x)
Explanation opens after your attempt
Correct Answer
A. (7) और (16x) / (7) and (16x)
Step 1
Concept
The constant corner is \(1\cdot 7=7\) and the (x)-terms are (14x+2x=16x). Exam tip: add the four parts separately.
Step 2
Why this answer is correct
The correct answer is A. (7) और (16x) / (7) and (16x). The constant corner is \(1\cdot 7=7\) and the (x)-terms are (14x+2x=16x). Exam tip: add the four parts separately.
Step 3
Exam Tip
स्थिर कोना \(1\cdot 7=7\) और (x) पद (14x+2x=16x) हैं। परीक्षा में चार भागों को अलग जोड़ें।
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चित्र में ((x+4)(x+7)) का आयत चार भागों में है। कौन सा भाग कोने के छोटे आयत का क्षेत्रफल होगा?
A rectangle for ((x+4)(x+7)) is divided into four parts. Which part is the area of the small corner rectangle?
#rectangle model
#constant product
#visual multiplication
A (11x)
B (28)
C (4x)
D (7x)
Explanation opens after your attempt
Step 1
Concept
The small corner area is \(4\cdot 7=28\). Exam tip: identify the product of constant parts separately.
Step 2
Why this answer is correct
The correct answer is B. (28). The small corner area is \(4\cdot 7=28\). Exam tip: identify the product of constant parts separately.
Step 3
Exam Tip
छोटे कोने का क्षेत्रफल \(4\cdot 7=28\) है। परीक्षा में स्थिर भागों के गुणन को अलग पहचानें।
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आयत मॉडल में ((2x+1)(3x+4)) के (x) वाले पदों का कुल क्षेत्र क्या होगा?
In the rectangle model of ((2x+1)(3x+4)), what is the total area of the (x)-terms?
#rectangle-expansion
#cross-terms
#visual-multiplication
A (8x)
B (11x)
C (6x)
D (12x)
Explanation opens after your attempt
Step 1
Concept
Here \(2x\times4=8x\) and \(1\times3x=3x\), so the total is (11x). Exam tip: add the cross rectangles.
Step 2
Why this answer is correct
The correct answer is B. (11x). Here \(2x\times4=8x\) and \(1\times3x=3x\), so the total is (11x). Exam tip: add the cross rectangles.
Step 3
Exam Tip
\(2x\times4=8x\) और \(1\times3x=3x\), इसलिए कुल (11x) है। परीक्षा में क्रॉस आयतों को जोड़ें।
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आयत मॉडल में ((x+3)(x+8)) के चार भागों का सही समूह कौन सा है?
In the rectangle model of ((x+3)(x+8)), which is the correct group of four parts?
#rectangle-expansion
#four-parts
#visual-multiplication
A \(x^2\), (3x), (8x), (24)
B \(x^2\), (11x), (24x), (1)
C \(x^2\), \(3x^2\), (8x), (24)
D \(x^2\), (24x), (11), (x)
Explanation opens after your attempt
Correct Answer
A. \(x^2\), (3x), (8x), (24)
Step 1
Concept
The rectangle parts come from \(x\times x\), \(x\times8\), \(3\times x\), and \(3\times8\). Exam tip: multiply each outside part.
Step 2
Why this answer is correct
The correct answer is A. \(x^2\), (3x), (8x), (24). The rectangle parts come from \(x\times x\), \(x\times8\), \(3\times x\), and \(3\times8\). Exam tip: multiply each outside part.
Step 3
Exam Tip
आयत के भाग \(x\times x\), \(x\times8\), \(3\times x\) और \(3\times8\) से बनते हैं। परीक्षा में हर बाहरी भाग का गुणन करें।
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एक आयत मॉडल में लंबाई (r+2) और चौड़ाई (r+3) है। कुल क्षेत्रफल कौन सा होगा?
In a rectangle model, the length is (r+2) and the breadth is (r+3). What is the total area?
#rectangle area
#visual multiplication
#identity
A \(r^2+6\)
B \(r^2+2r+3r\)
C \(r^2+5r+6\)
D \(r^2+6r+5\)
Explanation opens after your attempt
Correct Answer
C. \(r^2+5r+6\)
Step 1
Concept
The area is ((r+2)(r+3)), which becomes \(r^2+5r+6\). Exam tip: add the four parts of the rectangle.
Step 2
Why this answer is correct
The correct answer is C. \(r^2+5r+6\). The area is ((r+2)(r+3)), which becomes \(r^2+5r+6\). Exam tip: add the four parts of the rectangle.
Step 3
Exam Tip
क्षेत्रफल ((r+2)(r+3)) है जो \(r^2+5r+6\) बनता है। परीक्षा में आयत के चार भाग जोड़ें।
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दृश्य मॉडल में \((x+1)(x+4)\) का बीच वाला \(x\) पद किससे बनता है?
In the visual model of \((x+1)(x+4)\), how is the middle \(x\) term formed?
#middle term
#rectangle parts
#visual multiplication
A \(1x+4x\) से / From \(1x+4x\)
B \(1+4\) से / From \(1+4\)
C \(x^2+4\) से / From \(x^2+4\)
D \(x\times x\) से / From \(x\times x\)
Explanation opens after your attempt
Correct Answer
A. \(1x+4x\) से / From \(1x+4x\)
Step 1
Concept
Two rectangular parts \(x\) and \(4x\) combine to make \(5x\). Exam tip: add the \(x\)-terms.
Step 2
Why this answer is correct
The correct answer is A. \(1x+4x\) से / From \(1x+4x\). Two rectangular parts \(x\) and \(4x\) combine to make \(5x\). Exam tip: add the \(x\)-terms.
Step 3
Exam Tip
दो आयताकार भाग \(x\) और \(4x\) मिलकर \(5x\) बनाते हैं। परीक्षा में \(x\) वाले पद जोड़ें।
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यदि \((x+2)(x+3)\) को आयत से दिखाया जाए, तो चार भागों का योग क्या होगा?
If \((x+2)(x+3)\) is shown by a rectangle, what is the sum of its four parts?
#rectangle expansion
#visual multiplication
#identity
A \(x^2+5\)
B \(x^2+6x+5\)
C \(x^2+5x+6\)
D \(x^2+2x+3\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+5x+6\)
Step 1
Concept
The parts are \(x^2\), \(3x\), \(2x\), and \(6\). Exam tip: add \(3x+2x=5x\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+5x+6\). The parts are \(x^2\), \(3x\), \(2x\), and \(6\). Exam tip: add \(3x+2x=5x\).
Step 3
Exam Tip
भाग \(x^2\), \(3x\), \(2x\) और \(6\) हैं। परीक्षा में \(3x+2x=5x\) जोड़ें।
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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
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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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
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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