पहचान ( (a+b)2 ) का सही विस्तार क्या है?
What is the correct expansion of the identity ( (a+b)2 )?
#algebraic identities
#square identity
#binomial
A \(a^2+b^2\) / only square terms
B \(a^2+2ab+b^2\) / correct expansion
C \(a^2-ab+b^2\) / middle term negative
D (2a+2b) / double of terms
Explanation opens after your attempt
Correct Answer
B. \(a^2+2ab+b^2\) / correct expansion
Step 1
Concept
In ( (a+b)2 ), the middle term is (2ab). Exam tip: do not forget the middle term in square identities.
Step 2
Why this answer is correct
The correct answer is B. \(a^2+2ab+b^2\) / correct expansion. In ( (a+b)2 ), the middle term is (2ab). Exam tip: do not forget the middle term in square identities.
Step 3
Exam Tip
( (a+b)2 ) में बीच का पद (2ab) आता है। परीक्षा में वर्ग पहचान में मध्य पद न भूलें।
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पहचान ( (x-y)2 ) का सही विस्तार चुनिए।
Choose the correct expansion of the identity ( (x-y)2 ).
#algebraic identities
#minus square
#binomial
A \(x^2+2xy+y^2\) / plus middle term
B \(x^2-y^2\) / difference only
C \(x^2-2xy+y^2\) / correct expansion
D \(x^2+xy-y^2\) / mixed signs
Explanation opens after your attempt
Correct Answer
C. \(x^2-2xy+y^2\) / correct expansion
Step 1
Concept
In ( (x-y)2 ), the middle term is (-2xy). Exam tip: pay attention to the negative sign.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-2xy+y^2\) / correct expansion. In ( (x-y)2 ), the middle term is (-2xy). Exam tip: pay attention to the negative sign.
Step 3
Exam Tip
( (x-y)2 ) में बीच का पद (-2xy) होता है। परीक्षा में ऋण चिह्न पर ध्यान दें।
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पहचान ( (p+q)(p-q) ) किसके बराबर होती है?
The identity ( (p+q)(p-q) ) is equal to what?
#difference of squares
#identity
#algebra
A \(p^2-q^2\) / difference of squares
B \(p^2+q^2\) / sum of squares
C \(p^2+2pq+q^2\) / square of sum
D \(p^2-2pq+q^2\) / square of difference
Explanation opens after your attempt
Correct Answer
A. \(p^2-q^2\) / difference of squares
Step 1
Concept
( (p+q)(p-q)=p-2 -q-2 ). Exam tip: remember it as difference of squares.
Step 2
Why this answer is correct
The correct answer is A. \(p^2-q^2\) / difference of squares. ( (p+q)(p-q)=p-2 -q-2 ). Exam tip: remember it as difference of squares.
Step 3
Exam Tip
( (p+q)(p-q)=p-2 -q-2 ) होता है। परीक्षा में इसे वर्गों का अंतर याद रखें।
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( (m+n)2 ) में (2mn) को क्या कहा जा सकता है?
In ( (m+n)2 ), what can (2mn) be called?
#middle term
#binomial square
#identity
A पहला वर्ग / first square
B दूसरा वर्ग / second square
C स्थिर पद / constant term
D मध्य पद / middle term
Explanation opens after your attempt
Correct Answer
D. मध्य पद / middle term
Step 1
Concept
In ( (m+n)2 =m-2 +2mn+n-2 ), (2mn) is the middle term. Exam tip: identify all three terms.
Step 2
Why this answer is correct
The correct answer is D. मध्य पद / middle term. In ( (m+n)2 =m-2 +2mn+n-2 ), (2mn) is the middle term. Exam tip: identify all three terms.
Step 3
Exam Tip
( (m+n)2 =m-2 +2mn+n-2 ) में (2mn) मध्य पद है। परीक्षा में तीन पदों की पहचान करें।
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( (7+3)2 ) को पहचान से निकालने पर मान क्या होगा?
Using an identity, what is the value of ( (7+3)2 )?
#numerical identity
#square
#mental math
A (70)
B (100)
C (49)
D (60)
Explanation opens after your attempt
Step 1
Concept
( (7+3)2 =102 =100 ). Exam tip: identities make mental calculation faster.
Step 2
Why this answer is correct
The correct answer is B. (100). ( (7+3)2 =102 =100 ). Exam tip: identities make mental calculation faster.
Step 3
Exam Tip
( (7+3)2 =102 =100 ) होता है। परीक्षा में पहचान से मानसिक गणना तेज होती है।
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( (10-2)2 ) का मान कौन-सा है?
What is the value of ( (10-2)2 )?
#numerical square
#algebraic identities
#easy
A (144)
B (100)
C (64)
D (80)
Explanation opens after your attempt
Step 1
Concept
( (10-2)2 =82 =64 ). Exam tip: first find the value inside the bracket.
Step 2
Why this answer is correct
The correct answer is C. (64). ( (10-2)2 =82 =64 ). Exam tip: first find the value inside the bracket.
Step 3
Exam Tip
( (10-2)2 =82 =64 ) होता है। परीक्षा में पहले कोष्ठक का मान निकालें।
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\( 15^2-5^2 \) को किस पहचान से सरल किया जा सकता है?
Which identity can simplify \( 15^2-5^2 \)?
#difference of squares
#numerical identity
#factorisation
A ( (a+b)2 )
B ( (a-b)2 )
C \(a^2+b^2\)
D (a-2 -b-2 =(a+b)(a-b))
Explanation opens after your attempt
Correct Answer
D. (a-2 -b-2 =(a+b)(a-b))
Step 1
Concept
This is the form \(a^2-b^2\). Exam tip: convert difference of squares into a product.
Step 2
Why this answer is correct
The correct answer is D. (a-2 -b-2 =(a+b)(a-b)). This is the form \(a^2-b^2\). Exam tip: convert difference of squares into a product.
Step 3
Exam Tip
यह \(a^2-b^2\) का रूप है। परीक्षा में वर्गों के अंतर को गुणनफल में बदलें।
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( (x+4)2 ) का विस्तार क्या होगा?
What is the expansion of ( (x+4)2 )?
#expansion
#binomial square
#x plus number
A \(x^2+8x+16\)
B \(x^2+4x+16\)
C \(x^2+16x+4\)
D \(x^2-8x+16\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+8x+16\)
Step 1
Concept
( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 ). Exam tip: use (2ab).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+8x+16\). ( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 ). Exam tip: use (2ab).
Step 3
Exam Tip
( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 )। परीक्षा में (2ab) लगाएँ।
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( (y-5)2 ) का सही विस्तार चुनिए।
Choose the correct expansion of ( (y-5)2 ).
#expansion
#minus square
#y minus number
A \(y^2+10y+25\)
B \(y^2-10y+25\)
C \(y^2-5y+25\)
D \(y^2-25\)
Explanation opens after your attempt
Correct Answer
B. \(y^2-10y+25\)
Step 1
Concept
( (y-5)2 =y-2 -10y+25 ). Exam tip: keep the sign of the middle term correct.
Step 2
Why this answer is correct
The correct answer is B. \(y^2-10y+25\). ( (y-5)2 =y-2 -10y+25 ). Exam tip: keep the sign of the middle term correct.
Step 3
Exam Tip
( (y-5)2 =y-2 -10y+25 ) होता है। परीक्षा में मध्य पद का चिह्न सही रखें।
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( (3a+2b)2 ) में मध्य पद क्या है?
What is the middle term in ( (3a+2b)2 )?
#middle term
#binomial square
#algebra
A (6ab)
B \(9a^2\)
C (12ab)
D \(4b^2\)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot3a\cdot2b=12ab\). Exam tip: multiply both terms and then multiply by (2).
Step 2
Why this answer is correct
The correct answer is C. (12ab). The middle term is \(2\cdot3a\cdot2b=12ab\). Exam tip: multiply both terms and then multiply by (2).
Step 3
Exam Tip
मध्य पद \(2\cdot3a\cdot2b=12ab\) है। परीक्षा में दोनों पदों को गुणा करके (2) से गुणा करें।
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( (2x-3)2 ) का विस्तार क्या है?
What is the expansion of ( (2x-3)2 )?
#expansion
#binomial square
#negative middle term
A \(4x^2+12x+9\)
B \(2x^2-6x+9\)
C \(4x^2-6x+9\)
D \(4x^2-12x+9\)
Explanation opens after your attempt
Correct Answer
D. \(4x^2-12x+9\)
Step 1
Concept
( (2x-3)2 =4x-2 -12x+9 ). Exam tip: remember (-2ab).
Step 2
Why this answer is correct
The correct answer is D. \(4x^2-12x+9\). ( (2x-3)2 =4x-2 -12x+9 ). Exam tip: remember (-2ab).
Step 3
Exam Tip
( (2x-3)2 =4x-2 -12x+9 ) होता है। परीक्षा में (-2ab) का ध्यान रखें।
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( (a+6)(a-6) ) किसके बराबर है?
What is ( (a+6)(a-6) ) equal to?
#difference of squares
#factor product
#identity
A \(a^2-36\)
B \(a^2+36\)
C \(a^2+12a+36\)
D \(a^2-12a+36\)
Explanation opens after your attempt
Correct Answer
A. \(a^2-36\)
Step 1
Concept
( (a+6)(a-6)=a-2 -62 =a-2 -36 ). Exam tip: remember \(6^2=36\).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-36\). ( (a+6)(a-6)=a-2 -62 =a-2 -36 ). Exam tip: remember \(6^2=36\).
Step 3
Exam Tip
( (a+6)(a-6)=a-2 -62 =a-2 -36 )। परीक्षा में \(6^2=36\) याद रखें।
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( (x+2)(x+3) ) को सरल करने का सही परिणाम क्या है?
What is the correct simplified result of ( (x+2)(x+3) )?
#product identity
#x plus a
#x plus b
A \(x^2+5x+5\)
B \(x^2+5x+6\)
C \(x^2+6x+5\)
D \(x^2+2x+3\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+5x+6\)
Step 1
Concept
( (x+2)(x+3)=x-2 +5x+6 ). Exam tip: take product (6) and sum (5) of constants.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+5x+6\). ( (x+2)(x+3)=x-2 +5x+6 ). Exam tip: take product (6) and sum (5) of constants.
Step 3
Exam Tip
( (x+2)(x+3)=x-2 +5x+6 ) होता है। परीक्षा में स्थिर पदों का गुणन (6) और योग (5) लें।
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( (x+1)(x+7) ) में (x) का गुणांक क्या होगा?
What will be the coefficient of (x) in ( (x+1)(x+7) )?
#coefficient
#product identity
#algebra
A (7)
B (1)
C (8)
D (6)
Explanation opens after your attempt
Step 1
Concept
In ( (x+1)(x+7)=x-2 +8x+7 ), the coefficient of (x) is (8). Exam tip: add the constants.
Step 2
Why this answer is correct
The correct answer is C. (8). In ( (x+1)(x+7)=x-2 +8x+7 ), the coefficient of (x) is (8). Exam tip: add the constants.
Step 3
Exam Tip
( (x+1)(x+7)=x-2 +8x+7 ) में (x) का गुणांक (8) है। परीक्षा में स्थिर पदों का योग लें।
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( (t-4)(t+4) ) का परिणाम क्या है?
What is the result of ( (t-4)(t+4) )?
#difference of squares
#t variable
#identity
A \(t^2+16\)
B \(t^2-8t+16\)
C \(t^2+8t+16\)
D \(t^2-16\)
Explanation opens after your attempt
Correct Answer
D. \(t^2-16\)
Step 1
Concept
( (t-4)(t+4)=t-2 -16 ). Exam tip: use difference of squares for opposite signs.
Step 2
Why this answer is correct
The correct answer is D. \(t^2-16\). ( (t-4)(t+4)=t-2 -16 ). Exam tip: use difference of squares for opposite signs.
Step 3
Exam Tip
( (t-4)(t+4)=t-2 -16 ) होता है। परीक्षा में विपरीत चिह्नों पर वर्गों का अंतर लगाएँ।
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\( 99^2 \) को आसानी से निकालने के लिए कौन-सा रूप सबसे अच्छा है?
Which form is best for finding \( 99^2 \) easily?
#mental math
#square identity
#99 square
A ( (100-1)2 )
B ( (90+9)3 )
C ( (50+49) )
D ( (99+1)(99-1) )
Explanation opens after your attempt
Correct Answer
A. ( (100-1)2 )
Step 1
Concept
(992 =(100-1)2 ) is easy to use. Exam tip: use a nearby round number.
Step 2
Why this answer is correct
The correct answer is A. ( (100-1)2 ). (992 =(100-1)2 ) is easy to use. Exam tip: use a nearby round number.
Step 3
Exam Tip
(992 =(100-1)2 ) से आसानी से निकलेगा। परीक्षा में निकट पूर्ण संख्या का उपयोग करें।
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\( 101^2 \) के लिए पहचान ( (a+b)2 ) में (a) और (b) क्या लिए जा सकते हैं?
For \( 101^2 \), what can be taken as (a) and (b) in ( (a+b)2 )?
#mental math
#101 square
#algebraic identity
A (a=99), (b=2)
B (a=100), (b=1)
C (a=101), (b=0)
D (a=50), (b=51)
Explanation opens after your attempt
Correct Answer
B. (a=100), (b=1)
Step 1
Concept
Since (101=100+1), taking (a=100) and (b=1) is easy. Exam tip: choose an easy split.
Step 2
Why this answer is correct
The correct answer is B. (a=100), (b=1). Since (101=100+1), taking (a=100) and (b=1) is easy. Exam tip: choose an easy split.
Step 3
Exam Tip
(101=100+1) इसलिए (a=100) और (b=1) लेना आसान है। परीक्षा में आसान विभाजन चुनें।
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( (5x)2 ) का मान क्या है?
What is the value of ( (5x)2 )?
#square of monomial
#coefficient
#x square
A \(5x^2\)
B \(10x^2\)
C \(25x^2\)
D (25x)
Explanation opens after your attempt
Correct Answer
C. \(25x^2\)
Step 1
Concept
( (5x)2 =25x-2 ). Exam tip: square both the coefficient and the variable.
Step 2
Why this answer is correct
The correct answer is C. \(25x^2\). ( (5x)2 =25x-2 ). Exam tip: square both the coefficient and the variable.
Step 3
Exam Tip
( (5x)2 =25x-2 ) होता है। परीक्षा में गुणांक और चर दोनों का वर्ग करें।
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( (2a+5)2 ) में पहला पद कौन-सा होगा?
What will be the first term in ( (2a+5)2 )?
#first term
#binomial square
#2a plus 5
A \(2a^2\)
B (10a)
C (25)
D \(4a^2\)
Explanation opens after your attempt
Correct Answer
D. \(4a^2\)
Step 1
Concept
The first term is ( (2a)2 =4a-2 ). Exam tip: square the complete first term.
Step 2
Why this answer is correct
The correct answer is D. \(4a^2\). The first term is ( (2a)2 =4a-2 ). Exam tip: square the complete first term.
Step 3
Exam Tip
पहला पद ( (2a)2 =4a-2 ) होगा। परीक्षा में पहले पद का पूरा वर्ग करें।
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( (3x+1)2 ) का सही विस्तार क्या है?
What is the correct expansion of ( (3x+1)2 )?
#expansion
#3x plus 1
#binomial square
A \(9x^2+6x+1\)
B \(3x^2+6x+1\)
C \(9x^2+3x+1\)
D \(9x^2+1\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2+6x+1\)
Step 1
Concept
( (3x+1)2 =9x-2 +6x+1 ). Exam tip: write \(2\cdot3x\cdot1=6x\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2+6x+1\). ( (3x+1)2 =9x-2 +6x+1 ). Exam tip: write \(2\cdot3x\cdot1=6x\).
Step 3
Exam Tip
( (3x+1)2 =9x-2 +6x+1 ) होता है। परीक्षा में \(2\cdot3x\cdot1=6x\) लिखें।
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( (x-9)2 ) में स्थिर पद कौन-सा है?
What is the constant term in ( (x-9)2 )?
#constant term
#x minus 9
#square identity
A (9)
B (81)
C (-18x)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
In ( (x-9)2 =x-2 -18x+81 ), the constant term is (81). Exam tip: square the last term.
Step 2
Why this answer is correct
The correct answer is B. (81). In ( (x-9)2 =x-2 -18x+81 ), the constant term is (81). Exam tip: square the last term.
Step 3
Exam Tip
( (x-9)2 =x-2 -18x+81 ) में स्थिर पद (81) है। परीक्षा में अंतिम पद का वर्ग करें।
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( (4a-b)2 ) में मध्य पद क्या होगा?
What is the middle term in ( (4a-b)2 )?
#middle term
#4a minus b
#identity
A (8ab)
B (4ab)
C (-8ab)
D (-4ab)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(-2\cdot4a\cdot b=-8ab\). Exam tip: apply (2ab) with the negative sign.
Step 2
Why this answer is correct
The correct answer is C. (-8ab). The middle term is \(-2\cdot4a\cdot b=-8ab\). Exam tip: apply (2ab) with the negative sign.
Step 3
Exam Tip
मध्य पद \(-2\cdot4a\cdot b=-8ab\) है। परीक्षा में ऋण चिह्न सहित (2ab) लगाएँ।
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\( 51^2 \) को ( (50+1)2 ) से निकालने पर परिणाम क्या है?
Using ( (50+1)2 ), what is \( 51^2 \)?
#mental calculation
#51 square
#identity
A (2501)
B (2600)
C (2500)
D (2601)
Explanation opens after your attempt
Step 1
Concept
\(51^2=2500+100+1=2601\). Exam tip: add (2ab) separately.
Step 2
Why this answer is correct
The correct answer is D. (2601). \(51^2=2500+100+1=2601\). Exam tip: add (2ab) separately.
Step 3
Exam Tip
\(51^2=2500+100+1=2601\) होता है। परीक्षा में (2ab) को अलग से जोड़ें।
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\( 48^2 \) को किस रूप में लिखकर आसानी से निकाला जा सकता है?
Which form can be used to find \( 48^2 \) easily?
#mental math
#48 square
#minus identity
A ( (50-2)2 )
B ( (40+8)3 )
C ( (48+2)(48-2) )
D (48+48)
Explanation opens after your attempt
Correct Answer
A. ( (50-2)2 )
Step 1
Concept
Since (48=50-2), ( (50-2)2 ) is useful. Exam tip: write it using a nearby larger number.
Step 2
Why this answer is correct
The correct answer is A. ( (50-2)2 ). Since (48=50-2), ( (50-2)2 ) is useful. Exam tip: write it using a nearby larger number.
Step 3
Exam Tip
(48=50-2) इसलिए ( (50-2)2 ) उपयोगी है। परीक्षा में निकट बड़ी संख्या से घटाकर लिखें।
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( (a+b)2 -(a-b)2 ) का सरल रूप क्या है?
What is the simplified form of ( (a+b)2 -(a-b)2 )?
#identity comparison
#simplification
#4ab
A \(2a^2+2b^2\)
B (4ab)
C \(a^2-b^2\)
D (2ab)
Explanation opens after your attempt
Step 1
Concept
After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.
Step 2
Why this answer is correct
The correct answer is B. (4ab). After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.
Step 3
Exam Tip
दोनों विस्तार घटाने पर (4ab) बचता है। परीक्षा में पहले विस्तार करके समान पद काटें।
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( (x+5)2 -(x-5)2 ) का मान क्या होगा?
What is the value of ( (x+5)2 -(x-5)2 )?
#simplification
#identity
#20x
A (10x)
B (25x)
C (20x)
D (100)
Explanation opens after your attempt
Step 1
Concept
This is ( (a+b)2 -(a-b)2 =4ab ), so \(4\cdot x\cdot5=20x\). Exam tip: apply the identity directly.
Step 2
Why this answer is correct
The correct answer is C. (20x). This is ( (a+b)2 -(a-b)2 =4ab ), so \(4\cdot x\cdot5=20x\). Exam tip: apply the identity directly.
Step 3
Exam Tip
यह ( (a+b)2 -(a-b)2 =4ab ) है, इसलिए \(4\cdot x\cdot5=20x\)। परीक्षा में पहचान सीधे लगाएँ।
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( (a+b)2 +(a-b)2 ) का सरल रूप कौन-सा है?
Which is the simplified form of ( (a+b)2 +(a-b)2 )?
#sum of identities
#binomial square
#simplification
A (4ab)
B (2ab)
C \(a^2+b^2\)
D \(2a^2+2b^2\)
Explanation opens after your attempt
Correct Answer
D. \(2a^2+2b^2\)
Step 1
Concept
Adding both expansions cancels middle terms and gives \(2a^2+2b^2\). Exam tip: add like terms.
Step 2
Why this answer is correct
The correct answer is D. \(2a^2+2b^2\). Adding both expansions cancels middle terms and gives \(2a^2+2b^2\). Exam tip: add like terms.
Step 3
Exam Tip
दोनों विस्तार जोड़ने पर मध्य पद कटते हैं और \(2a^2+2b^2\) मिलता है। परीक्षा में समान पद जोड़ें।
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( (2x+3y)2 ) में अंतिम पद कौन-सा है?
What is the last term in ( (2x+3y)2 )?
#last term
#2x plus 3y
#square identity
A \(9y^2\)
B (6xy)
C \(4x^2\)
D (12xy)
Explanation opens after your attempt
Correct Answer
A. \(9y^2\)
Step 1
Concept
The last term is ( (3y)2 =9y-2 ). Exam tip: square the complete term.
Step 2
Why this answer is correct
The correct answer is A. \(9y^2\). The last term is ( (3y)2 =9y-2 ). Exam tip: square the complete term.
Step 3
Exam Tip
अंतिम पद ( (3y)2 =9y-2 ) है। परीक्षा में हर पद का पूरा वर्ग करें।
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( (2x+3y)2 ) का मध्य पद क्या होगा?
What is the middle term of ( (2x+3y)2 )?
#middle term
#2x plus 3y
#algebraic identity
A (5xy)
B (12xy)
C (6xy)
D (10xy)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot2x\cdot3y=12xy\). Exam tip: multiply first and then multiply by (2).
Step 2
Why this answer is correct
The correct answer is B. (12xy). The middle term is \(2\cdot2x\cdot3y=12xy\). Exam tip: multiply first and then multiply by (2).
Step 3
Exam Tip
मध्य पद \(2\cdot2x\cdot3y=12xy\) है। परीक्षा में पहले गुणा फिर (2) से गुणा करें।
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( (m+4)(m+6) ) का विस्तार क्या है?
What is the expansion of ( (m+4)(m+6) )?
#product identity
#m plus numbers
#expansion
A \(m^2+10m+24\)
B \(m^2+24m+10\)
C \(m^2+2m+24\)
D \(m^2+10m+10\)
Explanation opens after your attempt
Correct Answer
A. \(m^2+10m+24\)
Step 1
Concept
( (m+4)(m+6)=m-2 +10m+24 ). Exam tip: take (4+6=10) and \(4\cdot6=24\).
Step 2
Why this answer is correct
The correct answer is A. \(m^2+10m+24\). ( (m+4)(m+6)=m-2 +10m+24 ). Exam tip: take (4+6=10) and \(4\cdot6=24\).
Step 3
Exam Tip
( (m+4)(m+6)=m-2 +10m+24 ) होता है। परीक्षा में (4+6=10) और \(4\cdot6=24\) लें।
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( (x-2)(x-5) ) में स्थिर पद क्या है?
What is the constant term in ( (x-2)(x-5) )?
#constant term
#product identity
#negative constants
A (-7)
B (10)
C (-10)
D (7)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-2)(-5)=10). Exam tip: remember negative times negative is positive.
Step 2
Why this answer is correct
The correct answer is B. (10). The constant term is ((-2)(-5)=10). Exam tip: remember negative times negative is positive.
Step 3
Exam Tip
स्थिर पद ((-2)(-5)=10) होता है। परीक्षा में ऋण गुणा ऋण धन याद रखें।
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( (x-2)(x-5) ) में (x) का गुणांक क्या है?
What is the coefficient of (x) in ( (x-2)(x-5) )?
#coefficient
#product identity
#x minus numbers
A (7)
B (10)
C (-7)
D (-10)
Explanation opens after your attempt
Step 1
Concept
( (x-2)(x-5)=x-2 -7x+10 ). Exam tip: add the constants to get (-7).
Step 2
Why this answer is correct
The correct answer is C. (-7). ( (x-2)(x-5)=x-2 -7x+10 ). Exam tip: add the constants to get (-7).
Step 3
Exam Tip
( (x-2)(x-5)=x-2 -7x+10 ) है। परीक्षा में स्थिर पदों का योग (-7) लें।
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( (z+9)(z-9) ) का सही परिणाम चुनिए।
Choose the correct result of ( (z+9)(z-9) ).
#difference of squares
#z identity
#expansion
A \(z^2+81\)
B \(z^2+18z+81\)
C \(z^2-18z+81\)
D \(z^2-81\)
Explanation opens after your attempt
Correct Answer
D. \(z^2-81\)
Step 1
Concept
( (z+9)(z-9)=z-2 -81 ). Exam tip: keep \(9^2=81\) in mind.
Step 2
Why this answer is correct
The correct answer is D. \(z^2-81\). ( (z+9)(z-9)=z-2 -81 ). Exam tip: keep \(9^2=81\) in mind.
Step 3
Exam Tip
( (z+9)(z-9)=z-2 -81 ) है। परीक्षा में \(9^2=81\) रखें।
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( (a+b+c)2 ) में (2ab) के साथ कौन-से अन्य दो गुणन पद आते हैं?
In ( (a+b+c)2 ), which two other product terms come with (2ab)?
#three term square
#abc identity
#product terms
A (2ac) और (2bc)
B \(a^2\) और \(b^2\)
C (ab) और (bc)
D (3abc) और \(c^2\)
Explanation opens after your attempt
Correct Answer
A. (2ac) और (2bc)
Step 1
Concept
In ( (a+b+c)2 ), (2ab), (2bc), and (2ca) appear. Exam tip: remember the three pairwise product terms.
Step 2
Why this answer is correct
The correct answer is A. (2ac) और (2bc). In ( (a+b+c)2 ), (2ab), (2bc), and (2ca) appear. Exam tip: remember the three pairwise product terms.
Step 3
Exam Tip
( (a+b+c)2 ) में (2ab), (2bc), और (2ca) आते हैं। परीक्षा में तीन जोड़ी गुणन पद याद रखें।
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( (x+y+z)2 ) में वर्ग पद कौन-से हैं?
What are the square terms in ( (x+y+z)2 )?
#three term square
#square terms
#algebra
A (xy), (yz), (zx)
B \(x^2\), \(y^2\), \(z^2\)
C (2xy), (2yz), (2zx)
D (x+y+z)
Explanation opens after your attempt
Correct Answer
B. \(x^2\), \(y^2\), \(z^2\)
Step 1
Concept
The square terms are \(x^2\), \(y^2\), \(z^2\). Exam tip: distinguish square terms and product terms.
Step 2
Why this answer is correct
The correct answer is B. \(x^2\), \(y^2\), \(z^2\). The square terms are \(x^2\), \(y^2\), \(z^2\). Exam tip: distinguish square terms and product terms.
Step 3
Exam Tip
वर्ग पद \(x^2\), \(y^2\), \(z^2\) हैं। परीक्षा में वर्ग पद और गुणन पद अलग पहचानें।
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( (a+b+c)2 ) का पूरा विस्तार कौन-सा है?
Which is the full expansion of ( (a+b+c)2 )?
#three term identity
#full expansion
#algebra
A \(a^2+b^2+c^2+ab+bc+ca\)
B \(a^2+b^2+c^2+abc\)
C \(a^2+b^2+c^2+2ab+2bc+2ca\)
D \(a^2+b^2-c^2+2ab\)
Explanation opens after your attempt
Correct Answer
C. \(a^2+b^2+c^2+2ab+2bc+2ca\)
Step 1
Concept
The square of three terms has three square terms and three double product terms. Exam tip: write all terms with (2).
Step 2
Why this answer is correct
The correct answer is C. \(a^2+b^2+c^2+2ab+2bc+2ca\). The square of three terms has three square terms and three double product terms. Exam tip: write all terms with (2).
Step 3
Exam Tip
तीन पदों के वर्ग में तीन वर्ग पद और तीन दोहरे गुणन पद होते हैं। परीक्षा में सभी (2) वाले पद लिखें।
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( (x+2+y)2 ) में (2xy) क्यों आएगा?
Why will (2xy) appear in ( (x+2+y)2 )?
#three term square
#pair product
#2xy
A क्योंकि (x) और (y) दोनों वर्ग पद हैं / Because (x) and (y) are both square terms
B क्योंकि (x) और (y) की जोड़ी का दोहरा गुणन आता है / Because the double product of the pair (x) and (y) appears
C क्योंकि (2) हमेशा हट जाता है / Because (2) always disappears
D क्योंकि कोई गुणन पद नहीं आता / Because no product term appears
Explanation opens after your attempt
Correct Answer
B. क्योंकि (x) और (y) की जोड़ी का दोहरा गुणन आता है / Because the double product of the pair (x) and (y) appears
Step 1
Concept
In the square of three terms, the double product of each pair appears. Exam tip: write terms by making pairs.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि (x) और (y) की जोड़ी का दोहरा गुणन आता है / Because the double product of the pair (x) and (y) appears. In the square of three terms, the double product of each pair appears. Exam tip: write terms by making pairs.
Step 3
Exam Tip
तीन पदों के वर्ग में हर जोड़ी का दोहरा गुणन आता है। परीक्षा में जोड़ी बनाकर पद लिखें।
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\( a^2+2ab+b^2 \) को किस रूप में लिखा जा सकता है?
In which form can \( a^2+2ab+b^2 \) be written?
#factorisation
#square identity
#recognition
A ( (a-b)2 )
B \(a^2-b^2\)
C ( (a+b)2 )
D \(a+b^2\)
Explanation opens after your attempt
Correct Answer
C. ( (a+b)2 )
Step 1
Concept
This is the expansion of ( (a+b)2 ). Exam tip: identify positive square from (+2ab).
Step 2
Why this answer is correct
The correct answer is C. ( (a+b)2 ). This is the expansion of ( (a+b)2 ). Exam tip: identify positive square from (+2ab).
Step 3
Exam Tip
यह ( (a+b)2 ) का विस्तार है। परीक्षा में (+2ab) देखकर धन वर्ग पहचानें।
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\( x^2-6x+9 \) को किस रूप में लिखा जाएगा?
In which form will \( x^2-6x+9 \) be written?
#factorisation
#perfect square
#x minus 3
A ( (x+3)2 )
B \(x^2-9\)
C ( (x-6)2 )
D ( (x-3)2 )
Explanation opens after your attempt
Correct Answer
D. ( (x-3)2 )
Step 1
Concept
(x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 ). Exam tip: check the square root of the last term.
Step 2
Why this answer is correct
The correct answer is D. ( (x-3)2 ). (x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 ). Exam tip: check the square root of the last term.
Step 3
Exam Tip
(x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 )। परीक्षा में अंतिम पद का वर्गमूल देखें।
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\( y^2+12y+36 \) किसका वर्ग है?
\( y^2+12y+36 \) is the square of what?
#perfect square
#recognition
#y plus 6
A ( (y+6)2 )
B ( (y-6)2 )
C ( (y+12)2 )
D \(y^2-36\)
Explanation opens after your attempt
Correct Answer
A. ( (y+6)2 )
Step 1
Concept
\(36=6^2\) and \(12y=2\cdot y\cdot6\). Exam tip: identify perfect square trinomials.
Step 2
Why this answer is correct
The correct answer is A. ( (y+6)2 ). \(36=6^2\) and \(12y=2\cdot y\cdot6\). Exam tip: identify perfect square trinomials.
Step 3
Exam Tip
\(36=6^2\) और \(12y=2\cdot y\cdot6\) है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें।
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\( 49-r^2 \) को गुणनखंडों में कैसे लिखेंगे?
How will you factorise \( 49-r^2 \)?
#factorisation
#difference of squares
#49 minus r square
A ( (r+7)(r-7) )
B ( (7+r)(7-r) )
C ( (49+r)(49-r) )
D ( (7-r)2 )
Explanation opens after your attempt
Correct Answer
B. ( (7+r)(7-r) )
Step 1
Concept
(49-r-2 =72 -r-2 =(7+r)(7-r)). Exam tip: keep the larger square first.
Step 2
Why this answer is correct
The correct answer is B. ( (7+r)(7-r) ). (49-r-2 =72 -r-2 =(7+r)(7-r)). Exam tip: keep the larger square first.
Step 3
Exam Tip
(49-r-2 =72 -r-2 =(7+r)(7-r)) है। परीक्षा में बड़े वर्ग को पहले रखें।
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\( 25x^2-16 \) का सही गुणनखंडन क्या है?
What is the correct factorisation of \( 25x^2-16 \)?
#factorisation
#difference of squares
#25x square
A ( (5x-4)2 )
B ( (25x-4)(x+4) )
C ( (5x+4)(5x-4) )
D ( (5x+4)2 )
Explanation opens after your attempt
Correct Answer
C. ( (5x+4)(5x-4) )
Step 1
Concept
(25x-2 -16=(5x)2 -42 =(5x+4)(5x-4)). Exam tip: identify both squares.
Step 2
Why this answer is correct
The correct answer is C. ( (5x+4)(5x-4) ). (25x-2 -16=(5x)2 -42 =(5x+4)(5x-4)). Exam tip: identify both squares.
Step 3
Exam Tip
(25x-2 -16=(5x)2 -42 =(5x+4)(5x-4))। परीक्षा में दोनों वर्ग पहचानें।
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( (a+1)2 ) और \(a^2+1\) में क्या अंतर है?
What is the difference between ( (a+1)2 ) and \(a^2+1\)?
#common mistake
#middle term
#square identity
A दोनों हमेशा समान हैं / Both are always same
B ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a)
C \(a^2+1\) में (2a) होता है / \(a^2+1\) has (2a)
D दोनों में कोई वर्ग पद नहीं होता / Neither has square terms
Explanation opens after your attempt
Correct Answer
B. ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a)
Step 1
Concept
( (a+1)2 =a-2 +2a+1 ), so \(a^2+1\) is incomplete. Exam tip: do not omit the middle term.
Step 2
Why this answer is correct
The correct answer is B. ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a). ( (a+1)2 =a-2 +2a+1 ), so \(a^2+1\) is incomplete. Exam tip: do not omit the middle term.
Step 3
Exam Tip
( (a+1)2 =a-2 +2a+1 ), इसलिए \(a^2+1\) अधूरा है। परीक्षा में मध्य पद न छोड़ें।
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( (x-1)2 ) और \(x^2-1\) में सही अंतर कौन-सा है?
Which is the correct difference between ( (x-1)2 ) and \(x^2-1\)?
#common mistake
#x minus 1
#difference of squares
A ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1))
B दोनों हमेशा समान हैं / Both are always same
C \(x^2-1=x^2-2x+1\)
D ( (x-1)2 =x-2 +2x+1 )
Explanation opens after your attempt
Correct Answer
A. ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1))
Step 1
Concept
The first is a perfect square and the second is difference of squares. Exam tip: keep bracket square and difference of squares separate.
Step 2
Why this answer is correct
The correct answer is A. ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1)). The first is a perfect square and the second is difference of squares. Exam tip: keep bracket square and difference of squares separate.
Step 3
Exam Tip
पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर है। परीक्षा में कोष्ठक और वर्गों का अंतर अलग रखें।
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( (2a+3)(2a-3) ) को सरल कीजिए।
Simplify ( (2a+3)(2a-3) ).
#simplification
#difference of squares
#2a plus 3
A \(4a^2+9\)
B \(4a^2-9\)
C \(2a^2-9\)
D \(4a^2-12a+9\)
Explanation opens after your attempt
Correct Answer
B. \(4a^2-9\)
Step 1
Concept
This is ( (p+q)(p-q)=p-2 -q-2 ). Here take (p=2a) and (q=3).
Step 2
Why this answer is correct
The correct answer is B. \(4a^2-9\). This is ( (p+q)(p-q)=p-2 -q-2 ). Here take (p=2a) and (q=3).
Step 3
Exam Tip
यह ( (p+q)(p-q)=p-2 -q-2 ) है। यहाँ (p=2a) और (q=3) लें।
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( (6x+1)2 ) में (x) वाला पद क्या होगा?
What will be the term containing (x) in ( (6x+1)2 )?
#middle term
#6x plus 1
#square identity
A (6x)
B (36x)
C (12x)
D (1x)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot6x\cdot1=12x\). Exam tip: use (2ab).
Step 2
Why this answer is correct
The correct answer is C. (12x). The middle term is \(2\cdot6x\cdot1=12x\). Exam tip: use (2ab).
Step 3
Exam Tip
मध्य पद \(2\cdot6x\cdot1=12x\) है। परीक्षा में (2ab) का प्रयोग करें।
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( (4p-1)2 ) का विस्तार क्या है?
What is the expansion of ( (4p-1)2 )?
#expansion
#4p minus 1
#identity
A \(16p^2+8p+1\)
B \(16p^2-4p+1\)
C \(4p^2-8p+1\)
D \(16p^2-8p+1\)
Explanation opens after your attempt
Correct Answer
D. \(16p^2-8p+1\)
Step 1
Concept
( (4p-1)2 =16p-2 -8p+1 ). Exam tip: remember \(2\cdot4p\cdot1=8p\) and the negative sign.
Step 2
Why this answer is correct
The correct answer is D. \(16p^2-8p+1\). ( (4p-1)2 =16p-2 -8p+1 ). Exam tip: remember \(2\cdot4p\cdot1=8p\) and the negative sign.
Step 3
Exam Tip
( (4p-1)2 =16p-2 -8p+1 ) है। परीक्षा में \(2\cdot4p\cdot1=8p\) और ऋण चिह्न याद रखें।
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\( 104^2 \) को पहचान से निकालने के लिए सही रूप क्या है?
What is the correct form to find \( 104^2 \) using an identity?
#mental math
#104 square
#identity
A ( (100+4)2 )
B ( (104-4)2 )
C ( (50+54)(50-54) )
D \(104^2-4^2\)
Explanation opens after your attempt
Correct Answer
A. ( (100+4)2 )
Step 1
Concept
(104=100+4), so ( (100+4)2 ) is suitable. Exam tip: choose a nearby round number.
Step 2
Why this answer is correct
The correct answer is A. ( (100+4)2 ). (104=100+4), so ( (100+4)2 ) is suitable. Exam tip: choose a nearby round number.
Step 3
Exam Tip
(104=100+4), इसलिए ( (100+4)2 ) उपयुक्त है। परीक्षा में नजदीकी पूर्ण संख्या चुनें।
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( (x+8)2 ) और ( (x-8)2 ) में किस पद का चिह्न बदलता है?
In ( (x+8)2 ) and ( (x-8)2 ), which term changes sign?
#sign change
#middle term
#plus minus square
A वर्ग पद \(x^2\) / square term \(x^2\)
B मध्य पद (16x) / middle term (16x)
C स्थिर पद (64) / constant term (64)
D सभी पद / all terms
Explanation opens after your attempt
Correct Answer
B. मध्य पद (16x) / middle term (16x)
Step 1
Concept
In both, \(x^2\) and (64) remain same; only the sign of the middle term changes. Exam tip: compare signs.
Step 2
Why this answer is correct
The correct answer is B. मध्य पद (16x) / middle term (16x). In both, \(x^2\) and (64) remain same; only the sign of the middle term changes. Exam tip: compare signs.
Step 3
Exam Tip
दोनों में \(x^2\) और (64) समान रहते हैं, केवल मध्य पद का चिह्न बदलता है। परीक्षा में चिह्न तुलना करें।
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पहचानों का मुख्य उपयोग क्या है?
What is the main use of identities?
#algebraic identities
#use
#simplification
A सिर्फ आकृतियाँ बनाने में / only drawing figures
B सिर्फ भिन्नों को पढ़ने में / only reading fractions
C व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly
D केवल कोण नापने में / only measuring angles
Explanation opens after your attempt
Correct Answer
C. व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly
Step 1
Concept
Algebraic identities make calculation shorter and systematic. Exam tip: identify the identity and apply it directly.
Step 2
Why this answer is correct
The correct answer is C. व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly. Algebraic identities make calculation shorter and systematic. Exam tip: identify the identity and apply it directly.
Step 3
Exam Tip
बीजीय पहचानें गणना को छोटा और व्यवस्थित बनाती हैं। परीक्षा में पहचान पहचानकर सीधे लागू करें।
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