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
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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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
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 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
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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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
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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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
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 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
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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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
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 \(x^2+6x+8\) 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
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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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
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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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
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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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
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 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
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 (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
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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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
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 (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
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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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
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 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
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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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
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 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
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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(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
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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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
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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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
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 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
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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यदि दो वर्गों की भुजाएँ (x+k) और (x-k) हों, तो उनके क्षेत्रफल मॉडलों का अंतर किसके बराबर होगा?
If two squares have sides (x+k) and (x-k), what will the difference of their area models be?
#difference-of-area-models
#general-identity
#visual
A (4kx)
B (2kx)
C \(x^2-k^2\)
D \(2x^2+2k^2\)
Explanation opens after your attempt
Step 1
Concept
The difference of expansions is (x-2 +2kx+k-2 -\(x^2-2kx+k^2\)=4kx). In exams, cancel equal square terms.
Step 2
Why this answer is correct
The correct answer is A. (4kx). The difference of expansions is (x-2 +2kx+k-2 -\(x^2-2kx+k^2\)=4kx). In exams, cancel equal square terms.
Step 3
Exam Tip
विस्तारों का अंतर (x-2 +2kx+k-2 -\(x^2-2kx+k^2\)=4kx) है। परीक्षा में समान वर्ग पद काटें।
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एक (a-b) वर्ग मॉडल में \(a^2\) से दो (ab) पट्टियाँ हटाने के बाद कौन-सी त्रुटि हो सकती है?
In a square model of (a-b), after removing two (ab) strips from \(a^2\), what error may occur?
#common-error
#subtraction-square
#visual
A (a+b) को भुजा मानना / Taking (a+b) as the side
B \(a^2\) को दो बार जोड़ना / Adding \(a^2\) twice
C (ab) को धनात्मक रखना / Keeping (ab) positive
D \(b^2\) को वापस न जोड़ना / Not adding \(b^2\) back
Explanation opens after your attempt
Correct Answer
D. \(b^2\) को वापस न जोड़ना / Not adding \(b^2\) back
Step 1
Concept
The corner \(b^2\) is removed twice, so it must be added back. In exams, correct over-subtraction.
Step 2
Why this answer is correct
The correct answer is D. \(b^2\) को वापस न जोड़ना / Not adding \(b^2\) back. The corner \(b^2\) is removed twice, so it must be added back. In exams, correct over-subtraction.
Step 3
Exam Tip
कोने का \(b^2\) भाग दो बार हट जाता है, इसलिए उसे वापस जोड़ना जरूरी है। परीक्षा में अधिक घटाव ठीक करें।
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यदि \(x^2-12x+35\) की टाइलों से आयत बने, तो कौन-सी भुजाएँ मॉडल को सही बनाती हैं?
If tiles of \(x^2-12x+35\) form a rectangle, which sides make the model correct?
#signed-factorisation
#area-tiles
#visual
A (x-1) और (x-35) / (x-1) and (x-35)
B (x+5) और (x+7) / (x+5) and (x+7)
C (x-5) और (x-7) / (x-5) and (x-7)
D (x+12) और (x-35) / (x+12) and (x-35)
Explanation opens after your attempt
Correct Answer
C. (x-5) और (x-7) / (x-5) and (x-7)
Step 1
Concept
(-5+(-7)=-12) and ((-5)(-7)=35). In exams, product of two negative constants is positive.
Step 2
Why this answer is correct
The correct answer is C. (x-5) और (x-7) / (x-5) and (x-7). (-5+(-7)=-12) and ((-5)(-7)=35). In exams, product of two negative constants is positive.
Step 3
Exam Tip
(-5+(-7)=-12) और ((-5)(-7)=35) है। परीक्षा में दो ऋणात्मक स्थिर भागों का गुणन धनात्मक होता है।
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यदि ( (2x+7)2 ) के दृश्य मॉडल में \(4x^2\) और (49) पहले से हैं, तो छूटा पट्टी क्षेत्रफल क्या है?
If in the visual model of ( (2x+7)2 ), \(4x^2\) and (49) are already present, what is the missing strip area?
#missing-strips
#coefficient-square
#visual
A (28x)
B (14x)
C (7x)
D (21x)
Explanation opens after your attempt
Step 1
Concept
The total of two mixed rectangles is \(2\cdot2x\cdot7=28x\). In exams, find middle area with coefficients.
Step 2
Why this answer is correct
The correct answer is A. (28x). The total of two mixed rectangles is \(2\cdot2x\cdot7=28x\). In exams, find middle area with coefficients.
Step 3
Exam Tip
दो मिश्रित आयतों का कुल \(2\cdot2x\cdot7=28x\) है। परीक्षा में गुणांक सहित मध्य क्षेत्रफल निकालें।
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यदि ( (a+b+c)2 ) के दृश्य मॉडल में \(a^2+b^2+c^2\) और (2ab+2bc) दिख रहा है, तो कौन-सा भाग छूटा है?
If the model of ( (a+b+c)2 ) shows \(a^2+b^2+c^2\) and (2ab+2bc), which part is missing?
#missing-part
#three-term-square
#visual
A (ab+bc+ca)
B (abc)
C (2ca)
D (a+b+c)
Explanation opens after your attempt
Step 1
Concept
Among the three mixed pairs, the (ca) pair also appears twice. In exams, complete all pair combinations.
Step 2
Why this answer is correct
The correct answer is C. (2ca). Among the three mixed pairs, the (ca) pair also appears twice. In exams, complete all pair combinations.
Step 3
Exam Tip
तीन मिश्रित जोड़ियों में (ca) जोड़ी भी दो बार आती है। परीक्षा में सभी जोड़ी संयोजन पूरे करें।
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एक (x+y) वर्ग मॉडल में यदि दो (xy) आयतों को मिलाकर एक लंबा आयत बनाया जाए, तो उसका क्षेत्रफल क्या होगा?
In a square model of (x+y), if two (xy) rectangles are combined into one long rectangle, what is its area?
#rearranged-rectangles
#area-conservation
#visual
A (xy)
B (2xy)
C \(x^2+y^2\)
D (2x+2y)
Explanation opens after your attempt
Step 1
Concept
Combining two equal rectangles gives (2xy). In exams, rearrangement does not change area.
Step 2
Why this answer is correct
The correct answer is B. (2xy). Combining two equal rectangles gives (2xy). In exams, rearrangement does not change area.
Step 3
Exam Tip
दो समान आयतों को जोड़ने से (2xy) बनता है। परीक्षा में पुनर्व्यवस्था से क्षेत्रफल नहीं बदलता।
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एक जाली मॉडल में कुल क्षेत्रफल \(x^2+2kx+k^2\) है। यह कब पूर्ण वर्ग का दृश्य मॉडल होगा?
A grid model has total area \(x^2+2kx+k^2\). When will it be a visual model of a perfect square?
#general-model
#perfect-square
#visual
A कभी नहीं / Never
B केवल जब (k=0) / Only when (k=0)
C केवल जब (x=k) / Only when (x=k)
D हमेशा, भुजा (x+k) / Always, side (x+k)
Explanation opens after your attempt
Correct Answer
D. हमेशा, भुजा (x+k) / Always, side (x+k)
Step 1
Concept
It directly shows the four parts of ( (x+k)2 ). In exams, view (2kx) as two (kx) strips.
Step 2
Why this answer is correct
The correct answer is D. हमेशा, भुजा (x+k) / Always, side (x+k). It directly shows the four parts of ( (x+k)2 ). In exams, view (2kx) as two (kx) strips.
Step 3
Exam Tip
यह सीधे ( (x+k)2 ) के चार भाग दिखाता है। परीक्षा में (2kx) को दो (kx) पट्टियों के रूप में देखें।
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