एक वर्ग की भुजा (x+2) है। दृश्य मॉडल में \(x^2\) के साथ दो समान आयत और एक छोटा वर्ग है। पूरा क्षेत्रफल क्या होगा?
A square has side (x+2). In the visual model, \(x^2\) is shown with two equal rectangles and one small square. What is the total area?
#visual-model
#square-identity
#area
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A \(x^2+4x+4\)
B \(x^2+2x+4\)
C \(x^2+4x+2\)
D \(x^2+2x+2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+4\)
Step 1
Concept
The two rectangles give (2x+2x=4x), and the small square is (4). In exams, add both strips.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+4\). The two rectangles give (2x+2x=4x), and the small square is (4). In exams, add both strips.
Step 3
Exam Tip
दो आयतों का क्षेत्रफल (2x+2x=4x) और छोटा वर्ग (4) है। परीक्षा में दोनों पट्टियाँ जोड़ें।
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एक (y+6) भुजा वाले वर्ग में बड़ा वर्ग \(y^2\) है। दोनों पट्टियों का संयुक्त क्षेत्रफल कितना होगा?
In a square of side (y+6), the large square is \(y^2\). What is the combined area of both strips?
#strips
#area-model
#binomial-square
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A (6y)
B (12y)
C (36y)
D \(y^2+36\)
Explanation opens after your attempt
Step 1
Concept
Both strips are (6y) and (6y), so the total is (12y). In exams, count equal rectangles separately.
Step 2
Why this answer is correct
The correct answer is B. (12y). Both strips are (6y) and (6y), so the total is (12y). In exams, count equal rectangles separately.
Step 3
Exam Tip
दोनों पट्टियाँ (6y) और (6y) हैं इसलिए कुल (12y) होगा। परीक्षा में समान आयतों को अलग-अलग गिनें।
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यदि (a+5) भुजा वाले वर्ग का कोना (25) है, तो पूरा विस्तार कौन-सा होगा?
If the corner of a square of side (a+5) is (25), which expansion is complete?
#corner-square
#visual-expansion
#identity
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A \(a^2+5a+25\)
B \(a^2+25a+10\)
C \(a^2+10a+25\)
D \(a^2+10a+5\)
Explanation opens after your attempt
Correct Answer
C. \(a^2+10a+25\)
Step 1
Concept
Two (5a) strips combine to make (10a). In exams, do not omit the middle term with corner (25).
Step 2
Why this answer is correct
The correct answer is C. \(a^2+10a+25\). Two (5a) strips combine to make (10a). In exams, do not omit the middle term with corner (25).
Step 3
Exam Tip
दो (5a) पट्टियाँ मिलकर (10a) बनाती हैं। परीक्षा में कोने (25) के साथ मध्य पद न छोड़ें।
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एक वर्ग की भुजा (m-3 ) है। बड़े \(m^2\) वर्ग से दो पट्टियाँ हटाने और कोना वापस जोड़ने पर कौन-सा क्षेत्रफल मिलेगा?
A square has side (m-3 ). After removing two strips from the large \(m^2\) square and adding the corner back, which area is obtained?
#subtraction-model
#square-identity
#visual
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A \(m^2-3m+9\)
B \(m^2+6m+9\)
C \(m^2-9m+6\)
D \(m^2-6m+9\)
Explanation opens after your attempt
Correct Answer
D. \(m^2-6m+9\)
Step 1
Concept
Two (3m) strips are removed and the (9) corner is added. In exams, add back the corner in subtraction models.
Step 2
Why this answer is correct
The correct answer is D. \(m^2-6m+9\). Two (3m) strips are removed and the (9) corner is added. In exams, add back the corner in subtraction models.
Step 3
Exam Tip
दो (3m) पट्टियाँ घटती हैं और (9) कोना जुड़ता है। परीक्षा में घटाव वाले मॉडल में कोना वापस जोड़ें।
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एक आयत की भुजाएँ (p+4) और (p+7) हैं। क्षेत्रफल मॉडल से सरल रूप क्या होगा?
A rectangle has sides (p+4) and (p+7). What simplified form comes from the area model?
#rectangle-model
#product-expansion
#area
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A \(p^2+11p+28\)
B \(p^2+28p+11\)
C \(p^2+3p+28\)
D \(p^2+11p+11\)
Explanation opens after your attempt
Correct Answer
A. \(p^2+11p+28\)
Step 1
Concept
The parts are \(p^2\), (4p), (7p), and (28). In exams, add the linear terms.
Step 2
Why this answer is correct
The correct answer is A. \(p^2+11p+28\). The parts are \(p^2\), (4p), (7p), and (28). In exams, add the linear terms.
Step 3
Exam Tip
भाग \(p^2\), (4p), (7p) और (28) हैं। परीक्षा में रैखिक पद जोड़ें।
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यदि (r+8) और (r-8) वाली आयत बनाई जाए, तो कौन-सा परिणाम मिलेगा?
If a rectangle with sides (r+8) and (r-8) is made, what result is obtained?
#difference-of-squares
#rectangle
#visual
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A \(r^2+64\)
B \(r^2-64\)
C \(r^2-16r+64\)
D \(r^2+16r+64\)
Explanation opens after your attempt
Correct Answer
B. \(r^2-64\)
Step 1
Concept
This is a difference of squares model, so \(8^2=64\) is subtracted. In exams, identify ((r+8)(r-8)) directly.
Step 2
Why this answer is correct
The correct answer is B. \(r^2-64\). This is a difference of squares model, so \(8^2=64\) is subtracted. In exams, identify ((r+8)(r-8)) directly.
Step 3
Exam Tip
यह वर्गों के अंतर का मॉडल है इसलिए \(8^2=64\) घटता है। परीक्षा में ((r+8)(r-8)) को सीधे पहचानें।
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एक ग्रिड में \(x^2\), (9x), (2x) और (18) भाग हैं। इसे किन भुजाओं वाली आयत के रूप में देखा जा सकता है?
A grid has parts \(x^2\), (9x), (2x), and (18). It can be seen as a rectangle with which sides?
#grid-model
#factor-form
#area
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A (x+11) और (x+18) / (x+11) and (x+18)
B (x+9) और (x+9) / (x+9) and (x+9)
C (x+9) और (x+2) / (x+9) and (x+2)
D (x+18) और (x+2) / (x+18) and (x+2)
Explanation opens after your attempt
Correct Answer
C. (x+9) और (x+2) / (x+9) and (x+2)
Step 1
Concept
The strips are (9x) and (2x), and the corner is \(9\cdot2=18\). In exams, form sides from strip widths.
Step 2
Why this answer is correct
The correct answer is C. (x+9) और (x+2) / (x+9) and (x+2). The strips are (9x) and (2x), and the corner is \(9\cdot2=18\). In exams, form sides from strip widths.
Step 3
Exam Tip
पट्टियाँ (9x) और (2x) हैं तथा कोना \(9\cdot2=18\) है। परीक्षा में पट्टी की चौड़ाइयों से भुजाएँ बनाएं।
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एक (2x+5) भुजा वाले वर्ग का दृश्य मॉडल बनाया गया। सही विस्तार कौन-सा है?
A visual model is made for a square of side (2x+5). Which expansion is correct?
#coefficient-square
#visual-model
#identity
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A \(4x^2+10x+25\)
B \(4x^2+20x+25\)
C \(2x^2+20x+25\)
D \(4x^2+25x+20\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2+20x+25\)
Step 1
Concept
The combined middle area is \(2\cdot2x\cdot5=20x\). In exams, write the square of (2x) as \(4x^2\).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2+20x+25\). The combined middle area is \(2\cdot2x\cdot5=20x\). In exams, write the square of (2x) as \(4x^2\).
Step 3
Exam Tip
बीच का संयुक्त क्षेत्रफल \(2\cdot2x\cdot5=20x\) है। परीक्षा में (2x) का वर्ग \(4x^2\) लिखें।
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यदि (3a+1) भुजा वाले वर्ग में बड़ा भाग \(9a^2\) है, तो दोनों पट्टियों का कुल क्षेत्रफल क्या होगा?
If the large part in a square of side (3a+1) is \(9a^2\), what is the total area of both strips?
#middle-term
#visual-square
#area
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A (3a)
B (9a)
C (6a)
D (1)
Explanation opens after your attempt
Step 1
Concept
Both strips are (3a) and (3a), so the total is (6a). In exams, take equal strips twice.
Step 2
Why this answer is correct
The correct answer is C. (6a). Both strips are (3a) and (3a), so the total is (6a). In exams, take equal strips twice.
Step 3
Exam Tip
दोनों पट्टियाँ (3a) और (3a) हैं इसलिए कुल (6a) है। परीक्षा में समान पट्टियों को दो बार लें।
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एक मॉडल \(4b^2+12b+9\) को पूर्ण वर्ग दिखाता है। वर्ग की भुजा क्या होगी?
A model shows \(4b^2+12b+9\) as a perfect square. What will be the side of the square?
#perfect-square
#reverse-model
#visual
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A (4b+3)
B (2b+6)
C (2b-3)
D (2b+3)
Explanation opens after your attempt
Step 1
Concept
(4b-2 =(2b)2 ) and \(9=3^2\). In exams, confirm using the middle term (12b).
Step 2
Why this answer is correct
The correct answer is D. (2b+3). (4b-2 =(2b)2 ) and \(9=3^2\). In exams, confirm using the middle term (12b).
Step 3
Exam Tip
(4b-2 =(2b)2 ) और \(9=3^2\) है। परीक्षा में मध्य पद (12b) से पुष्टि करें।
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एक क्षेत्रफल मॉडल में \(z^2+16z+64\) है। छोटा कोना किस क्षेत्रफल का होगा?
An area model has \(z^2+16z+64\). What is the area of the small corner?
#constant-corner
#area-model
#square
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A (64)
B (16z)
C (8z)
D \(z^2\)
Explanation opens after your attempt
Step 1
Concept
The small corner is the constant square \(8^2=64\). In exams, treat the constant term as the corner area.
Step 2
Why this answer is correct
The correct answer is A. (64). The small corner is the constant square \(8^2=64\). In exams, treat the constant term as the corner area.
Step 3
Exam Tip
छोटा कोना स्थिर वर्ग \(8^2=64\) है। परीक्षा में स्थिर पद को कोने का क्षेत्रफल समझें।
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(n-5) भुजा वाले वर्ग में हटाई गई दो पट्टियों का कुल क्षेत्रफल क्या है?
In a square of side (n-5), what is the total area of the two removed strips?
#removed-strips
#minus-square
#visual
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A (5n)
B (10n)
C (25n)
D (25)
Explanation opens after your attempt
Step 1
Concept
The two strips are (5n) and (5n), so total (10n) is removed. In exams, add both removed parts.
Step 2
Why this answer is correct
The correct answer is B. (10n). The two strips are (5n) and (5n), so total (10n) is removed. In exams, add both removed parts.
Step 3
Exam Tip
दो पट्टियाँ (5n) और (5n) हैं इसलिए कुल (10n) घटता है। परीक्षा में दोनों हटे भाग जोड़ें।
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यदि (q-4) भुजा वाले वर्ग का अंतिम क्षेत्रफल चाहिए, तो सही विस्तार कौन-सा होगा?
If the final area of a square of side (q-4) is needed, which expansion is correct?
#minus-square
#visual-expansion
#identity
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A \(q^2-4q+16\)
B \(q^2+8q+16\)
C \(q^2-8q+16\)
D \(q^2-16q+8\)
Explanation opens after your attempt
Correct Answer
C. \(q^2-8q+16\)
Step 1
Concept
The middle term is \(-2\cdot q\cdot4=-8q\). In exams, count (4) in two strips.
Step 2
Why this answer is correct
The correct answer is C. \(q^2-8q+16\). The middle term is \(-2\cdot q\cdot4=-8q\). In exams, count (4) in two strips.
Step 3
Exam Tip
बीच का पद \(-2\cdot q\cdot4=-8q\) है। परीक्षा में (4) को दो पट्टियों में गिनें।
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एक आयत मॉडल में भुजाएँ (s+3) और (s-3 ) हैं। कौन-सा क्षेत्रफल सही है?
In a rectangle model, the sides are (s+3) and (s-3 ). Which area is correct?
#conjugate-rectangle
#difference-of-squares
#visual
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A \(s^2-9\)
B \(s^2+9\)
C \(s^2-6s+9\)
D \(s^2+6s+9\)
Explanation opens after your attempt
Correct Answer
A. \(s^2-9\)
Step 1
Concept
Equal and opposite (3s) strips cancel. In exams, identify the difference of squares model.
Step 2
Why this answer is correct
The correct answer is A. \(s^2-9\). Equal and opposite (3s) strips cancel. In exams, identify the difference of squares model.
Step 3
Exam Tip
समान और विपरीत (3s) पट्टियाँ कट जाती हैं। परीक्षा में वर्गों के अंतर का मॉडल पहचानें।
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क्षेत्रफल टाइलों में \(t^2+7t+12\) है। सही आयत भुजाएँ कौन-सी हैं?
Area tiles show \(t^2+7t+12\). Which rectangle sides are correct?
#tile-model
#factorisation
#rectangle
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A (t+1) और (t+12) / (t+1) and (t+12)
B (t+3) और (t+4) / (t+3) and (t+4)
C (t+2) और (t+6) / (t+2) and (t+6)
D (t+7) और (t+12) / (t+7) and (t+12)
Explanation opens after your attempt
Correct Answer
B. (t+3) और (t+4) / (t+3) and (t+4)
Step 1
Concept
(3+4=7) and \(3\cdot4=12\). In exams, match both sum and product.
Step 2
Why this answer is correct
The correct answer is B. (t+3) और (t+4) / (t+3) and (t+4). (3+4=7) and \(3\cdot4=12\). In exams, match both sum and product.
Step 3
Exam Tip
(3+4=7) और \(3\cdot4=12\) है। परीक्षा में योग और गुणनफल दोनों मिलाएँ।
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एक (u+9) वर्ग मॉडल में \(u^2\) और (81) दिख रहे हैं। कौन-सा भाग गायब है?
In a square model of (u+9), \(u^2\) and (81) are shown. Which part is missing?
#missing-term
#square-model
#visual
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A (9u)
B (18u)
C (81u)
D \(u^2+81\)
Explanation opens after your attempt
Step 1
Concept
Two (9u) strips are missing, so (18u) is needed. In exams, identify the missing middle term.
Step 2
Why this answer is correct
The correct answer is B. (18u). Two (9u) strips are missing, so (18u) is needed. In exams, identify the missing middle term.
Step 3
Exam Tip
दो (9u) पट्टियाँ गायब हैं इसलिए (18u) चाहिए। परीक्षा में गायब मध्य पद पहचानें।
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एक छात्र ने ( (x+6)2 ) को \(x^2+36\) लिखा। दृश्य मॉडल के अनुसार कौन-सा भाग छूटा?
A student wrote ( (x+6)2 ) as \(x^2+36\). According to the visual model, which part is missing?
#common-error
#missing-middle
#visual
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A (6x)
B (36x)
C (12x)
D (6)
Explanation opens after your attempt
Step 1
Concept
Two (6x) rectangles are missing. In exams, always write the middle term in square expansion.
Step 2
Why this answer is correct
The correct answer is C. (12x). Two (6x) rectangles are missing. In exams, always write the middle term in square expansion.
Step 3
Exam Tip
दो (6x) आयत छूट गए हैं। परीक्षा में वर्ग विस्तार में मध्य पद जरूर लिखें।
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यदि (a+b) वर्ग में \(a^2\) और \(b^2\) को अलग रंग दिया गया है, तो बाकी दो आयतों का क्षेत्रफल क्या होगा?
If \(a^2\) and \(b^2\) are colored separately in an (a+b) square, what is the area of the remaining two rectangles?
#mixed-rectangles
#binomial-square
#area
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A \(a^2+b^2\)
B (ab)
C (2ab)
D (a+b)
Explanation opens after your attempt
Step 1
Concept
The remaining two rectangles are (ab) and (ab). In exams, add both mixed parts.
Step 2
Why this answer is correct
The correct answer is C. (2ab). The remaining two rectangles are (ab) and (ab). In exams, add both mixed parts.
Step 3
Exam Tip
बाकी दो आयत (ab) और (ab) हैं। परीक्षा में दोनों मिश्रित भागों को जोड़ें।
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एक वर्ग मॉडल \(c^2-12c+36\) दिखाता है। इसकी भुजा क्या होगी?
A square model shows \(c^2-12c+36\). What will be its side?
#perfect-square
#minus-model
#visual
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A (c+6)
B (c-6)
C (c-12)
D (c+12)
Explanation opens after your attempt
Step 1
Concept
\(36=6^2\) and \(-12c=-2\cdot c\cdot6\). In exams, identify the subtractive side from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. (c-6). \(36=6^2\) and \(-12c=-2\cdot c\cdot6\). In exams, identify the subtractive side from the negative middle term.
Step 3
Exam Tip
\(36=6^2\) और \(-12c=-2\cdot c\cdot6\) है। परीक्षा में ऋण मध्य पद से घटाव वाली भुजा पहचानें।
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एक (4x+3) भुजा वाले वर्ग में छोटे कोने का क्षेत्रफल कितना होगा?
In a square of side (4x+3), what will be the area of the small corner?
#constant-corner
#coefficient-model
#square
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A \(16x^2\)
B (12x)
C (24x)
D (9)
Explanation opens after your attempt
Step 1
Concept
The small constant corner is \(3^2=9\). In exams, take the corner area as the square of the constant number.
Step 2
Why this answer is correct
The correct answer is D. (9). The small constant corner is \(3^2=9\). In exams, take the corner area as the square of the constant number.
Step 3
Exam Tip
छोटा स्थिर कोना \(3^2=9\) है। परीक्षा में कोने का क्षेत्रफल स्थिर संख्या के वर्ग से लें।
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(4x+3) भुजा वाले वर्ग में दोनों मिश्रित पट्टियों का कुल क्षेत्रफल क्या होगा?
In a square of side (4x+3), what is the total area of both mixed strips?
#mixed-strips
#visual-square
#area
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A (24x)
B (12x)
C \(16x^2\)
D (9x)
Explanation opens after your attempt
Step 1
Concept
Both strips are \(4x\cdot3\) and \(4x\cdot3\). In exams, double the mixed strips.
Step 2
Why this answer is correct
The correct answer is A. (24x). Both strips are \(4x\cdot3\) and \(4x\cdot3\). In exams, double the mixed strips.
Step 3
Exam Tip
दोनों पट्टियाँ \(4x\cdot3\) और \(4x\cdot3\) हैं। परीक्षा में मिश्रित पट्टियों को दोगुना करें।
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एक आयत की भुजाएँ (2x+1) और (x+5) हैं। क्षेत्रफल मॉडल का सही विस्तार क्या है?
A rectangle has sides (2x+1) and (x+5). What is the correct expansion of the area model?
#rectangle-expansion
#area-model
#product
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A \(2x^2+10x+5\)
B \(2x^2+11x+5\)
C \(2x^2+7x+5\)
D \(2x^2+5x+11\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2+11x+5\)
Step 1
Concept
The parts are \(2x^2\), (10x), (x), and (5). In exams, combine (10x+x=11x).
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+11x+5\). The parts are \(2x^2\), (10x), (x), and (5). In exams, combine (10x+x=11x).
Step 3
Exam Tip
भाग \(2x^2\), (10x), (x) और (5) हैं। परीक्षा में (10x+x=11x) करें।
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यदि (3y+2) और (y+4) से आयत बने, तो स्थिर कोना कितना होगा?
If a rectangle is formed by (3y+2) and (y+4), what will be the constant corner?
#constant-corner
#rectangle-model
#visual
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A (6)
B (8)
C (12)
D (2y)
Explanation opens after your attempt
Step 1
Concept
The constant corner is \(2\cdot4=8\). In exams, multiply only the constant parts.
Step 2
Why this answer is correct
The correct answer is B. (8). The constant corner is \(2\cdot4=8\). In exams, multiply only the constant parts.
Step 3
Exam Tip
स्थिर कोना \(2\cdot4=8\) है। परीक्षा में स्थिर भागों को ही गुणा करें।
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(3y+2) और (y+4) के आयत मॉडल में कुल (y) वाला पद क्या होगा?
In the rectangle model of (3y+2) and (y+4), what is the total (y)-term?
#linear-term
#rectangle-model
#area
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A (14y)
B (6y)
C (12y)
D (2y)
Explanation opens after your attempt
Step 1
Concept
The linear parts are (12y) and (2y), so the total is (14y). The correct expansion is \(3y^2+14y+8\).
Step 2
Why this answer is correct
The correct answer is C. (12y). The linear parts are (12y) and (2y), so the total is (14y). The correct expansion is \(3y^2+14y+8\).
Step 3
Exam Tip
रैखिक भाग (12y) और (2y) हैं इसलिए कुल (14y) होता है। सही विस्तार \(3y^2+14y+8\) है।
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एक दृश्य मॉडल में (x+10) और (x-10) की आयत है। कौन-सा भाग कट जाता है?
A visual model has a rectangle with (x+10) and (x-10). Which part cancels?
#cancellation
#difference-of-squares
#visual
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A (10x) और (-10x) / (10x) and (-10x)
B \(x^2\) और (-100) / \(x^2\) and (-100)
C (100) और (100) / (100) and (100)
D (x) और (10) / (x) and (10)
Explanation opens after your attempt
Correct Answer
A. (10x) और (-10x) / (10x) and (-10x)
Step 1
Concept
The equal but opposite (10x) parts cancel. In exams, the linear terms cancel in conjugate sides.
Step 2
Why this answer is correct
The correct answer is A. (10x) और (-10x) / (10x) and (-10x). The equal but opposite (10x) parts cancel. In exams, the linear terms cancel in conjugate sides.
Step 3
Exam Tip
समान पर विपरीत चिह्न वाले (10x) भाग कटते हैं। परीक्षा में संयुग्म भुजाओं में रैखिक पद कटता है।
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यदि (5a+2) भुजा वाले वर्ग का मॉडल बने, तो कुल क्षेत्रफल क्या होगा?
If a model is made for a square of side (5a+2), what will be the total area?
#coefficient-binomial
#visual-square
#area
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A \(25a^2+10a+4\)
B \(25a^2+20a+4\)
C \(5a^2+20a+4\)
D \(25a^2+20a+2\)
Explanation opens after your attempt
Correct Answer
B. \(25a^2+20a+4\)
Step 1
Concept
Two mixed strips of (5a) and (2) give total (20a). In exams, square with coefficients.
Step 2
Why this answer is correct
The correct answer is B. \(25a^2+20a+4\). Two mixed strips of (5a) and (2) give total (20a). In exams, square with coefficients.
Step 3
Exam Tip
(5a) और (2) की दो मिश्रित पट्टियाँ कुल (20a) देती हैं। परीक्षा में गुणांक सहित वर्ग करें।
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(2p-7) भुजा वाले वर्ग में कौन-सा विस्तार दृश्य मॉडल से सही है?
Which expansion is correct from the visual model of a square with side (2p-7)?
#minus-binomial
#visual-square
#identity
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A \(4p^2-14p+49\)
B \(4p^2+28p+49\)
C \(4p^2-28p+49\)
D \(2p^2-28p+49\)
Explanation opens after your attempt
Correct Answer
C. \(4p^2-28p+49\)
Step 1
Concept
The middle term is \(-2\cdot2p\cdot7=-28p\). In exams, include both removed strips.
Step 2
Why this answer is correct
The correct answer is C. \(4p^2-28p+49\). The middle term is \(-2\cdot2p\cdot7=-28p\). In exams, include both removed strips.
Step 3
Exam Tip
मध्य पद \(-2\cdot2p\cdot7=-28p\) है। परीक्षा में घटाई गई दोनों पट्टियों को शामिल करें।
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एक मॉडल \(x^2+17x+72\) को आयत के रूप में दिखाता है। कौन-सी भुजाएँ सही हैं?
A model shows \(x^2+17x+72\) as a rectangle. Which sides are correct?
#factorisation
#area-tiles
#rectangle
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A (x+8) और (x+9) / (x+8) and (x+9)
B (x+6) और (x+12) / (x+6) and (x+12)
C (x+4) और (x+18) / (x+4) and (x+18)
D (x+7) और (x+10) / (x+7) and (x+10)
Explanation opens after your attempt
Correct Answer
A. (x+8) और (x+9) / (x+8) and (x+9)
Step 1
Concept
(8+9=17) and \(8\cdot9=72\). In exams, check both constant widths.
Step 2
Why this answer is correct
The correct answer is A. (x+8) और (x+9) / (x+8) and (x+9). (8+9=17) and \(8\cdot9=72\). In exams, check both constant widths.
Step 3
Exam Tip
(8+9=17) और \(8\cdot9=72\) है। परीक्षा में दोनों स्थिर चौड़ाइयों को जाँचें।
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यदि \(v^2+20v+100\) का वर्ग मॉडल बनाया जाए, तो वर्ग की भुजा क्या होगी?
If a square model is made for \(v^2+20v+100\), what will be the side of the square?
#perfect-square
#reverse-visual
#area
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A (v+20)
B (v+5)
C (v+10)
D (v-10)
Explanation opens after your attempt
Step 1
Concept
\(100=10^2\) and \(20v=2\cdot v\cdot10\). In exams, take the square root of the constant square.
Step 2
Why this answer is correct
The correct answer is C. (v+10). \(100=10^2\) and \(20v=2\cdot v\cdot10\). In exams, take the square root of the constant square.
Step 3
Exam Tip
\(100=10^2\) और \(20v=2\cdot v\cdot10\) है। परीक्षा में स्थिर वर्ग का वर्गमूल लें।
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एक (k+3) वर्ग मॉडल में यदि दोनों पट्टियों का संयुक्त क्षेत्रफल (24) है, तो (k) का मान क्या होगा?
In a square model of (k+3), if the combined area of both strips is (24), what is the value of (k)?
#unknown-value
#strip-area
#visual
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Both strips together give (6k), and (6k=24). In exams, connect combined strips with the middle term.
Step 2
Why this answer is correct
The correct answer is B. (4). Both strips together give (6k), and (6k=24). In exams, connect combined strips with the middle term.
Step 3
Exam Tip
दोनों पट्टियाँ मिलकर (6k) देती हैं और (6k=24) है। परीक्षा में संयुक्त पट्टियों को मध्य पद से जोड़ें।
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यदि बाहरी वर्ग की भुजा (x+5) और अंदर के वर्ग की भुजा (x) है, तो सीमा क्षेत्रफल क्या होगा?
If the outer square has side (x+5) and the inner square has side (x), what is the border area?
#border-area
#square-difference
#visual
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A (10x+25)
B (5x+25)
C \(x^2+25\)
D (10x+5)
Explanation opens after your attempt
Correct Answer
A. (10x+25)
Step 1
Concept
The border area is ((x+5)2 -x-2 =10x+25). In exams, subtract the inner area from the outer area.
Step 2
Why this answer is correct
The correct answer is A. (10x+25). The border area is ((x+5)2 -x-2 =10x+25). In exams, subtract the inner area from the outer area.
Step 3
Exam Tip
सीमा क्षेत्रफल ((x+5)2 -x-2 =10x+25) है। परीक्षा में बाहरी क्षेत्र से अंदर का क्षेत्र घटाएँ।
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एक आयत मॉडल में (x+6) और (x+6) भुजाएँ हैं। यह किस विशेष मॉडल के बराबर है?
A rectangle model has sides (x+6) and (x+6). Which special model is it equal to?
#square-recognition
#rectangle-model
#visual
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A (x+12) भुजा वाला वर्ग / Square of side (x+12)
B (x+6) भुजा वाला वर्ग / Square of side (x+6)
C (x-6) भुजा वाला वर्ग / Square of side (x-6)
D (6x) भुजा वाला वर्ग / Square of side (6x)
Explanation opens after your attempt
Correct Answer
B. (x+6) भुजा वाला वर्ग / Square of side (x+6)
Step 1
Concept
Both sides are equal, so it is a square of side (x+6). In exams, treat equal sides as a square model.
Step 2
Why this answer is correct
The correct answer is B. (x+6) भुजा वाला वर्ग / Square of side (x+6). Both sides are equal, so it is a square of side (x+6). In exams, treat equal sides as a square model.
Step 3
Exam Tip
दोनों भुजाएँ समान हैं इसलिए यह (x+6) भुजा का वर्ग है। परीक्षा में समान भुजाओं को वर्ग मॉडल समझें।
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यदि (a+2b) भुजा वाले वर्ग का मॉडल बने, तो दोनों मिश्रित आयतों का कुल क्षेत्रफल क्या होगा?
If a model is made for a square of side (a+2b), what is the total area of both mixed rectangles?
#mixed-terms
#binomial-square
#visual
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A (2ab)
B (4ab)
C \(2b^2\)
D \(a^2+4b^2\)
Explanation opens after your attempt
Step 1
Concept
One mixed rectangle is (2ab), and there are two such rectangles. In exams, count the mixed rectangle twice.
Step 2
Why this answer is correct
The correct answer is B. (4ab). One mixed rectangle is (2ab), and there are two such rectangles. In exams, count the mixed rectangle twice.
Step 3
Exam Tip
एक मिश्रित आयत (2ab) है और ऐसे दो आयत होते हैं। परीक्षा में मिश्रित आयत को दो बार गिनें।
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(a+2b) भुजा वाले वर्ग में छोटे वर्ग का क्षेत्रफल क्या होगा?
In a square of side (a+2b), what is the area of the small square?
#small-square
#coefficient
#visual-model
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A \(2b^2\)
B \(4b^2\)
C (2ab)
D \(a^2\)
Explanation opens after your attempt
Correct Answer
B. \(4b^2\)
Step 1
Concept
The small square has side (2b), so its area is \(4b^2\). In exams, square the whole (2b).
Step 2
Why this answer is correct
The correct answer is B. \(4b^2\). The small square has side (2b), so its area is \(4b^2\). In exams, square the whole (2b).
Step 3
Exam Tip
छोटे वर्ग की भुजा (2b) है इसलिए क्षेत्रफल \(4b^2\) है। परीक्षा में (2b) को पूरा वर्ग करें।
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यदि (2a-b) भुजा वाले वर्ग का दृश्य मॉडल बने, तो विस्तार क्या होगा?
If a visual model is made for a square of side (2a-b), what will be the expansion?
#minus-square
#coefficients
#visual
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A \(4a^2-4ab+b^2\)
B \(4a^2-2ab+b^2\)
C \(2a^2-4ab+b^2\)
D \(4a^2+4ab+b^2\)
Explanation opens after your attempt
Correct Answer
A. \(4a^2-4ab+b^2\)
Step 1
Concept
The subtracted middle term is \(2\cdot2a\cdot b=4ab\). In exams, keep both the negative sign and coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(4a^2-4ab+b^2\). The subtracted middle term is \(2\cdot2a\cdot b=4ab\). In exams, keep both the negative sign and coefficient.
Step 3
Exam Tip
बीच का घटा पद \(2\cdot2a\cdot b=4ab\) है। परीक्षा में ऋण चिह्न और गुणांक दोनों रखें।
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एक आयत मॉडल (3x+2) और (3x-2) से बना है। क्षेत्रफल क्या होगा?
A rectangle model is formed by (3x+2) and (3x-2). What will be the area?
#difference-of-squares
#coefficient
#rectangle
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A \(9x^2+4\)
B \(9x^2-4\)
C \(3x^2-4\)
D \(9x^2-12x+4\)
Explanation opens after your attempt
Correct Answer
B. \(9x^2-4\)
Step 1
Concept
This is the visual model of ((3x)2 -22 ). In exams, middle terms cancel in conjugate sides.
Step 2
Why this answer is correct
The correct answer is B. \(9x^2-4\). This is the visual model of ((3x)2 -22 ). In exams, middle terms cancel in conjugate sides.
Step 3
Exam Tip
यह ((3x)2 -22 ) का दृश्य मॉडल है। परीक्षा में संयुग्म भुजाओं में बीच के पद कटते हैं।
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यदि \(x^2+6x+8\) का टाइल मॉडल आयत बनाता है, तो कौन-सी भुजाएँ सही हैं?
If the tile model of \(x^2+6x+8\) forms a rectangle, which sides are correct?
#tile-factorisation
#rectangle
#visual
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A (x+1) और (x+8) / (x+1) and (x+8)
B (x+2) और (x+4) / (x+2) and (x+4)
C (x+3) और (x+3) / (x+3) and (x+3)
D (x+6) और (x+8) / (x+6) and (x+8)
Explanation opens after your attempt
Correct Answer
B. (x+2) और (x+4) / (x+2) and (x+4)
Step 1
Concept
(2+4=6) and \(2\cdot4=8\). In exams, check both the corner and the strips.
Step 2
Why this answer is correct
The correct answer is B. (x+2) और (x+4) / (x+2) and (x+4). (2+4=6) and \(2\cdot4=8\). In exams, check both the corner and the strips.
Step 3
Exam Tip
(2+4=6) और \(2\cdot4=8\) है। परीक्षा में कोना और पट्टियाँ दोनों जाँचें।
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एक (x+1) वर्ग और एक (x-1) वर्ग के क्षेत्रफल का अंतर क्या होगा?
What is the difference between the areas of a square of side (x+1) and a square of side (x-1)?
#area-difference
#square-model
#visual
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A (2x)
B (4x)
C \(x^2-1\)
D (2)
Explanation opens after your attempt
Step 1
Concept
((x+1)2 -(x-1)2 =4x). In exams, apply the difference of squares quickly.
Step 2
Why this answer is correct
The correct answer is B. (4x). ((x+1)2 -(x-1)2 =4x). In exams, apply the difference of squares quickly.
Step 3
Exam Tip
((x+1)2 -(x-1)2 =4x) होता है। परीक्षा में वर्गों के अंतर को तेजी से लागू करें।
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यदि (x+4) वर्ग से (x) वर्ग हटाया जाए, तो कौन-सा दृश्य क्षेत्र बचेगा?
If an (x) square is removed from an (x+4) square, which visual area remains?
#border-model
#area-difference
#square
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A (8x+16)
B (4x+16)
C \(x^2+16\)
D (8x+4)
Explanation opens after your attempt
Correct Answer
A. (8x+16)
Step 1
Concept
The remaining area is ((x+4)2 -x-2 =8x+16). In exams, find border area using area difference.
Step 2
Why this answer is correct
The correct answer is A. (8x+16). The remaining area is ((x+4)2 -x-2 =8x+16). In exams, find border area using area difference.
Step 3
Exam Tip
बचा क्षेत्र ((x+4)2 -x-2 =8x+16) है। परीक्षा में सीमा क्षेत्र को क्षेत्रफल अंतर से निकालें।
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एक तीन-भाग वर्ग मॉडल में भुजा (a+b+c) है। केवल छोटे वर्गों का कुल क्षेत्रफल क्या होगा?
In a three-part square model, the side is (a+b+c). What is the total area of only the small squares?
#three-term-square
#small-squares
#visual
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A \(a^2+b^2+c^2\)
B (ab+bc+ca)
C (2ab+2bc+2ca)
D (a+b+c)
Explanation opens after your attempt
Correct Answer
A. \(a^2+b^2+c^2\)
Step 1
Concept
The small squares have sides (a), (b), and (c). In exams, distinguish square parts from rectangle parts.
Step 2
Why this answer is correct
The correct answer is A. \(a^2+b^2+c^2\). The small squares have sides (a), (b), and (c). In exams, distinguish square parts from rectangle parts.
Step 3
Exam Tip
छोटे वर्गों की भुजाएँ (a), (b) और (c) हैं। परीक्षा में वर्ग और आयत भाग अलग पहचानें।
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(a+b+c) वर्ग मॉडल में मिश्रित आयतों का कुल क्षेत्रफल क्या होगा?
In the square model of (a+b+c), what is the total area of the mixed rectangles?
#mixed-rectangles
#three-term-square
#area
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A (ab+bc+ca)
B (2ab+2bc+2ca)
C \(a^2+b^2+c^2\)
D (3abc)
Explanation opens after your attempt
Correct Answer
B. (2ab+2bc+2ca)
Step 1
Concept
Each pair has two rectangles, so the total is (2ab+2bc+2ca). In exams, count each mixed pair twice.
Step 2
Why this answer is correct
The correct answer is B. (2ab+2bc+2ca). Each pair has two rectangles, so the total is (2ab+2bc+2ca). In exams, count each mixed pair twice.
Step 3
Exam Tip
हर जोड़ी के दो आयत होते हैं इसलिए कुल (2ab+2bc+2ca) है। परीक्षा में हर मिश्रित जोड़ी दो बार गिनें।
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एक मॉडल \(x^2-5x-14\) को चिह्नित टाइलों से आयत बनाता है। कौन-सी भुजाएँ सही हैं?
A model forms a rectangle from \(x^2-5x-14\) using signed tiles. Which sides are correct?
#signed-tiles
#factorisation
#visual
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A (x-7) और (x+2) / (x-7) and (x+2)
B (x+7) और (x-2) / (x+7) and (x-2)
C (x-14) और (x+1) / (x-14) and (x+1)
D (x-5) और (x-14) / (x-5) and (x-14)
Explanation opens after your attempt
Correct Answer
A. (x-7) और (x+2) / (x-7) and (x+2)
Step 1
Concept
(-7+2=-5) and ((-7)\cdot2=-14). In exams, check sum and product with signs.
Step 2
Why this answer is correct
The correct answer is A. (x-7) और (x+2) / (x-7) and (x+2). (-7+2=-5) and ((-7)\cdot2=-14). In exams, check sum and product with signs.
Step 3
Exam Tip
(-7+2=-5) और ((-7)\cdot2=-14) है। परीक्षा में चिह्नों के साथ योग और गुणनफल जाँचें।
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एक चिह्नित आयत मॉडल (x+3) और (x-5) से बनता है। कुल क्षेत्रफल क्या होगा?
A signed rectangle model is formed by (x+3) and (x-5). What will be the total area?
#signed-area
#rectangle-expansion
#visual
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A \(x^2-2x-15\)
B \(x^2+8x-15\)
C \(x^2-15x-2\)
D \(x^2-8x+15\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2x-15\)
Step 1
Concept
The parts are \(x^2\), (-5x), (3x), and (-15). In exams, combine (-5x+3x=-2x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2x-15\). The parts are \(x^2\), (-5x), (3x), and (-15). In exams, combine (-5x+3x=-2x).
Step 3
Exam Tip
भाग \(x^2\), (-5x), (3x) और (-15) हैं। परीक्षा में (-5x+3x=-2x) करें।
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यदि (x-2) और (x-9) की चिह्नित आयत बने, तो स्थिर कोना क्या होगा?
If a signed rectangle of (x-2) and (x-9) is made, what will be the constant corner?
#signed-corner
#rectangle-model
#area
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A (18)
B (-18)
C (11)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The constant part is ((-2)(-9)=18). In exams, product of two negative parts is positive.
Step 2
Why this answer is correct
The correct answer is A. (18). The constant part is ((-2)(-9)=18). In exams, product of two negative parts is positive.
Step 3
Exam Tip
स्थिर भाग ((-2)(-9)=18) है। परीक्षा में दो ऋणात्मक भागों का गुणन धनात्मक होता है।
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एक वर्ग मॉडल में \(9x^2-30x+25\) है। वर्ग की भुजा क्या होगी?
A square model has \(9x^2-30x+25\). What will be the side of the square?
#reverse-square
#minus-model
#visual
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A (3x+5)
B (9x-5)
C (3x-5)
D (x-15)
Explanation opens after your attempt
Step 1
Concept
(9x-2 =(3x)2 ), \(25=5^2\), and the middle term is negative. In exams, check \(-2\cdot3x\cdot5\).
Step 2
Why this answer is correct
The correct answer is C. (3x-5). (9x-2 =(3x)2 ), \(25=5^2\), and the middle term is negative. In exams, check \(-2\cdot3x\cdot5\).
Step 3
Exam Tip
(9x-2 =(3x)2 ), \(25=5^2\) और मध्य पद ऋणात्मक है। परीक्षा में \(-2\cdot3x\cdot5\) जाँचें।
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यदि ( (x+7)2 ) से ( (x+2)2 ) घटाया जाए, तो दृश्य अंतर क्या होगा?
If ( (x+2)2 ) is subtracted from ( (x+7)2 ), what is the visual difference?
#square-difference
#visual-area
#comparison
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A (10x+45)
B (5x+49)
C (9x+25)
D (5x+45)
Explanation opens after your attempt
Correct Answer
A. (10x+45)
Step 1
Concept
The difference is (x-2 +14x+49-\(x^2+4x+4\)=10x+45). In exams, cancel equal \(x^2\).
Step 2
Why this answer is correct
The correct answer is A. (10x+45). The difference is (x-2 +14x+49-\(x^2+4x+4\)=10x+45). In exams, cancel equal \(x^2\).
Step 3
Exam Tip
अंतर (x-2 +14x+49-\(x^2+4x+4\)=10x+45) है। परीक्षा में समान \(x^2\) काट दें।
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एक (x+5) वर्ग और (x+1) वर्ग के क्षेत्रफल मॉडलों का अंतर किसके बराबर है?
What is the difference between the area models of squares (x+5) and (x+1)?
#area-comparison
#square-model
#identity
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A (8x+24)
B (4x+24)
C (6x+20)
D (10x+26)
Explanation opens after your attempt
Correct Answer
A. (8x+24)
Step 1
Concept
((x+5)2 -(x+1)2 =8x+24). In exams, you may also use (\(A^2-B^2\)=(A+B)(A-B)).
Step 2
Why this answer is correct
The correct answer is A. (8x+24). ((x+5)2 -(x+1)2 =8x+24). In exams, you may also use (\(A^2-B^2\)=(A+B)(A-B)).
Step 3
Exam Tip
((x+5)2 -(x+1)2 =8x+24) है। परीक्षा में (\(A^2-B^2\)) को ((A+B)(A-B)) भी मान सकते हैं।
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एक (x+3) वर्ग मॉडल में \(x^2\) और दो (3x) पट्टियाँ हैं। यदि कोना नहीं जोड़ा गया, तो क्षेत्रफल क्या होगा?
In a square model of (x+3), there are \(x^2\) and two (3x) strips. If the corner is not added, what will be the area?
#incomplete-square
#visual-model
#area
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A \(x^2+3x\)
B \(x^2+6x\)
C \(x^2+9\)
D \(x^2+6x+9\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6x\)
Step 1
Concept
Without the corner, only \(x^2+3x+3x\) remains. In exams, the model becomes a complete square only after adding the corner.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6x\). Without the corner, only \(x^2+3x+3x\) remains. In exams, the model becomes a complete square only after adding the corner.
Step 3
Exam Tip
बिना कोने के केवल \(x^2+3x+3x\) बचेगा। परीक्षा में कोना जोड़ने पर ही पूर्ण वर्ग बनता है।
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यदि \(x^2+10x\) को वर्ग पूरा करने के दृश्य मॉडल से दिखाना हो, तो कौन-सा कोना जोड़ना होगा?
If \(x^2+10x\) is to be shown by completing a square visually, which corner must be added?
#complete-square
#corner-area
#visual
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A (5)
B (10)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
(10x) comes from two (5x) strips, so the corner must be \(5^2=25\). In exams, take half of the middle coefficient and square it.
Step 2
Why this answer is correct
The correct answer is D. (25). (10x) comes from two (5x) strips, so the corner must be \(5^2=25\). In exams, take half of the middle coefficient and square it.
Step 3
Exam Tip
(10x) दो (5x) पट्टियों से बनता है, इसलिए कोना \(5^2=25\) चाहिए। परीक्षा में मध्य पद का आधा लेकर वर्ग करें।
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एक दृश्य मॉडल में \(x^2-6x\) को वर्ग पूरा करना है। कौन-सा कोना जोड़कर पूर्ण वर्ग मिलेगा?
In a visual model, \(x^2-6x\) must be completed into a square. Which corner should be added to get a perfect square?
#complete-square
#minus-model
#visual
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A (6)
B (9)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
(-6x) comes from two (-3x) strips, so the corner \(3^2=9\) is needed. In exams, square half the coefficient.
Step 2
Why this answer is correct
The correct answer is B. (9). (-6x) comes from two (-3x) strips, so the corner \(3^2=9\) is needed. In exams, square half the coefficient.
Step 3
Exam Tip
(-6x) दो (-3x) पट्टियों से बनता है, इसलिए कोना \(3^2=9\) चाहिए। परीक्षा में आधे गुणांक का वर्ग लें।
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