क्षेत्रफल चित्र में भुजा (a+1) वाले वर्ग को चार भागों में बाँटा गया है। कुल क्षेत्रफल कौन सा होगा?
In an area diagram, a square of side (a+1) is divided into four parts. What will be the total area?
#area model
#square identity
#visual algebra
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A \(a^2+2a+1\)
B \(a^2+a+1\)
C \(a^2+1\)
D \(2a^2+1\)
Explanation opens after your attempt
Correct Answer
A. \(a^2+2a+1\)
Step 1
Concept
The side is (a+1), so the area is ((a+1)2 ). Exam tip: check the sum of all four parts.
Step 2
Why this answer is correct
The correct answer is A. \(a^2+2a+1\). The side is (a+1), so the area is ((a+1)2 ). Exam tip: check the sum of all four parts.
Step 3
Exam Tip
भुजा (a+1) है इसलिए क्षेत्रफल ((a+1)2 ) होगा। परीक्षा में चारों भागों का योग देखें।
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एक टाइल मॉडल में \(x^2\), दो (3x) आयत और (9) का छोटा वर्ग है। पूरा वर्ग किस भुजा का है?
A tile model has \(x^2\), two (3x) rectangles, and a small square (9). What is the side of the complete square?
#algebra tiles
#perfect square
#side
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A (x+9)
B (x+3)
C (x-3)
D (3x+1)
Explanation opens after your attempt
Step 1
Concept
Two (3x) rectangles and \(9=3^2\) form ((x+3)2 ). Exam tip: the small square tells the side part.
Step 2
Why this answer is correct
The correct answer is B. (x+3). Two (3x) rectangles and \(9=3^2\) form ((x+3)2 ). Exam tip: the small square tells the side part.
Step 3
Exam Tip
दो (3x) आयत और \(9=3^2\) मिलकर ((x+3)2 ) बनाते हैं। परीक्षा में छोटा वर्ग भुजा बताता है।
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भुजाएँ (p+4) और (p-4) वाले आयत का दृश्य मॉडल किस क्षेत्रफल को दिखाता है?
What area is shown by the visual model of a rectangle with sides (p+4) and (p-4)?
#difference of squares
#rectangle model
#visual identity
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A \(p^2+16\)
B \(p^2+8p+16\)
C \(p^2-16\)
D \(p^2-8p+16\)
Explanation opens after your attempt
Correct Answer
C. \(p^2-16\)
Step 1
Concept
This is the product of sum and difference, so it gives \(p^2-16\). Exam tip: identify \(4^2\).
Step 2
Why this answer is correct
The correct answer is C. \(p^2-16\). This is the product of sum and difference, so it gives \(p^2-16\). Exam tip: identify \(4^2\).
Step 3
Exam Tip
यह योग और अंतर का गुणन है इसलिए \(p^2-16\) मिलता है। परीक्षा में \(4^2\) को पहचानें।
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यदि वर्ग मॉडल में बाहरी भुजा (y+6) है, तो छोटा कोना कौन सा होगा?
If the outer side in a square model is (y+6), what will be the small corner?
#corner square
#area model
#constant term
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A (6y)
B (12y)
C \(y^2\)
D (36)
Explanation opens after your attempt
Step 1
Concept
The small corner has side (6), so its area is (36). Exam tip: square the constant part.
Step 2
Why this answer is correct
The correct answer is D. (36). The small corner has side (6), so its area is (36). Exam tip: square the constant part.
Step 3
Exam Tip
छोटे कोने की भुजा (6) है इसलिए उसका क्षेत्रफल (36) है। परीक्षा में स्थिर भाग का वर्ग लें।
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भुजा (m+2) वाले वर्ग में दो समान आयतों का कुल क्षेत्रफल क्या होगा?
In a square of side (m+2), what will be the total area of the two equal rectangles?
#middle term
#rectangle parts
#square model
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A (4m)
B (2m)
C \(m^2\)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of the two rectangles is \(2\cdot m\cdot 2=4m\). Exam tip: add both middle rectangles.
Step 2
Why this answer is correct
The correct answer is A. (4m). The sum of the two rectangles is \(2\cdot m\cdot 2=4m\). Exam tip: add both middle rectangles.
Step 3
Exam Tip
दो आयतों का योग \(2\cdot m\cdot 2=4m\) होता है। परीक्षा में बीच के दोनों आयत जोड़ें।
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एक चित्र में बड़ा वर्ग \(b^2\) है और उससे छोटा वर्ग \(c^2\) हटाया गया है। बचा क्षेत्रफल किससे बने आयत के बराबर है?
A diagram shows a big square \(b^2\) and a small square \(c^2\) removed from it. The remaining area equals a rectangle made by which sides?
#cut model
#difference of squares
#area
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A (b+c) और (b-c) / (b+c) and (b-c)
B (b) और (c) / (b) and (c)
C (b+c) और (c) / (b+c) and (c)
D (b-c) और (c) / (b-c) and (c)
Explanation opens after your attempt
Correct Answer
A. (b+c) और (b-c) / (b+c) and (b-c)
Step 1
Concept
The remaining area is (b-2 -c-2 =(b+c)(b-c)). Exam tip: connect difference of squares with a rectangle.
Step 2
Why this answer is correct
The correct answer is A. (b+c) और (b-c) / (b+c) and (b-c). The remaining area is (b-2 -c-2 =(b+c)(b-c)). Exam tip: connect difference of squares with a rectangle.
Step 3
Exam Tip
बचा क्षेत्रफल (b-2 -c-2 =(b+c)(b-c)) है। परीक्षा में वर्गों के अंतर को आयत से जोड़ें।
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यदि \(x^2+4x+4\) को वर्गाकार टाइलों से बनाया जाए, तो बाहरी भुजा क्या होगी?
If \(x^2+4x+4\) is made using square tiles, what will be the outer side?
#tile model
#complete square
#visual identity
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A (x+4)
B (x+2)
C (x-2)
D (2x+2)
Explanation opens after your attempt
Step 1
Concept
Since \(4=2^2\) and the middle term is (4x), the side is (x+2). Exam tip: check the square root of the last term.
Step 2
Why this answer is correct
The correct answer is B. (x+2). Since \(4=2^2\) and the middle term is (4x), the side is (x+2). Exam tip: check the square root of the last term.
Step 3
Exam Tip
\(4=2^2\) और बीच का पद (4x) है इसलिए भुजा (x+2) है। परीक्षा में अंतिम पद का वर्गमूल देखें।
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आयत मॉडल में ((r+3)(r+5)) को फैलाने पर (r) वाले पदों का योग क्या होगा?
In the rectangle model of ((r+3)(r+5)), what will be the sum of the (r)-terms?
#rectangle multiplication
#like terms
#area split
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A (3r)
B (5r)
C (8r)
D (15r)
Explanation opens after your attempt
Step 1
Concept
The like terms (3r) and (5r) combine to make (8r). Exam tip: add like terms.
Step 2
Why this answer is correct
The correct answer is C. (8r). The like terms (3r) and (5r) combine to make (8r). Exam tip: add like terms.
Step 3
Exam Tip
(3r) और (5r) जैसे पद मिलकर (8r) बनाते हैं। परीक्षा में समान पद जोड़ें।
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भुजा (n-5) वाले वर्ग के मॉडल में अंतिम पद क्या होगा?
In the model of a square with side (n-5), what will be the last term?
#square of difference
#last term
#visual model
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A (25)
B (-25)
C (5n)
D (-10n)
Explanation opens after your attempt
Step 1
Concept
((-5)2 =25), so the last term is positive. Exam tip: keep the square of a negative number positive.
Step 2
Why this answer is correct
The correct answer is A. (25). ((-5)2 =25), so the last term is positive. Exam tip: keep the square of a negative number positive.
Step 3
Exam Tip
((-5)2 =25) होता है इसलिए अंतिम पद धनात्मक है। परीक्षा में ऋण संख्या का वर्ग धनात्मक रखें।
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एक वर्ग मॉडल में \(u^2\), (10u) और (25) भाग मिलते हैं। यह किस भुजा का वर्ग है?
A square model has parts \(u^2\), (10u), and (25). It is the square of which side?
#perfect square
#area parts
#side identification
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A (u+10)
B (u+25)
C (u+5)
D (u-5)
Explanation opens after your attempt
Step 1
Concept
\(25=5^2\) and \(2\cdot u\cdot 5=10u\). Exam tip: identify the perfect square form.
Step 2
Why this answer is correct
The correct answer is C. (u+5). \(25=5^2\) and \(2\cdot u\cdot 5=10u\). Exam tip: identify the perfect square form.
Step 3
Exam Tip
\(25=5^2\) और \(2\cdot u\cdot 5=10u\) है। परीक्षा में पूर्ण वर्ग रूप पहचानें।
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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
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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 भुजा (a+b) वाले वर्ग में \(a^2\) और \(b^2\) वर्गों के अलावा दो समान भाग हैं, तो वे भाग किस आकार के हैं?
If a square of side (a+b) has two equal parts besides the \(a^2\) and \(b^2\) squares, what shape are those parts?
#ab rectangles
#square model
#visual proof
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A भुजाएँ (a) और (b) वाले आयत / Rectangles with sides (a) and (b)
B भुजा (a) वाले वर्ग / Squares with side (a)
C भुजा (b) वाले वर्ग / Squares with side (b)
D भुजा (a+b) वाले वर्ग / Squares with side (a+b)
Explanation opens after your attempt
Correct Answer
A. भुजाएँ (a) और (b) वाले आयत / Rectangles with sides (a) and (b)
Step 1
Concept
Both equal parts have area (ab). Exam tip: understand the middle term (2ab) through two rectangles.
Step 2
Why this answer is correct
The correct answer is A. भुजाएँ (a) और (b) वाले आयत / Rectangles with sides (a) and (b). Both equal parts have area (ab). Exam tip: understand the middle term (2ab) through two rectangles.
Step 3
Exam Tip
दोनों समान भागों का क्षेत्रफल (ab) होता है। परीक्षा में बीच के पद (2ab) को दो आयतों से समझें।
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दृश्य मॉडल में \(k^2-16\) को किस रूप में लिखा जा सकता है?
In a visual model, \(k^2-16\) can be written in which form?
#difference of squares
#factor form
#visual model
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A ((k+4)(k-4))
B ((k+8)(k-8))
C ((k+4)2 )
D ((k-4)2 )
Explanation opens after your attempt
Correct Answer
A. ((k+4)(k-4))
Step 1
Concept
Since \(16=4^2\), (k-2 -16=(k+4)(k-4)). Exam tip: identify difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ((k+4)(k-4)). Since \(16=4^2\), (k-2 -16=(k+4)(k-4)). Exam tip: identify difference of squares.
Step 3
Exam Tip
\(16=4^2\) है इसलिए (k-2 -16=(k+4)(k-4)) होता है। परीक्षा में वर्गों का अंतर पहचानें।
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एक वर्ग मॉडल की भुजा (2x+1) है। उसका कुल क्षेत्रफल कौन सा होगा?
A square model has side (2x+1). What will be its total area?
#binomial square
#coefficient
#area model
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A \(2x^2+2x+1\)
B \(4x^2+4x+1\)
C \(4x^2+1\)
D \(2x^2+4x+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2+4x+1\)
Step 1
Concept
((2x+1)2 =4x-2 +4x+1). Exam tip: write the square of (2x) as \(4x^2\).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2+4x+1\). ((2x+1)2 =4x-2 +4x+1). Exam tip: write the square of (2x) as \(4x^2\).
Step 3
Exam Tip
((2x+1)2 =4x-2 +4x+1) होता है। परीक्षा में (2x) का वर्ग \(4x^2\) लिखें।
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यदि आयत मॉडल की एक भुजा (t) और दूसरी (t+7) है, तो क्षेत्रफल क्या होगा?
If one side of a rectangle model is (t) and the other is (t+7), what will be the area?
#distributive model
#rectangle area
#visual algebra
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A \(t^2+7t\)
B \(t^2+7\)
C \(7t^2\)
D (t+7t)
Explanation opens after your attempt
Correct Answer
A. \(t^2+7t\)
Step 1
Concept
The area is (t(t+7)=t-2 +7t). Exam tip: multiply both sides of the rectangle.
Step 2
Why this answer is correct
The correct answer is A. \(t^2+7t\). The area is (t(t+7)=t-2 +7t). Exam tip: multiply both sides of the rectangle.
Step 3
Exam Tip
क्षेत्रफल (t(t+7)=t-2 +7t) है। परीक्षा में आयत की दोनों भुजाएँ गुणा करें।
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एक क्षेत्रफल चित्र में ((a-b)2 ) दिखाने के लिए कौन सा मध्य पद आता है?
In an area diagram showing ((a-b)2 ), which middle term appears?
#square of difference
#middle term
#sign
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A (2ab)
B (-2ab)
C \(ab^2\)
D \(a^2b\)
Explanation opens after your attempt
Step 1
Concept
((a-b)2 =a-2 -2ab+b-2 ). Exam tip: keep the middle term negative in a subtraction model.
Step 2
Why this answer is correct
The correct answer is B. (-2ab). ((a-b)2 =a-2 -2ab+b-2 ). Exam tip: keep the middle term negative in a subtraction model.
Step 3
Exam Tip
((a-b)2 =a-2 -2ab+b-2 ) होता है। परीक्षा में घटाव वाले मॉडल में मध्य पद ऋणात्मक रखें।
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भुजा (q+8) वाले वर्ग में दो समान आयतों का क्षेत्रफल अलग अलग कितना होगा?
In a square of side (q+8), what is the area of each of the two equal rectangles?
#equal rectangles
#area model
#binomial square
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A (8q)
B (16q)
C (64)
D \(q^2\)
Explanation opens after your attempt
Step 1
Concept
Each rectangle has sides (q) and (8), so its area is (8q). Exam tip: distinguish one rectangle from both rectangles.
Step 2
Why this answer is correct
The correct answer is A. (8q). Each rectangle has sides (q) and (8), so its area is (8q). Exam tip: distinguish one rectangle from both rectangles.
Step 3
Exam Tip
प्रत्येक आयत की भुजाएँ (q) और (8) हैं इसलिए क्षेत्रफल (8q) है। परीक्षा में एक आयत और दोनों आयतों में अंतर रखें।
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यदि \(z^2-12z+36\) का दृश्य वर्ग बनाया जाए, तो उसकी भुजा क्या होगी?
If a visual square is made for \(z^2-12z+36\), what will be its side?
#negative square
#visual model
#side
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A (z+6)
B (z-6)
C (z-12)
D (z+36)
Explanation opens after your attempt
Step 1
Concept
Since \(36=6^2\) and the middle term is (-12z), the side is (z-6). Exam tip: identify the sign from the middle term.
Step 2
Why this answer is correct
The correct answer is B. (z-6). Since \(36=6^2\) and the middle term is (-12z), the side is (z-6). Exam tip: identify the sign from the middle term.
Step 3
Exam Tip
\(36=6^2\) और मध्य पद (-12z) है इसलिए भुजा (z-6) है। परीक्षा में चिन्ह मध्य पद से पहचानें।
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एक आयत मॉडल में ((x+1)(x+9)) है। कुल क्षेत्रफल में स्थिर पद क्या होगा?
A rectangle model represents ((x+1)(x+9)). What will be the constant term in the total area?
#constant term
#rectangle model
#area
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A (1)
B (9)
C (10)
D (90)
Explanation opens after your attempt
Step 1
Concept
The constant term is \(1\cdot 9=9\). Exam tip: treat the small corner rectangle as the constant term.
Step 2
Why this answer is correct
The correct answer is B. (9). The constant term is \(1\cdot 9=9\). Exam tip: treat the small corner rectangle as the constant term.
Step 3
Exam Tip
स्थिर पद \(1\cdot 9=9\) है। परीक्षा में कोने के छोटे आयत को स्थिर पद मानें।
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भुजाएँ (a+2) और (a-2) वाले आयत में मध्य पद क्यों नहीं बचता?
Why does the middle term not remain in a rectangle with sides (a+2) and (a-2)?
#cancellation
#sum difference
#rectangle model
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A क्योंकि (2a) और (-2a) कट जाते हैं / Because (2a) and (-2a) cancel
B क्योंकि \(a^2\) शून्य हो जाता है / Because \(a^2\) becomes zero
C क्योंकि (4) जुड़ जाता है / Because (4) is added
D क्योंकि भुजाएँ बराबर नहीं हैं / Because the sides are not equal
Explanation opens after your attempt
Correct Answer
A. क्योंकि (2a) और (-2a) कट जाते हैं / Because (2a) and (-2a) cancel
Step 1
Concept
In product of sum and difference, equal middle terms cancel with opposite signs. Exam tip: identify the cancelling terms.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (2a) और (-2a) कट जाते हैं / Because (2a) and (-2a) cancel. In product of sum and difference, equal middle terms cancel with opposite signs. Exam tip: identify the cancelling terms.
Step 3
Exam Tip
योग और अंतर के गुणन में समान मध्य पद विपरीत चिन्हों से कटते हैं। परीक्षा में कटने वाले पद पहचानें।
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यदि वर्ग मॉडल का कुल क्षेत्रफल \(x^2+14x+49\) है, तो छोटे कोने की भुजा क्या है?
If the total area of a square model is \(x^2+14x+49\), what is the side of the small corner?
#corner side
#perfect square
#area model
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A (14)
B (49)
C (7)
D (21)
Explanation opens after your attempt
Step 1
Concept
The small corner area is (49), so its side is (7). Exam tip: take the square root of the area.
Step 2
Why this answer is correct
The correct answer is C. (7). The small corner area is (49), so its side is (7). Exam tip: take the square root of the area.
Step 3
Exam Tip
छोटे कोने का क्षेत्रफल (49) है इसलिए उसकी भुजा (7) है। परीक्षा में क्षेत्रफल का वर्गमूल लें।
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एक मॉडल में \(s^2-25\) बचा क्षेत्रफल है। यह किस बड़े और छोटे वर्ग का अंतर हो सकता है?
In a model, the remaining area is \(s^2-25\). It can be the difference of which big and small squares?
#visual removal
#difference of squares
#side
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A भुजाएँ (s) और (5) वाले वर्ग / Squares with sides (s) and (5)
B भुजाएँ (s) और (25) वाले वर्ग / Squares with sides (s) and (25)
C भुजाएँ (s+5) और (s-5 ) वाले वर्ग / Squares with sides (s+5) and (s-5 )
D भुजाएँ (5s) और (s) वाले वर्ग / Squares with sides (5s) and (s)
Explanation opens after your attempt
Correct Answer
A. भुजाएँ (s) और (5) वाले वर्ग / Squares with sides (s) and (5)
Step 1
Concept
Since \(25=5^2\), it is the difference of squares with sides (s) and (5). Exam tip: identify the side of the removed square.
Step 2
Why this answer is correct
The correct answer is A. भुजाएँ (s) और (5) वाले वर्ग / Squares with sides (s) and (5). Since \(25=5^2\), it is the difference of squares with sides (s) and (5). Exam tip: identify the side of the removed square.
Step 3
Exam Tip
\(25=5^2\) है इसलिए यह भुजा (s) और (5) वाले वर्गों का अंतर है। परीक्षा में घटाए गए वर्ग की भुजा पहचानें।
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भुजा (3x+2) वाले वर्ग में छोटे कोने का क्षेत्रफल क्या है?
In a square with side (3x+2), what is the area of the small corner?
#small corner
#coefficient model
#square area
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A (3x)
B (6x)
C (4)
D \(9x^2\)
Explanation opens after your attempt
Step 1
Concept
The small corner has side (2), so its area is (4). Exam tip: square the constant part separately.
Step 2
Why this answer is correct
The correct answer is C. (4). The small corner has side (2), so its area is (4). Exam tip: square the constant part separately.
Step 3
Exam Tip
छोटे कोने की भुजा (2) है इसलिए क्षेत्रफल (4) है। परीक्षा में स्थिर भाग को अलग वर्ग करें।
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क्षेत्रफल मॉडल में ((x+4)2 ) का कुल मध्य भाग कौन सा है?
In an area model, what is the total middle part of ((x+4)2 )?
#middle part
#area model
#binomial square
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A (4x)
B (8x)
C (16x)
D (16)
Explanation opens after your attempt
Step 1
Concept
The total middle part is \(2\cdot x\cdot 4=8x\). Exam tip: add the two equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. (8x). The total middle part is \(2\cdot x\cdot 4=8x\). Exam tip: add the two equal rectangles.
Step 3
Exam Tip
कुल मध्य भाग \(2\cdot x\cdot 4=8x\) है। परीक्षा में दो समान आयतों का योग करें।
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यदि किसी वर्ग का दृश्य विस्तार \(w^2+6w+9\) है, तो बाहरी भुजा कौन सी होगी?
If the visual expansion of a square is \(w^2+6w+9\), what will be the outer side?
#visual expansion
#outer side
#perfect square
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A (w+6)
B (w+3)
C (w-3)
D (w+9)
Explanation opens after your attempt
Step 1
Concept
This is the expansion of ((w+3)2 ). Exam tip: see (9) as \(3^2\).
Step 2
Why this answer is correct
The correct answer is B. (w+3). This is the expansion of ((w+3)2 ). Exam tip: see (9) as \(3^2\).
Step 3
Exam Tip
यह ((w+3)2 ) का विस्तार है। परीक्षा में (9) को \(3^2\) की तरह देखें।
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एक आयत में लंबाई (2a+1) और चौड़ाई (a) है। क्षेत्रफल मॉडल का विस्तार क्या होगा?
A rectangle has length (2a+1) and breadth (a). What is the expansion of its area model?
#rectangle area
#distributive law
#visual algebra
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A \(2a^2+a\)
B \(2a^2+1\)
C (3a+1)
D \(2a+a^2\)
Explanation opens after your attempt
Correct Answer
A. \(2a^2+a\)
Step 1
Concept
(a(2a+1)=2a-2 +a). Exam tip: multiply one side by both parts of the other side.
Step 2
Why this answer is correct
The correct answer is A. \(2a^2+a\). (a(2a+1)=2a-2 +a). Exam tip: multiply one side by both parts of the other side.
Step 3
Exam Tip
(a(2a+1)=2a-2 +a) होता है। परीक्षा में एक भुजा को दोनों भागों से गुणा करें।
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भुजा (x-2) वाले वर्ग में मध्य भाग का कुल क्षेत्रफल क्या होगा?
In a square with side (x-2), what will be the total area of the middle part?
#negative middle
#subtraction square
#visual model
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A (4x)
B (-4x)
C (2x)
D (-2x)
Explanation opens after your attempt
Step 1
Concept
In ((x-2)2 ), the middle part is \(2\cdot x\cdot -2=-4x\). Exam tip: keep the sign of the subtraction part.
Step 2
Why this answer is correct
The correct answer is B. (-4x). In ((x-2)2 ), the middle part is \(2\cdot x\cdot -2=-4x\). Exam tip: keep the sign of the subtraction part.
Step 3
Exam Tip
((x-2)2 ) में मध्य भाग \(2\cdot x\cdot -2=-4x\) है। परीक्षा में घटाव वाले भाग का चिन्ह रखें।
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वर्गों के अंतर के मॉडल में यदि बड़े वर्ग की भुजा (9) और छोटे की भुजा (2) है, तो बचा क्षेत्रफल क्या होगा?
In a difference of squares model, if the big square has side (9) and the small square has side (2), what is the remaining area?
#numeric model
#difference of squares
#remaining area
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A (77)
B (81)
C (79)
D (85)
Explanation opens after your attempt
Step 1
Concept
The remaining area is \(9^2-2^2=81-4=77\). Exam tip: find the areas of both squares first.
Step 2
Why this answer is correct
The correct answer is A. (77). The remaining area is \(9^2-2^2=81-4=77\). Exam tip: find the areas of both squares first.
Step 3
Exam Tip
बचा क्षेत्रफल \(9^2-2^2=81-4=77\) है। परीक्षा में पहले दोनों वर्गों का क्षेत्रफल निकालें।
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एक वर्ग मॉडल में \(v^2+16v+64\) दिखता है। कौन सा कथन सही है?
A square model shows \(v^2+16v+64\). Which statement is correct?
#perfect square
#outer side
#area model
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A बाहरी भुजा (v+8) है / The outer side is (v+8)
B बाहरी भुजा (v+16) है / The outer side is (v+16)
C छोटे कोने की भुजा (16) है / The small corner side is (16)
D मध्य पद (8v) है / The middle term is (8v)
Explanation opens after your attempt
Correct Answer
A. बाहरी भुजा (v+8) है / The outer side is (v+8)
Step 1
Concept
\(64=8^2\) and \(2\cdot v\cdot 8=16v\). Exam tip: check both conditions.
Step 2
Why this answer is correct
The correct answer is A. बाहरी भुजा (v+8) है / The outer side is (v+8). \(64=8^2\) and \(2\cdot v\cdot 8=16v\). Exam tip: check both conditions.
Step 3
Exam Tip
\(64=8^2\) और \(2\cdot v\cdot 8=16v\) है। परीक्षा में दोनों शर्तें जाँचें।
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यदि \(a^2-b^2\) मॉडल को आयत में सजाया जाए, तो आयत का क्षेत्रफल किसके बराबर रहेगा?
If the \(a^2-b^2\) model is rearranged into a rectangle, what will the rectangle area remain equal to?
#rearrangement
#area preservation
#difference of squares
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A \(a^2+b^2\)
B (2ab)
C \(a^2-b^2\)
D (a+b)
Explanation opens after your attempt
Correct Answer
C. \(a^2-b^2\)
Step 1
Concept
Rearrangement changes the shape but keeps the area the same. Exam tip: area is preserved in rearrangement.
Step 2
Why this answer is correct
The correct answer is C. \(a^2-b^2\). Rearrangement changes the shape but keeps the area the same. Exam tip: area is preserved in rearrangement.
Step 3
Exam Tip
कटाकर सजाने से आकार बदलता है पर क्षेत्रफल वही रहता है। परीक्षा में पुनर्व्यवस्था में क्षेत्रफल सुरक्षित रहता है।
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भुजा (a+3b) वाले वर्ग में \(b^2\) वाले छोटे वर्ग का क्षेत्रफल कौन सा होगा?
In a square of side (a+3b), what will be the area of the small square containing \(b^2\)?
#coefficient square
#small square
#visual model
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A \(3b^2\)
B (6ab)
C \(9b^2\)
D \(a^2\)
Explanation opens after your attempt
Correct Answer
C. \(9b^2\)
Step 1
Concept
The small part has side (3b), so its area is \(9b^2\). Exam tip: square the coefficient too.
Step 2
Why this answer is correct
The correct answer is C. \(9b^2\). The small part has side (3b), so its area is \(9b^2\). Exam tip: square the coefficient too.
Step 3
Exam Tip
छोटे भाग की भुजा (3b) है इसलिए क्षेत्रफल \(9b^2\) है। परीक्षा में गुणांक का भी वर्ग करें।
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एक आयत मॉडल में ((x+5)(x+5)) दिखाया गया है। यह किस प्रकार का दृश्य मॉडल है?
A rectangle model shows ((x+5)(x+5)). What type of visual model is this?
#square model
#equal sides
#visual identity
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A वर्ग का मॉडल / Square model
B वर्गों के अंतर का मॉडल / Difference of squares model
C केवल रेखा मॉडल / Line model
D त्रिभुज मॉडल / Triangle model
Explanation opens after your attempt
Correct Answer
A. वर्ग का मॉडल / Square model
Step 1
Concept
Both sides are equal, so it is a square model of side (x+5). Exam tip: identify a square from equal sides.
Step 2
Why this answer is correct
The correct answer is A. वर्ग का मॉडल / Square model. Both sides are equal, so it is a square model of side (x+5). Exam tip: identify a square from equal sides.
Step 3
Exam Tip
दोनों भुजाएँ समान हैं इसलिए यह भुजा (x+5) वाले वर्ग का मॉडल है। परीक्षा में समान भुजाएँ देखकर वर्ग पहचानें।
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यदि चित्र में \(x^2\) वर्ग से (4x) की दो पट्टियाँ हटती हैं और (16) वापस जुड़ता है, तो कौन सा वर्ग बनता है?
If a diagram removes two strips of (4x) from an \(x^2\) square and adds back (16), which square is formed?
#strip removal
#square of difference
#visual proof
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A ((x+4)2 )
B ((x-4)2 )
C \(x^2-16\)
D \(x^2+16\)
Explanation opens after your attempt
Correct Answer
B. ((x-4)2 )
Step 1
Concept
This is the subtraction model of ((x-4)2 =x-2 -8x+16). Exam tip: understand the two strips as total (8x).
Step 2
Why this answer is correct
The correct answer is B. ((x-4)2 ). This is the subtraction model of ((x-4)2 =x-2 -8x+16). Exam tip: understand the two strips as total (8x).
Step 3
Exam Tip
यह ((x-4)2 =x-2 -8x+16) का घटाव मॉडल है। परीक्षा में दो पट्टियों का कुल (8x) समझें।
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भुजाएँ (x+3) और (x+4) वाले आयत में (x) वाले दो भाग कौन से होंगे?
In a rectangle with sides (x+3) and (x+4), what will be the two (x)-parts?
#rectangle parts
#area split
#like terms
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A (3x) और (4x) / (3x) and (4x)
B \(x^2\) और (12) / \(x^2\) and (12)
C (7x) और (12) / (7x) and (12)
D (x+3) और (x+4) / (x+3) and (x+4)
Explanation opens after your attempt
Correct Answer
A. (3x) और (4x) / (3x) and (4x)
Step 1
Concept
The four parts include (3x) and (4x). Exam tip: divide the rectangle into four regions.
Step 2
Why this answer is correct
The correct answer is A. (3x) और (4x) / (3x) and (4x). The four parts include (3x) and (4x). Exam tip: divide the rectangle into four regions.
Step 3
Exam Tip
चार भागों में (3x) और (4x) जैसे पद आते हैं। परीक्षा में आयत को चार क्षेत्रों में बाँटें।
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दृश्य मॉडल में \(a^2+2ab+b^2\) को किस एक क्षेत्रफल के रूप में पढ़ा जा सकता है?
In a visual model, \(a^2+2ab+b^2\) can be read as which single area?
#sum of parts
#whole square
#visual proof
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A ((a-b)2 )
B \(a^2-b^2\)
C ((a+b)2 )
D (ab)
Explanation opens after your attempt
Correct Answer
C. ((a+b)2 )
Step 1
Concept
It is the area of the whole square with side (a+b). Exam tip: match the sum of parts with the outer side.
Step 2
Why this answer is correct
The correct answer is C. ((a+b)2 ). It is the area of the whole square with side (a+b). Exam tip: match the sum of parts with the outer side.
Step 3
Exam Tip
यह भुजा (a+b) वाले पूरे वर्ग का क्षेत्रफल है। परीक्षा में भागों के योग को बाहरी भुजा से मिलाएँ।
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यदि \(x^2+2xy+y^2\) को क्षेत्रफल मॉडल से समझाया जाए, तो बाहरी भुजा क्या होगी?
If \(x^2+2xy+y^2\) is explained by an area model, what will be the outer side?
#xy rectangles
#outer side
#square identity
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A (x-y)
B (x+y)
C (2x+y)
D (x+2y)
Explanation opens after your attempt
Step 1
Concept
This is the expansion of ((x+y)2 ), so the outer side is (x+y). Exam tip: look for two (xy) rectangles.
Step 2
Why this answer is correct
The correct answer is B. (x+y). This is the expansion of ((x+y)2 ), so the outer side is (x+y). Exam tip: look for two (xy) rectangles.
Step 3
Exam Tip
यह ((x+y)2 ) का विस्तार है इसलिए बाहरी भुजा (x+y) है। परीक्षा में दो (xy) आयत देखें।
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एक आयत मॉडल में कुल क्षेत्रफल \(x^2+11x+30\) है। कौन सी भुजाएँ सही हो सकती हैं?
A rectangle model has total area \(x^2+11x+30\). Which sides can be correct?
#factor rectangle
#area model
#quadratic
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A (x+5) और (x+6) / (x+5) and (x+6)
B (x+3) और (x+10) / (x+3) and (x+10)
C (x+2) और (x+15) / (x+2) and (x+15)
D (x+1) और (x+30) / (x+1) and (x+30)
Explanation opens after your attempt
Correct Answer
A. (x+5) और (x+6) / (x+5) and (x+6)
Step 1
Concept
\(5\cdot 6=30\) and (5+6=11). Exam tip: check both constant product and middle sum.
Step 2
Why this answer is correct
The correct answer is A. (x+5) और (x+6) / (x+5) and (x+6). \(5\cdot 6=30\) and (5+6=11). Exam tip: check both constant product and middle sum.
Step 3
Exam Tip
\(5\cdot 6=30\) और (5+6=11) है। परीक्षा में स्थिर गुणन और मध्य योग दोनों जाँचें।
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यदि भुजा (g-1 ) वाले वर्ग का मॉडल बने, तो कुल क्षेत्रफल क्या होगा?
If a model of a square with side (g-1 ) is made, what will be the total area?
#square of difference
#area model
#visual algebra
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A \(g^2-1\)
B \(g^2+2g+1\)
C \(g^2-2g+1\)
D \(g^2-g+1\)
Explanation opens after your attempt
Correct Answer
C. \(g^2-2g+1\)
Step 1
Concept
((g-1 )2 =g-2 -2g+1). Exam tip: remember the two removed strips of (1).
Step 2
Why this answer is correct
The correct answer is C. \(g^2-2g+1\). ((g-1 )2 =g-2 -2g+1). Exam tip: remember the two removed strips of (1).
Step 3
Exam Tip
((g-1 )2 =g-2 -2g+1) होता है। परीक्षा में (1) की दो घटाई गई पट्टियाँ याद रखें।
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भुजा (2a+3) वाले वर्ग में बड़े वर्गाकार भाग का क्षेत्रफल क्या होगा?
In a square with side (2a+3), what will be the area of the large square part?
#large square
#coefficient square
#visual model
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A \(2a^2\)
B \(4a^2\)
C (6a)
D (9)
Explanation opens after your attempt
Correct Answer
B. \(4a^2\)
Step 1
Concept
The large square part has side (2a), so its area is \(4a^2\). Exam tip: square the whole term (2a).
Step 2
Why this answer is correct
The correct answer is B. \(4a^2\). The large square part has side (2a), so its area is \(4a^2\). Exam tip: square the whole term (2a).
Step 3
Exam Tip
बड़े वर्गाकार भाग की भुजा (2a) है इसलिए क्षेत्रफल \(4a^2\) है। परीक्षा में पूरे पद (2a) का वर्ग करें।
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किस क्षेत्रफल मॉडल में बाहरी भुजा (x+10) और छोटे कोने का क्षेत्रफल (100) होगा?
Which area model has outer side (x+10) and small corner area (100)?
#outer side
#corner area
#square model
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A ((x+10)2 )
B ((x-10)2 )
C \(x^2-100\)
D (10x)
Explanation opens after your attempt
Correct Answer
A. ((x+10)2 )
Step 1
Concept
In a square of side (x+10), the small corner area is \(10^2=100\). Exam tip: identify the model from the outer side.
Step 2
Why this answer is correct
The correct answer is A. ((x+10)2 ). In a square of side (x+10), the small corner area is \(10^2=100\). Exam tip: identify the model from the outer side.
Step 3
Exam Tip
भुजा (x+10) वाले वर्ग में छोटे कोने का क्षेत्रफल \(10^2=100\) होता है। परीक्षा में बाहरी भुजा से मॉडल पहचानें।
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यदि \(x^2-9\) के दृश्य मॉडल में छोटा वर्ग हटाया गया है, तो छोटे वर्ग की भुजा क्या है?
If a small square is removed in the visual model of \(x^2-9\), what is the side of the small square?
#removed square
#difference of squares
#side
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A (9)
B (3)
C (x-3)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
Since \(9=3^2\), the side of the removed small square is (3). Exam tip: take the square root of the removed area.
Step 2
Why this answer is correct
The correct answer is B. (3). Since \(9=3^2\), the side of the removed small square is (3). Exam tip: take the square root of the removed area.
Step 3
Exam Tip
\(9=3^2\) है इसलिए हटाए गए छोटे वर्ग की भुजा (3) है। परीक्षा में हटे हुए क्षेत्रफल का वर्गमूल लें।
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एक वर्ग मॉडल में \(x^2\) और (25) कोने हैं। पूर्ण वर्ग बनने के लिए कुल मध्य पद क्या होना चाहिए?
A square model has corner parts \(x^2\) and (25). What should the total middle term be to make a perfect square?
#missing middle
#complete square
#area tiles
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A (5x)
B (10x)
C (25x)
D (50x)
Explanation opens after your attempt
Step 1
Concept
Since \(25=5^2\), the total middle term is \(2\cdot x\cdot 5=10x\). Exam tip: add both equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. (10x). Since \(25=5^2\), the total middle term is \(2\cdot x\cdot 5=10x\). Exam tip: add both equal rectangles.
Step 3
Exam Tip
\(25=5^2\) है इसलिए कुल मध्य पद \(2\cdot x\cdot 5=10x\) होगा। परीक्षा में दोनों बराबर आयत जोड़ें।
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भुजाएँ (h+6) और (h-6) वाले आयत का क्षेत्रफल कौन सा है?
What is the area of a rectangle with sides (h+6) and (h-6)?
#rectangle model
#sum difference
#identity
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A \(h^2-36\)
B \(h^2+36\)
C \(h^2-12h+36\)
D \(h^2+12h+36\)
Explanation opens after your attempt
Correct Answer
A. \(h^2-36\)
Step 1
Concept
((h+6)(h-6)=h-2 -36). Exam tip: quickly identify product of sum and difference.
Step 2
Why this answer is correct
The correct answer is A. \(h^2-36\). ((h+6)(h-6)=h-2 -36). Exam tip: quickly identify product of sum and difference.
Step 3
Exam Tip
((h+6)(h-6)=h-2 -36) है। परीक्षा में योग और अंतर का गुणन तुरंत पहचानें।
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यदि वर्ग मॉडल में \(x^2+20x+100\) दिखता है, तो दो समान आयतों में प्रत्येक का क्षेत्रफल क्या है?
If a square model shows \(x^2+20x+100\), what is the area of each of the two equal rectangles?
#equal rectangles
#middle term
#perfect square
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A (20x)
B (10x)
C (100x)
D (5x)
Explanation opens after your attempt
Step 1
Concept
The total middle term is (20x), so each rectangle is (10x). Exam tip: divide the total middle term into two equal parts.
Step 2
Why this answer is correct
The correct answer is B. (10x). The total middle term is (20x), so each rectangle is (10x). Exam tip: divide the total middle term into two equal parts.
Step 3
Exam Tip
कुल मध्य पद (20x) है इसलिए प्रत्येक आयत (10x) है। परीक्षा में कुल मध्य पद को दो बराबर भागों में बाँटें।
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एक आयत का दृश्य मॉडल \(x^2+13x+40\) देता है। छोटे कोने के लिए कौन सा गुणन सही है?
A visual rectangle model gives \(x^2+13x+40\). Which multiplication is correct for the small corner?
#corner product
#factor model
#visual rectangle
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A \(5\cdot 8=40\)
B \(4\cdot 10=13\)
C \(13\cdot 40=x\)
D \(1\cdot 40=13\)
Explanation opens after your attempt
Correct Answer
A. \(5\cdot 8=40\)
Step 1
Concept
The numbers (5) and (8) have product (40) and sum (13). Exam tip: match the corner and middle term together.
Step 2
Why this answer is correct
The correct answer is A. \(5\cdot 8=40\). The numbers (5) and (8) have product (40) and sum (13). Exam tip: match the corner and middle term together.
Step 3
Exam Tip
(5) और (8) का गुणन (40) और योग (13) है। परीक्षा में कोना और मध्य पद साथ मिलाएँ।
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यदि (a+b) भुजा वाले वर्ग का कुल क्षेत्रफल \(a^2+2ab+b^2\) है, तो \(a^2\) भाग किससे आता है?
If the total area of a square with side (a+b) is \(a^2+2ab+b^2\), where does the \(a^2\) part come from?
#a square
#area partition
#visual identity
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A भुजा (a) वाले वर्ग से / From a square of side (a)
B भुजा (b) वाले वर्ग से / From a square of side (b)
C दो (ab) आयतों से / From two (ab) rectangles
D बाहरी परिमाप से / From outer perimeter
Explanation opens after your attempt
Correct Answer
A. भुजा (a) वाले वर्ग से / From a square of side (a)
Step 1
Concept
The \(a^2\) part is the area of a small square of side (a). Exam tip: identify the shape for each term.
Step 2
Why this answer is correct
The correct answer is A. भुजा (a) वाले वर्ग से / From a square of side (a). The \(a^2\) part is the area of a small square of side (a). Exam tip: identify the shape for each term.
Step 3
Exam Tip
\(a^2\) भाग भुजा (a) वाले छोटे वर्ग का क्षेत्रफल है। परीक्षा में हर पद का आकार पहचानें।
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भुजा (x+2y) वाले वर्ग में संयुक्त मध्य पद क्या होगा?
In a square of side (x+2y), what will be the combined middle term?
#middle term
#binomial square
#visual area
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A (2xy)
B (4xy)
C \(2y^2\)
D \(4y^2\)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot x\cdot 2y=4xy\). Exam tip: treat the second part (2y) as a whole.
Step 2
Why this answer is correct
The correct answer is B. (4xy). The middle term is \(2\cdot x\cdot 2y=4xy\). Exam tip: treat the second part (2y) as a whole.
Step 3
Exam Tip
मध्य पद \(2\cdot x\cdot 2y=4xy\) है। परीक्षा में दूसरे भाग (2y) को पूरा मानें।
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यदि ((x-7)2 ) का क्षेत्रफल मॉडल बनाया जाए, तो विस्तार कौन सा होगा?
If an area model of ((x-7)2 ) is made, what will be the expansion?
#square of difference
#expansion
#area model
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A \(x^2-14x+49\)
B \(x^2+14x+49\)
C \(x^2-49\)
D \(x^2-7x+49\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-14x+49\)
Step 1
Concept
In ((x-7)2 ), the middle term is (-14x) and the last term is (49). Exam tip: remember \(2\cdot 7\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-14x+49\). In ((x-7)2 ), the middle term is (-14x) and the last term is (49). Exam tip: remember \(2\cdot 7\).
Step 3
Exam Tip
((x-7)2 ) में बीच का पद (-14x) और अंतिम पद (49) है। परीक्षा में \(2\cdot 7\) याद रखें।
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किस मॉडल में \(x^2\) से \(y^2\) हटाकर बचा भाग ((x+y)(x-y)) के बराबर दिखता है?
In which model does removing \(y^2\) from \(x^2\) show the remaining part equal to ((x+y)(x-y))?
#difference of squares
#cut and paste
#visual proof
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A वर्गों के अंतर का मॉडल / Difference of squares model
B योग के वर्ग का मॉडल / Square of sum model
C घटाव के वर्ग का मॉडल / Square of difference model
D आयत के परिमाप का मॉडल / Rectangle perimeter model
Explanation opens after your attempt
Correct Answer
A. वर्गों के अंतर का मॉडल / Difference of squares model
Step 1
Concept
\(x^2-y^2\) can be cut and rearranged into a ((x+y)(x-y)) rectangle. Exam tip: observe the removed square.
Step 2
Why this answer is correct
The correct answer is A. वर्गों के अंतर का मॉडल / Difference of squares model. \(x^2-y^2\) can be cut and rearranged into a ((x+y)(x-y)) rectangle. Exam tip: observe the removed square.
Step 3
Exam Tip
\(x^2-y^2\) को काटकर ((x+y)(x-y)) आयत बनाया जा सकता है। परीक्षा में हटाए गए वर्ग को देखें।
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एक वर्ग मॉडल में भुजा (c+d) है। बाहरी सीमा से क्षेत्रफल और अंदर के भागों से क्षेत्रफल क्यों बराबर होंगे?
A square model has side (c+d). Why will the area from the outer boundary and the area from inner parts be equal?
#visual proof
#same area
#square partition
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A क्योंकि दोनों उसी एक वर्ग का क्षेत्रफल बताते हैं / Because both describe the area of the same square
B क्योंकि दोनों अलग आकृतियाँ हैं / Because both are different figures
C क्योंकि परिमाप और क्षेत्रफल हमेशा समान होते हैं / Because perimeter and area are always equal
D क्योंकि अंदर के भागों का क्षेत्रफल शून्य है / Because the inner parts have zero area
Explanation opens after your attempt
Correct Answer
A. क्योंकि दोनों उसी एक वर्ग का क्षेत्रफल बताते हैं / Because both describe the area of the same square
Step 1
Concept
Reading the same square from outside and from parts gives equal area. Exam tip: this is the main idea of visual proof.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि दोनों उसी एक वर्ग का क्षेत्रफल बताते हैं / Because both describe the area of the same square. Reading the same square from outside and from parts gives equal area. Exam tip: this is the main idea of visual proof.
Step 3
Exam Tip
एक ही वर्ग को बाहर से और भागों से पढ़ने पर समान क्षेत्रफल मिलता है। परीक्षा में यही दृश्य प्रमाण का मुख्य विचार है।
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