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
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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
Explanation
Simple Explanation
( (a+b)2 ) में बीच का पद (2ab) आता है। परीक्षा में वर्ग पहचान में मध्य पद न भूलें। / In ( (a+b)2 ), the middle term is (2ab). Exam tip: do not forget the middle term in square identities.
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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
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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
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Correct Answer
C. \(x^2-2xy+y^2\) / correct expansion
Explanation
Simple Explanation
( (x-y)2 ) में बीच का पद (-2xy) होता है। परीक्षा में ऋण चिह्न पर ध्यान दें। / In ( (x-y)2 ), the middle term is (-2xy). Exam tip: pay attention to the negative sign.
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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
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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
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Correct Answer
A. \(p^2-q^2\) / difference of squares
Explanation
Simple Explanation
( (p+q)(p-q)=p-2 -q-2 ) होता है। परीक्षा में इसे वर्गों का अंतर याद रखें। / ( (p+q)(p-q)=p-2 -q-2 ). Exam tip: remember it as difference of squares.
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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
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A पहला वर्ग / first square
B दूसरा वर्ग / second square
C स्थिर पद / constant term
D मध्य पद / middle term
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Correct Answer
D. मध्य पद / middle term
Explanation
Simple Explanation
( (m+n)2 =m-2 +2mn+n-2 ) में (2mn) मध्य पद है। परीक्षा में तीन पदों की पहचान करें। / In ( (m+n)2 =m-2 +2mn+n-2 ), (2mn) is the middle term. Exam tip: identify all three terms.
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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
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A (70)
B (100)
C (49)
D (60)
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Explanation
Simple Explanation
( (7+3)2 =102 =100 ) होता है। परीक्षा में पहचान से मानसिक गणना तेज होती है। / ( (7+3)2 =102 =100 ). Exam tip: identities make mental calculation faster.
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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
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A (144)
B (100)
C (64)
D (80)
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Explanation
Simple Explanation
( (10-2)2 =82 =64 ) होता है। परीक्षा में पहले कोष्ठक का मान निकालें। / ( (10-2)2 =82 =64 ). Exam tip: first find the value inside the bracket.
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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
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A ( (a+b)2 )
B ( (a-b)2 )
C \(a^2+b^2\)
D (a-2 -b-2 =(a+b)(a-b))
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Correct Answer
D. (a-2 -b-2 =(a+b)(a-b))
Explanation
Simple Explanation
यह \(a^2-b^2\) का रूप है। परीक्षा में वर्गों के अंतर को गुणनफल में बदलें। / This is the form \(a^2-b^2\). Exam tip: convert difference of squares into a product.
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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
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A \(x^2+8x+16\)
B \(x^2+4x+16\)
C \(x^2+16x+4\)
D \(x^2-8x+16\)
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Correct Answer
A. \(x^2+8x+16\)
Explanation
Simple Explanation
( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 )। परीक्षा में (2ab) लगाएँ। / ( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 ). Exam tip: use (2ab).
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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
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A \(y^2+10y+25\)
B \(y^2-10y+25\)
C \(y^2-5y+25\)
D \(y^2-25\)
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Correct Answer
B. \(y^2-10y+25\)
Explanation
Simple Explanation
( (y-5)2 =y-2 -10y+25 ) होता है। परीक्षा में मध्य पद का चिह्न सही रखें। / ( (y-5)2 =y-2 -10y+25 ). Exam tip: keep the sign of the middle term correct.
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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
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A (6ab)
B \(9a^2\)
C (12ab)
D \(4b^2\)
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Explanation
Simple Explanation
मध्य पद \(2\cdot3a\cdot2b=12ab\) है। परीक्षा में दोनों पदों को गुणा करके (2) से गुणा करें। / The middle term is \(2\cdot3a\cdot2b=12ab\). Exam tip: multiply both terms and then multiply by (2).
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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
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A \(4x^2+12x+9\)
B \(2x^2-6x+9\)
C \(4x^2-6x+9\)
D \(4x^2-12x+9\)
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Correct Answer
D. \(4x^2-12x+9\)
Explanation
Simple Explanation
( (2x-3)2 =4x-2 -12x+9 ) होता है। परीक्षा में (-2ab) का ध्यान रखें। / ( (2x-3)2 =4x-2 -12x+9 ). Exam tip: remember (-2ab).
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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
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A \(a^2-36\)
B \(a^2+36\)
C \(a^2+12a+36\)
D \(a^2-12a+36\)
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Correct Answer
A. \(a^2-36\)
Explanation
Simple Explanation
( (a+6)(a-6)=a-2 -62 =a-2 -36 )। परीक्षा में \(6^2=36\) याद रखें। / ( (a+6)(a-6)=a-2 -62 =a-2 -36 ). Exam tip: remember \(6^2=36\).
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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
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A \(x^2+5x+5\)
B \(x^2+5x+6\)
C \(x^2+6x+5\)
D \(x^2+2x+3\)
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Correct Answer
B. \(x^2+5x+6\)
Explanation
Simple Explanation
( (x+2)(x+3)=x-2 +5x+6 ) होता है। परीक्षा में स्थिर पदों का गुणन (6) और योग (5) लें। / ( (x+2)(x+3)=x-2 +5x+6 ). Exam tip: take product (6) and sum (5) of constants.
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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
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A (7)
B (1)
C (8)
D (6)
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Explanation
Simple Explanation
( (x+1)(x+7)=x-2 +8x+7 ) में (x) का गुणांक (8) है। परीक्षा में स्थिर पदों का योग लें। / In ( (x+1)(x+7)=x-2 +8x+7 ), the coefficient of (x) is (8). Exam tip: add the constants.
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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
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A \(t^2+16\)
B \(t^2-8t+16\)
C \(t^2+8t+16\)
D \(t^2-16\)
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Correct Answer
D. \(t^2-16\)
Explanation
Simple Explanation
( (t-4)(t+4)=t-2 -16 ) होता है। परीक्षा में विपरीत चिह्नों पर वर्गों का अंतर लगाएँ। / ( (t-4)(t+4)=t-2 -16 ). Exam tip: use difference of squares for opposite signs.
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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
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A ( (100-1)2 )
B ( (90+9)3 )
C ( (50+49) )
D ( (99+1)(99-1) )
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Correct Answer
A. ( (100-1)2 )
Explanation
Simple Explanation
(992 =(100-1)2 ) से आसानी से निकलेगा। परीक्षा में निकट पूर्ण संख्या का उपयोग करें। / (992 =(100-1)2 ) is easy to use. Exam tip: use a nearby round number.
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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
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A (a=99), (b=2)
B (a=100), (b=1)
C (a=101), (b=0)
D (a=50), (b=51)
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Correct Answer
B. (a=100), (b=1)
Explanation
Simple Explanation
(101=100+1) इसलिए (a=100) और (b=1) लेना आसान है। परीक्षा में आसान विभाजन चुनें। / Since (101=100+1), taking (a=100) and (b=1) is easy. Exam tip: choose an easy split.
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( (5x)2 ) का मान क्या है?
What is the value of ( (5x)2 )?
#square of monomial
#coefficient
#x square
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A \(5x^2\)
B \(10x^2\)
C \(25x^2\)
D (25x)
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Correct Answer
C. \(25x^2\)
Explanation
Simple Explanation
( (5x)2 =25x-2 ) होता है। परीक्षा में गुणांक और चर दोनों का वर्ग करें। / ( (5x)2 =25x-2 ). Exam tip: square both the coefficient and the variable.
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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
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A \(2a^2\)
B (10a)
C (25)
D \(4a^2\)
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Correct Answer
D. \(4a^2\)
Explanation
Simple Explanation
पहला पद ( (2a)2 =4a-2 ) होगा। परीक्षा में पहले पद का पूरा वर्ग करें। / The first term is ( (2a)2 =4a-2 ). Exam tip: square the complete first term.
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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
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A \(9x^2+6x+1\)
B \(3x^2+6x+1\)
C \(9x^2+3x+1\)
D \(9x^2+1\)
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Correct Answer
A. \(9x^2+6x+1\)
Explanation
Simple Explanation
( (3x+1)2 =9x-2 +6x+1 ) होता है। परीक्षा में \(2\cdot3x\cdot1=6x\) लिखें। / ( (3x+1)2 =9x-2 +6x+1 ). Exam tip: write \(2\cdot3x\cdot1=6x\).
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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
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A (9)
B (81)
C (-18x)
D \(x^2\)
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Explanation
Simple Explanation
( (x-9)2 =x-2 -18x+81 ) में स्थिर पद (81) है। परीक्षा में अंतिम पद का वर्ग करें। / In ( (x-9)2 =x-2 -18x+81 ), the constant term is (81). Exam tip: square the last term.
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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
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A (8ab)
B (4ab)
C (-8ab)
D (-4ab)
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Explanation
Simple Explanation
मध्य पद \(-2\cdot4a\cdot b=-8ab\) है। परीक्षा में ऋण चिह्न सहित (2ab) लगाएँ। / The middle term is \(-2\cdot4a\cdot b=-8ab\). Exam tip: apply (2ab) with the negative sign.
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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
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A (2501)
B (2600)
C (2500)
D (2601)
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Explanation
Simple Explanation
\(51^2=2500+100+1=2601\) होता है। परीक्षा में (2ab) को अलग से जोड़ें। / \(51^2=2500+100+1=2601\). Exam tip: add (2ab) separately.
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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
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A ( (50-2)2 )
B ( (40+8)3 )
C ( (48+2)(48-2) )
D (48+48)
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Correct Answer
A. ( (50-2)2 )
Explanation
Simple Explanation
(48=50-2) इसलिए ( (50-2)2 ) उपयोगी है। परीक्षा में निकट बड़ी संख्या से घटाकर लिखें। / Since (48=50-2), ( (50-2)2 ) is useful. Exam tip: write it using a nearby larger number.
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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
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A \(2a^2+2b^2\)
B (4ab)
C \(a^2-b^2\)
D (2ab)
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Explanation
Simple Explanation
दोनों विस्तार घटाने पर (4ab) बचता है। परीक्षा में पहले विस्तार करके समान पद काटें। / After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.
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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
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A (10x)
B (25x)
C (20x)
D (100)
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Explanation
Simple Explanation
यह ( (a+b)2 -(a-b)2 =4ab ) है, इसलिए \(4\cdot x\cdot5=20x\)। परीक्षा में पहचान सीधे लगाएँ। / This is ( (a+b)2 -(a-b)2 =4ab ), so \(4\cdot x\cdot5=20x\). Exam tip: apply the identity directly.
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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
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A (4ab)
B (2ab)
C \(a^2+b^2\)
D \(2a^2+2b^2\)
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Correct Answer
D. \(2a^2+2b^2\)
Explanation
Simple Explanation
दोनों विस्तार जोड़ने पर मध्य पद कटते हैं और \(2a^2+2b^2\) मिलता है। परीक्षा में समान पद जोड़ें। / Adding both expansions cancels middle terms and gives \(2a^2+2b^2\). Exam tip: add like terms.
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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
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A \(9y^2\)
B (6xy)
C \(4x^2\)
D (12xy)
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Correct Answer
A. \(9y^2\)
Explanation
Simple Explanation
अंतिम पद ( (3y)2 =9y-2 ) है। परीक्षा में हर पद का पूरा वर्ग करें। / The last term is ( (3y)2 =9y-2 ). Exam tip: square the complete term.
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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
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A (5xy)
B (12xy)
C (6xy)
D (10xy)
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Explanation
Simple Explanation
मध्य पद \(2\cdot2x\cdot3y=12xy\) है। परीक्षा में पहले गुणा फिर (2) से गुणा करें। / The middle term is \(2\cdot2x\cdot3y=12xy\). Exam tip: multiply first and then multiply by (2).
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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
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A \(m^2+10m+24\)
B \(m^2+24m+10\)
C \(m^2+2m+24\)
D \(m^2+10m+10\)
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Correct Answer
A. \(m^2+10m+24\)
Explanation
Simple Explanation
( (m+4)(m+6)=m-2 +10m+24 ) होता है। परीक्षा में (4+6=10) और \(4\cdot6=24\) लें। / ( (m+4)(m+6)=m-2 +10m+24 ). Exam tip: take (4+6=10) and \(4\cdot6=24\).
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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
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A (-7)
B (10)
C (-10)
D (7)
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Explanation
Simple Explanation
स्थिर पद ((-2)(-5)=10) होता है। परीक्षा में ऋण गुणा ऋण धन याद रखें। / The constant term is ((-2)(-5)=10). Exam tip: remember negative times negative is positive.
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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
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A (7)
B (10)
C (-7)
D (-10)
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Explanation
Simple Explanation
( (x-2)(x-5)=x-2 -7x+10 ) है। परीक्षा में स्थिर पदों का योग (-7) लें। / ( (x-2)(x-5)=x-2 -7x+10 ). Exam tip: add the constants to get (-7).
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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
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A \(z^2+81\)
B \(z^2+18z+81\)
C \(z^2-18z+81\)
D \(z^2-81\)
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Correct Answer
D. \(z^2-81\)
Explanation
Simple Explanation
( (z+9)(z-9)=z-2 -81 ) है। परीक्षा में \(9^2=81\) रखें। / ( (z+9)(z-9)=z-2 -81 ). Exam tip: keep \(9^2=81\) in mind.
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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
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A (2ac) और (2bc)
B \(a^2\) और \(b^2\)
C (ab) और (bc)
D (3abc) और \(c^2\)
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Correct Answer
A. (2ac) और (2bc)
Explanation
Simple Explanation
( (a+b+c)2 ) में (2ab), (2bc), और (2ca) आते हैं। परीक्षा में तीन जोड़ी गुणन पद याद रखें। / In ( (a+b+c)2 ), (2ab), (2bc), and (2ca) appear. Exam tip: remember the three pairwise product terms.
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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
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A (xy), (yz), (zx)
B \(x^2\), \(y^2\), \(z^2\)
C (2xy), (2yz), (2zx)
D (x+y+z)
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Correct Answer
B. \(x^2\), \(y^2\), \(z^2\)
Explanation
Simple Explanation
वर्ग पद \(x^2\), \(y^2\), \(z^2\) हैं। परीक्षा में वर्ग पद और गुणन पद अलग पहचानें। / The square terms are \(x^2\), \(y^2\), \(z^2\). Exam tip: distinguish square terms and product terms.
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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
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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 \(a^2+b^2-c^2+2ab\)
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Correct Answer
C. \(a^2+b^2+c^2+2ab+2bc+2ca\)
Explanation
Simple Explanation
तीन पदों के वर्ग में तीन वर्ग पद और तीन दोहरे गुणन पद होते हैं। परीक्षा में सभी (2) वाले पद लिखें। / The square of three terms has three square terms and three double product terms. Exam tip: write all terms with (2).
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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
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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
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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
Explanation
Simple Explanation
तीन पदों के वर्ग में हर जोड़ी का दोहरा गुणन आता है। परीक्षा में जोड़ी बनाकर पद लिखें। / In the square of three terms, the double product of each pair appears. Exam tip: write terms by making pairs.
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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
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A ( (a-b)2 )
B \(a^2-b^2\)
C ( (a+b)2 )
D \(a+b^2\)
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Correct Answer
C. ( (a+b)2 )
Explanation
Simple Explanation
यह ( (a+b)2 ) का विस्तार है। परीक्षा में (+2ab) देखकर धन वर्ग पहचानें। / This is the expansion of ( (a+b)2 ). Exam tip: identify positive square from (+2ab).
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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
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A ( (x+3)2 )
B \(x^2-9\)
C ( (x-6)2 )
D ( (x-3)2 )
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Correct Answer
D. ( (x-3)2 )
Explanation
Simple Explanation
(x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 )। परीक्षा में अंतिम पद का वर्गमूल देखें। / (x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 ). Exam tip: check the square root of the last term.
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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
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A ( (y+6)2 )
B ( (y-6)2 )
C ( (y+12)2 )
D \(y^2-36\)
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Correct Answer
A. ( (y+6)2 )
Explanation
Simple Explanation
\(36=6^2\) और \(12y=2\cdot y\cdot6\) है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें। / \(36=6^2\) and \(12y=2\cdot y\cdot6\). Exam tip: identify perfect square trinomials.
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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
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A ( (r+7)(r-7) )
B ( (7+r)(7-r) )
C ( (49+r)(49-r) )
D ( (7-r)2 )
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Correct Answer
B. ( (7+r)(7-r) )
Explanation
Simple Explanation
(49-r-2 =72 -r-2 =(7+r)(7-r)) है। परीक्षा में बड़े वर्ग को पहले रखें। / (49-r-2 =72 -r-2 =(7+r)(7-r)). Exam tip: keep the larger square first.
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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
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A ( (5x-4)2 )
B ( (25x-4)(x+4) )
C ( (5x+4)(5x-4) )
D ( (5x+4)2 )
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Correct Answer
C. ( (5x+4)(5x-4) )
Explanation
Simple Explanation
(25x-2 -16=(5x)2 -42 =(5x+4)(5x-4))। परीक्षा में दोनों वर्ग पहचानें। / (25x-2 -16=(5x)2 -42 =(5x+4)(5x-4)). Exam tip: identify both squares.
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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
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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
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Correct Answer
B. ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a)
Explanation
Simple Explanation
( (a+1)2 =a-2 +2a+1 ), इसलिए \(a^2+1\) अधूरा है। परीक्षा में मध्य पद न छोड़ें। / ( (a+1)2 =a-2 +2a+1 ), so \(a^2+1\) is incomplete. Exam tip: do not omit the middle term.
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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
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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 )
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Correct Answer
A. ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1))
Explanation
Simple Explanation
पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर है। परीक्षा में कोष्ठक और वर्गों का अंतर अलग रखें। / The first is a perfect square and the second is difference of squares. Exam tip: keep bracket square and difference of squares separate.
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( (2a+3)(2a-3) ) को सरल कीजिए।
Simplify ( (2a+3)(2a-3) ).
#simplification
#difference of squares
#2a plus 3
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A \(4a^2+9\)
B \(4a^2-9\)
C \(2a^2-9\)
D \(4a^2-12a+9\)
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Correct Answer
B. \(4a^2-9\)
Explanation
Simple Explanation
यह ( (p+q)(p-q)=p-2 -q-2 ) है। यहाँ (p=2a) और (q=3) लें। / This is ( (p+q)(p-q)=p-2 -q-2 ). Here take (p=2a) and (q=3).
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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
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A (6x)
B (36x)
C (12x)
D (1x)
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Explanation
Simple Explanation
मध्य पद \(2\cdot6x\cdot1=12x\) है। परीक्षा में (2ab) का प्रयोग करें। / The middle term is \(2\cdot6x\cdot1=12x\). Exam tip: use (2ab).
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( (4p-1)2 ) का विस्तार क्या है?
What is the expansion of ( (4p-1)2 )?
#expansion
#4p minus 1
#identity
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A \(16p^2+8p+1\)
B \(16p^2-4p+1\)
C \(4p^2-8p+1\)
D \(16p^2-8p+1\)
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Correct Answer
D. \(16p^2-8p+1\)
Explanation
Simple Explanation
( (4p-1)2 =16p-2 -8p+1 ) है। परीक्षा में \(2\cdot4p\cdot1=8p\) और ऋण चिह्न याद रखें। / ( (4p-1)2 =16p-2 -8p+1 ). Exam tip: remember \(2\cdot4p\cdot1=8p\) and the negative sign.
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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
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A ( (100+4)2 )
B ( (104-4)2 )
C ( (50+54)(50-54) )
D \(104^2-4^2\)
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Correct Answer
A. ( (100+4)2 )
Explanation
Simple Explanation
(104=100+4), इसलिए ( (100+4)2 ) उपयुक्त है। परीक्षा में नजदीकी पूर्ण संख्या चुनें। / (104=100+4), so ( (100+4)2 ) is suitable. Exam tip: choose a nearby round number.
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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
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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)
Explanation
Simple Explanation
दोनों में \(x^2\) और (64) समान रहते हैं, केवल मध्य पद का चिह्न बदलता है। परीक्षा में चिह्न तुलना करें। / In both, \(x^2\) and (64) remain same; only the sign of the middle term changes. Exam tip: compare signs.
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पहचानों का मुख्य उपयोग क्या है?
What is the main use of identities?
#algebraic identities
#use
#simplification
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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
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Correct Answer
C. व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly
Explanation
Simple Explanation
बीजीय पहचानें गणना को छोटा और व्यवस्थित बनाती हैं। परीक्षा में पहचान पहचानकर सीधे लागू करें। / Algebraic identities make calculation shorter and systematic. Exam tip: identify the identity and apply it directly.
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