80 results found for "Exploring Algebraic Identities" in all classes.
( (2x+y+3)2 -(2x-y+3)2 ) का सरल रूप कौन-सा है?
Which is the simplified form of ( (2x+y+3)2 -(2x-y+3)2 )?
#grouping identity
#square difference
#three terms
A (4y(2x+3)) / सही समूह रूप
B (2y(2x+3)) / आधा मान
C \(4x^2-y^2+9\) / गलत पहचान
D (8xy+6y) / स्थिर भाग अधूरा
Explanation opens after your attempt
Correct Answer
A. (4y(2x+3)) / सही समूह रूप
Step 1
Concept
Take (A=2x+3) and (B=y), then apply ( (A+B)2 -(A-B)2 =4AB ). Exam tip: identify the complete group.
Step 2
Why this answer is correct
The correct answer is A. (4y(2x+3)) / सही समूह रूप. Take (A=2x+3) and (B=y), then apply ( (A+B)2 -(A-B)2 =4AB ). Exam tip: identify the complete group.
Step 3
Exam Tip
इसे (A=2x+3) और (B=y) मानकर ( (A+B)2 -(A-B)2 =4AB ) लगाएँ। परीक्षा में पूरा समूह पहचानें।
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यदि (a+b=9) और (ab=20) हो तो \(a^3+b^3\) का मान क्या है?
If (a+b=9) and (ab=20), what is the value of \(a^3+b^3\)?
#given values
#sum of cubes
#identity application
A (729) / केवल योग का घन
B (540) / केवल (3ab(a+b))
C (189) / सही मान
D (209) / घटाव गलती
Explanation opens after your attempt
Correct Answer
C. (189) / सही मान
Step 1
Concept
Apply (a-3 +b-3 =(a+b)3 -3ab(a+b)). We get (729-540=189).
Step 2
Why this answer is correct
The correct answer is C. (189) / सही मान. Apply (a-3 +b-3 =(a+b)3 -3ab(a+b)). We get (729-540=189).
Step 3
Exam Tip
(a-3 +b-3 =(a+b)3 -3ab(a+b)) लगाएँ। (729-540=189) मिलता है।
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\(125x^3+216y^3\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(125x^3+216y^3\)?
#sum of cubes
#factorisation
#125x cube 216y cube
A ( (5x-6y)\(25x^2+30xy+36y^2\) ) / अंतर का घन
B ( (5x+6y)\(25x^2-30xy+36y^2\) ) / सही रूप
C ( (125x+216y)\(x^2-xy+y^2\) ) / घनमूल गलत
D ( (5x+6y)3 ) / अलग विस्तार
Explanation opens after your attempt
Correct Answer
B. ( (5x+6y)\(25x^2-30xy+36y^2\) ) / सही रूप
Step 1
Concept
This is ( (5x)3 +(6y)3 ). In sum of cubes, the second factor has the form \(a^2-ab+b^2\).
Step 2
Why this answer is correct
The correct answer is B. ( (5x+6y)\(25x^2-30xy+36y^2\) ) / सही रूप. This is ( (5x)3 +(6y)3 ). In sum of cubes, the second factor has the form \(a^2-ab+b^2\).
Step 3
Exam Tip
यह ( (5x)3 +(6y)3 ) है। घनों के योग में दूसरा गुणनखंड \(a^2-ab+b^2\) रूप का होता है।
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( (x+2y)3 +(x-2y)3 ) का सरल रूप क्या है?
What is the simplified form of ( (x+2y)3 +(x-2y)3 )?
#cube identity
#sum of cubes forms
#simplification
A \(2x^3+24xy^2\) / सही रूप
B \(2x^3+12xy^2\) / आधा पद
C \(2x^3+8y^3\) / घन पद गलत
D \(6x^2y+16y^3\) / गलत पद
Explanation opens after your attempt
Correct Answer
A. \(2x^3+24xy^2\) / सही रूप
Step 1
Concept
Use ( (a+b)3 +(a-b)3 =2a-3 +6ab-2 ). Here (a=x) and (b=2y), so the result is \(2x^3+24xy^2\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^3+24xy^2\) / सही रूप. Use ( (a+b)3 +(a-b)3 =2a-3 +6ab-2 ). Here (a=x) and (b=2y), so the result is \(2x^3+24xy^2\).
Step 3
Exam Tip
( (a+b)3 +(a-b)3 =2a-3 +6ab-2 ) लगाएँ। यहाँ (a=x) और (b=2y) लेने से \(2x^3+24xy^2\) मिलता है।
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यदि (a+b+c=9) और (ab+bc+ca=20) है तो \(a^2+b^2+c^2\) कितना होगा?
If (a+b+c=9) and (ab+bc+ca=20), what is \(a^2+b^2+c^2\)?
#three term square
#given values
#sum of squares
A (41)
B (49)
C (61)
D (81)
Explanation opens after your attempt
Step 1
Concept
(a-2 +b-2 +c-2 =(a+b+c)2 -2(ab+bc+ca)=81-40=41). Exam tip: directly use the square identity of three terms.
Step 2
Why this answer is correct
The correct answer is A. (41). (a-2 +b-2 +c-2 =(a+b+c)2 -2(ab+bc+ca)=81-40=41). Exam tip: directly use the square identity of three terms.
Step 3
Exam Tip
(a-2 +b-2 +c-2 =(a+b+c)2 -2(ab+bc+ca)=81-40=41)। परीक्षा में तीन पदों की वर्ग पहचान सीधे लगाएँ।
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\(27a^3+8b^3\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factor form of \(27a^3+8b^3\)?
#sum of cubes
#factorization
#algebraic identities
A ( (3a-2b)\(9a^2+6ab+4b^2\) )
B ( (3a+2b)\(9a^2+6ab+4b^2\) )
C ( (27a+8b)\(a^2-ab+b^2\) )
D ( (3a+2b)\(9a^2-6ab+4b^2\) )
Explanation opens after your attempt
Correct Answer
D. ( (3a+2b)\(9a^2-6ab+4b^2\) )
Step 1
Concept
This is ((3a)3 +(2b)3 ), so the sum of cubes identity applies. Exam tip: the middle term inside the second factor is negative.
Step 2
Why this answer is correct
The correct answer is D. ( (3a+2b)\(9a^2-6ab+4b^2\) ). This is ((3a)3 +(2b)3 ), so the sum of cubes identity applies. Exam tip: the middle term inside the second factor is negative.
Step 3
Exam Tip
यह ((3a)3 +(2b)3 ) है इसलिए \(a^3+b^3\) की पहचान लगेगी। परीक्षा में योग घन में बीच वाला पद ऋणात्मक होता है।
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यदि \(x+\frac{1}{x}=7\) है तो \(x^3+\frac{1}{x^3}\) का मान क्या होगा?
If \(x+\frac{1}{x}=7\), what is the value of \(x^3+\frac{1}{x^3}\)?
#reciprocal identity
#cube identity
#expert
A (336)
B (322)
C (343)
D (364)
Explanation opens after your attempt
Step 1
Concept
Use (a-3 +b-3 =(a+b)3 -3ab(a+b)) where (ab=1). Exam tip: remember \(7^3-3\times7=322\).
Step 2
Why this answer is correct
The correct answer is B. (322). Use (a-3 +b-3 =(a+b)3 -3ab(a+b)) where (ab=1). Exam tip: remember \(7^3-3\times7=322\).
Step 3
Exam Tip
पहचान (a-3 +b-3 =(a+b)3 -3ab(a+b)) लगाएँ जहाँ (ab=1)। परीक्षा में \(7^3-3\times7=322\) याद रखें।
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( (x+6)2 -(x+2)(x+10) ) का सरल मान क्या है?
What is the simplified value of ( (x+6)2 -(x+2)(x+10) )?
#combined identities
#binomial product
#simplification
A (8)
B (12)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
The first expansion is \(x^2+12x+36\) and the second is \(x^2+12x+20\). Exam tip: cancel like terms and compare constants.
Step 2
Why this answer is correct
The correct answer is C. (16). The first expansion is \(x^2+12x+36\) and the second is \(x^2+12x+20\). Exam tip: cancel like terms and compare constants.
Step 3
Exam Tip
पहला विस्तार \(x^2+12x+36\) और दूसरा \(x^2+12x+20\) है। परीक्षा में समान पद काटकर स्थिर पदों का अंतर लें।
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विशेष बीजीय पहचान लगाते समय सबसे सुरक्षित जाँच कौन-सी है?
What is the safest check while applying a special algebraic identity?
#exam strategy
#algebraic identities
#accuracy
A पूरे पद, चिह्न, घात और मध्य पद को अलग-अलग जाँचना / check complete terms, signs, powers, and middle term separately
B केवल पहली संख्या देखकर उत्तर लिखना / write the answer by seeing only the first number
C हर व्यंजक को \(a^2-b^2\) मान लेना / treat every expression as \(a^2-b^2\)
D मध्य पद को हमेशा छोड़ देना / always omit the middle term
Explanation opens after your attempt
Correct Answer
A. पूरे पद, चिह्न, घात और मध्य पद को अलग-अलग जाँचना / check complete terms, signs, powers, and middle term separately
Step 1
Concept
Most mistakes happen due to incomplete terms or wrong signs. Exam tip: identify the terms before applying the formula.
Step 2
Why this answer is correct
The correct answer is A. पूरे पद, चिह्न, घात और मध्य पद को अलग-अलग जाँचना / check complete terms, signs, powers, and middle term separately. Most mistakes happen due to incomplete terms or wrong signs. Exam tip: identify the terms before applying the formula.
Step 3
Exam Tip
अधिकतर गलतियाँ अधूरे पद या गलत चिह्न से होती हैं। परीक्षा में सूत्र लगाने से पहले पदों की पहचान करें।
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( (4a+b)3 -(4a-b)3 ) में \(ab^2\) वाला पद क्या होगा?
What will be the term containing \(ab^2\) in ( (4a+b)3 -(4a-b)3 )?
#cube difference
#term identification
#ab square
A \(24ab^2\) / सही पद
B \(12ab^2\) / आधा पद
C \(8ab^2\) / कम गुणक
D \(32a^3\) / घन पद
Explanation opens after your attempt
Correct Answer
A. \(24ab^2\) / सही पद
Step 1
Concept
On expanding both cubes, the \(ab^2\) terms \(12ab^2\) and \(-12ab^2\) combine under subtraction to give \(24ab^2\).
Step 2
Why this answer is correct
The correct answer is A. \(24ab^2\) / सही पद. On expanding both cubes, the \(ab^2\) terms \(12ab^2\) and \(-12ab^2\) combine under subtraction to give \(24ab^2\).
Step 3
Exam Tip
दोनों घन फैलाने पर \(ab^2\) वाले पद \(12ab^2\) और \(-12ab^2\) घटाव से मिलकर \(24ab^2\) देते हैं।
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( (3x+2)2 -(3x-2)2 +(x+5)(x-5) ) का सरल रूप क्या है?
What is the simplified form of ( (3x+2)2 -(3x-2)2 +(x+5)(x-5) )?
#mixed identities
#simplification
#expert
A \(x^2+24x-25\) / सही रूप
B \(x^2+12x-25\) / आधा अंतर
C \(9x^2+24x-25\) / गलत वर्ग पद
D (24x+25) / वर्गों का अंतर गलत
Explanation opens after your attempt
Correct Answer
A. \(x^2+24x-25\) / सही रूप
Step 1
Concept
The difference of the first two squares is (24x), and ( (x+5)(x-5)=x-2 -25 ). Exam tip: combine identities while solving.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+24x-25\) / सही रूप. The difference of the first two squares is (24x), and ( (x+5)(x-5)=x-2 -25 ). Exam tip: combine identities while solving.
Step 3
Exam Tip
पहले दो वर्गों का अंतर (24x) है और ( (x+5)(x-5)=x-2 -25 ) है। परीक्षा में पहचानें जोड़कर हल करें।
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( (2x+3y+4)2 ) में (xy), (x) और (y) वाले पदों का योग क्या है?
What is the sum of the terms containing (xy), (x), and (y) in ( (2x+3y+4)2 )?
#three term square
#pair products
#constant term
A (12xy+16x+24y) / सही योग
B (6xy+8x+12y) / आधा परिणाम
C (24xy+16x+12y) / (xy) पद गलत
D \(4x^2+9y^2+16\) / वर्ग पद
Explanation opens after your attempt
Correct Answer
A. (12xy+16x+24y) / सही योग
Step 1
Concept
The pair terms are \(2\cdot2x\cdot3y=12xy\), \(2\cdot2x\cdot4=16x\), and \(2\cdot3y\cdot4=24y\).
Step 2
Why this answer is correct
The correct answer is A. (12xy+16x+24y) / सही योग. The pair terms are \(2\cdot2x\cdot3y=12xy\), \(2\cdot2x\cdot4=16x\), and \(2\cdot3y\cdot4=24y\).
Step 3
Exam Tip
जोड़ी पद \(2\cdot2x\cdot3y=12xy\), \(2\cdot2x\cdot4=16x\), और \(2\cdot3y\cdot4=24y\) हैं।
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( (x+y+4)2 -(x-y+4)2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+y+4)2 -(x-y+4)2 )?
#grouping identity
#square difference
#expert
A (4y(x+4)) / सही रूप
B (2y(x+4)) / आधा मान
C (4xy+4y) / स्थिर भाग अधूरा
D (4x+16y) / गुणन पद गलत
Explanation opens after your attempt
Correct Answer
A. (4y(x+4)) / सही रूप
Step 1
Concept
Take (A=x+4) and use ( (A+y)2 -(A-y)2 =4Ay ). Exam tip: group terms and take the complete term.
Step 2
Why this answer is correct
The correct answer is A. (4y(x+4)) / सही रूप. Take (A=x+4) and use ( (A+y)2 -(A-y)2 =4Ay ). Exam tip: group terms and take the complete term.
Step 3
Exam Tip
इसे (A=x+4) मानकर ( (A+y)2 -(A-y)2 =4Ay ) लगाएँ। परीक्षा में समूह बनाकर पूरा पद लें।
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यदि (a+b+c=12) और \(a^2+b^2+c^2=54\) हो तो (ab+bc+ca) क्या होगा?
If (a+b+c=12) and \(a^2+b^2+c^2=54\), what is (ab+bc+ca)?
#three term identity
#given values
#ab bc ca
A (45) / सही मान
B (90) / दोहरा गुणन योग
C (144) / केवल योग का वर्ग
D (54) / वर्गों का योग
Explanation opens after your attempt
Correct Answer
A. (45) / सही मान
Step 1
Concept
(144=54+2(ab+bc+ca)), so (2(ab+bc+ca)=90), and the value is (45).
Step 2
Why this answer is correct
The correct answer is A. (45) / सही मान. (144=54+2(ab+bc+ca)), so (2(ab+bc+ca)=90), and the value is (45).
Step 3
Exam Tip
(144=54+2(ab+bc+ca)) इसलिए (2(ab+bc+ca)=90) और मान (45) है।
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( (x-5)3 -\(x^3-125\) ) का सरल रूप कौन-सा है?
Which is the simplified form of ( (x-5)3 -\(x^3-125\) )?
#cube simplification
#x minus 5
#factor form
A - (15x(x-5)) / सही रूप
B (15x(x-5)) / चिह्न गलत
C \(x^2-25\) / अलग पहचान
D (0) / मध्य पद बचते हैं
Explanation opens after your attempt
Correct Answer
A. - (15x(x-5)) / सही रूप
Step 1
Concept
( (x-5)3 =x-3 -15x-2 +75x-125 ). Subtracting gives (-15x-2 +75x=-15x(x-5)).
Step 2
Why this answer is correct
The correct answer is A. - (15x(x-5)) / सही रूप. ( (x-5)3 =x-3 -15x-2 +75x-125 ). Subtracting gives (-15x-2 +75x=-15x(x-5)).
Step 3
Exam Tip
( (x-5)3 =x-3 -15x-2 +75x-125 ) है। घटाने पर (-15x-2 +75x=-15x(x-5)) मिलता है।
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( (x+2)3 -\(x^3+8\) ) का सरल रूप क्या है?
What is the simplified form of ( (x+2)3 -\(x^3+8\) )?
#cube expansion
#simplification
#x plus 2
A (6x(x+2)) / सही रूप
B (6x(x-2)) / चिह्न गलत
C \(x^2+4\) / अधूरा
D (0) / मध्य पद बचते हैं
Explanation opens after your attempt
Correct Answer
A. (6x(x+2)) / सही रूप
Step 1
Concept
( (x+2)3 =x-3 +6x-2 +12x+8 ). The middle terms form (6x(x+2)).
Step 2
Why this answer is correct
The correct answer is A. (6x(x+2)) / सही रूप. ( (x+2)3 =x-3 +6x-2 +12x+8 ). The middle terms form (6x(x+2)).
Step 3
Exam Tip
( (x+2)3 =x-3 +6x-2 +12x+8 ) है। बीच के पद (6x(x+2)) बनाते हैं।
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\(216p^3-125q^3\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(216p^3-125q^3\)?
#difference of cubes
#factorisation
#216p cube
A ( (6p-5q)\(36p^2+30pq+25q^2\) ) / सही रूप
B ( (6p+5q)\(36p^2-30pq+25q^2\) ) / योग का घन
C ( (216p-125q)\(p^2+pq+q^2\) ) / घनमूल गलत
D ( (6p-5q)3 ) / अलग पहचान
Explanation opens after your attempt
Correct Answer
A. ( (6p-5q)\(36p^2+30pq+25q^2\) ) / सही रूप
Step 1
Concept
This is ( (6p)3 -(5q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.
Step 2
Why this answer is correct
The correct answer is A. ( (6p-5q)\(36p^2+30pq+25q^2\) ) / सही रूप. This is ( (6p)3 -(5q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.
Step 3
Exam Tip
यह ( (6p)3 -(5q)3 ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड धन पदों वाला रखें।
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\( 27a^3+64b^3 \) का गुणनखंडन कौन-सा है?
Which is the factorisation of \(27a^3+64b^3\)?
#sum of cubes
#factorisation
#27a cube 64b cube
A ( (3a+4b)\(9a^2-12ab+16b^2\) ) / सही रूप
B ( (3a-4b)\(9a^2+12ab+16b^2\) ) / अंतर का घन
C ( (27a+64b)\(a^2-ab+b^2\) ) / घनमूल गलत
D ( (3a+4b)3 ) / अलग विस्तार
Explanation opens after your attempt
Correct Answer
A. ( (3a+4b)\(9a^2-12ab+16b^2\) ) / सही रूप
Step 1
Concept
This is ( (3a)3 +(4b)3 ). Exam tip: identify cube roots and apply the sum of cubes identity.
Step 2
Why this answer is correct
The correct answer is A. ( (3a+4b)\(9a^2-12ab+16b^2\) ) / सही रूप. This is ( (3a)3 +(4b)3 ). Exam tip: identify cube roots and apply the sum of cubes identity.
Step 3
Exam Tip
यह ( (3a)3 +(4b)3 ) है। परीक्षा में घनमूल पहचानकर घनों के योग की पहचान लगाएँ।
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( (3x+4)3 ) का सही विस्तार क्या है?
What is the correct expansion of ( (3x+4)3 )?
#cube identity
#3x plus 4
#expansion
A \(27x^3+108x^2+144x+64\) / सही विस्तार
B \(27x^3+36x^2+144x+64\) / \(x^2\) पद गलत
C \(3x^3+36x^2+64\) / पद छूटे
D \(27x^3-108x^2+144x-64\) / गलत चिह्न
Explanation opens after your attempt
Correct Answer
A. \(27x^3+108x^2+144x+64\) / सही विस्तार
Step 1
Concept
( (3x)3 =27x-3 ), (3(3x)2 \cdot4=108x-2 ), and (3(3x)\cdot16=144x). Exam tip: check the power of every term.
Step 2
Why this answer is correct
The correct answer is A. \(27x^3+108x^2+144x+64\) / सही विस्तार. ( (3x)3 =27x-3 ), (3(3x)2 \cdot4=108x-2 ), and (3(3x)\cdot16=144x). Exam tip: check the power of every term.
Step 3
Exam Tip
( (3x)3 =27x-3 ), (3(3x)2 \cdot4=108x-2 ), और (3(3x)\cdot16=144x) है। परीक्षा में हर पद की घात जाँचें।
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( (x-4)3 ) का सही विस्तार कौन-सा है?
Which is the correct expansion of ( (x-4)3 )?
#cube expansion
#x minus 4
#signs
A \(x^3-12x^2+48x-64\) / सही विस्तार
B \(x^3+12x^2+48x+64\) / चिह्न गलत
C \(x^3-64\) / मध्य पद नहीं
D \(x^3-4x^2+16x-64\) / गुणांक गलत
Explanation opens after your attempt
Correct Answer
A. \(x^3-12x^2+48x-64\) / सही विस्तार
Step 1
Concept
In the cube of a difference, signs follow (+), (-), (+), (-). Exam tip: check both \(4^2\) and \(4^3\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-12x^2+48x-64\) / सही विस्तार. In the cube of a difference, signs follow (+), (-), (+), (-). Exam tip: check both \(4^2\) and \(4^3\).
Step 3
Exam Tip
घटाव के घन में चिह्न (+), (-), (+), (-) क्रम में आते हैं। परीक्षा में \(4^2\) और \(4^3\) दोनों देखें।
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( (2x+5y)3 ) में \(xy^2\) का गुणांक क्या होगा?
What is the coefficient of \(xy^2\) in ( (2x+5y)3 )?
#cube expansion
#coefficient
#xy square
A (150) / सही गुणांक
B (75) / आधा मान
C (50) / कम मान
D (250) / गलत घात
Explanation opens after your attempt
Correct Answer
A. (150) / सही गुणांक
Step 1
Concept
(3(2x)(5y)2 =150xy-2 ). Exam tip: square the second term completely.
Step 2
Why this answer is correct
The correct answer is A. (150) / सही गुणांक. (3(2x)(5y)2 =150xy-2 ). Exam tip: square the second term completely.
Step 3
Exam Tip
(3(2x)(5y)2 =150xy-2 ) है। परीक्षा में दूसरे पद का वर्ग पूरा करें।
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( (5x-4y)2 -25x-2 -16y-2 ) का सरल रूप क्या है?
What is the simplified form of ( (5x-4y)2 -25x-2 -16y-2 )?
#minus square
#negative middle term
#simplification
A (40xy) / चिह्न गलत
B (-40xy) / सही रूप
C \(25x^2-16y^2\) / वर्गों का अंतर
D (0) / मध्य पद बचता है
Explanation opens after your attempt
Correct Answer
B. (-40xy) / सही रूप
Step 1
Concept
( (5x-4y)2 =25x-2 -40xy+16y-2 ). After square terms are removed, (-40xy) remains.
Step 2
Why this answer is correct
The correct answer is B. (-40xy) / सही रूप. ( (5x-4y)2 =25x-2 -40xy+16y-2 ). After square terms are removed, (-40xy) remains.
Step 3
Exam Tip
( (5x-4y)2 =25x-2 -40xy+16y-2 ) है। वर्ग पद हटने पर (-40xy) बचता है।
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( (x+3y)2 -x-2 -9y-2 -6xy ) का मान क्या है?
What is the value of ( (x+3y)2 -x-2 -9y-2 -6xy )?
#identity verification
#zero
#binomial square
A (0) / सही मान
B (6xy) / मध्य पद
C (3xy) / आधा पद
D \(x^2-9y^2\) / अलग पहचान
Explanation opens after your attempt
Correct Answer
A. (0) / सही मान
Step 1
Concept
( (x+3y)2 =x-2 +6xy+9y-2 ). Subtracting all terms gives (0).
Step 2
Why this answer is correct
The correct answer is A. (0) / सही मान. ( (x+3y)2 =x-2 +6xy+9y-2 ). Subtracting all terms gives (0).
Step 3
Exam Tip
( (x+3y)2 =x-2 +6xy+9y-2 ) है। सभी पद घटाने पर (0) मिलता है।
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( (2x+1)(2x+5)(2x+9) ) में पहले ( (2x+1)(2x+9) ) लगाने पर क्या मिलेगा?
When first applying ( (2x+1)(2x+9) ) in ( (2x+1)(2x+5)(2x+9) ), what is obtained?
#partial expansion
#three factors
#step method
A \(4x^2+20x+9\) / सही आंशिक विस्तार
B \(4x^2+10x+9\) / मध्य पद कम
C \(4x^2+18x+5\) / स्थिर पद गलत
D \(8x^3+45\) / पूरा विस्तार नहीं
Explanation opens after your attempt
Correct Answer
A. \(4x^2+20x+9\) / सही आंशिक विस्तार
Step 1
Concept
( (2x+1)(2x+9)=4x-2 +20x+9 ). Exam tip: do long multiplication in small steps.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+20x+9\) / सही आंशिक विस्तार. ( (2x+1)(2x+9)=4x-2 +20x+9 ). Exam tip: do long multiplication in small steps.
Step 3
Exam Tip
( (2x+1)(2x+9)=4x-2 +20x+9 ) है। परीक्षा में लंबा गुणन छोटे चरणों में करें।
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( (x+3)(x+5)(x+7) ) का पूरा विस्तार क्या है?
What is the full expansion of ( (x+3)(x+5)(x+7) )?
#three factors
#polynomial expansion
#expert
A \(x^3+15x^2+71x+105\) / सही विस्तार
B \(x^3+12x^2+71x+105\) / \(x^2\) पद गलत
C \(x^3+15x+105\) / पद छूटे
D \(x^3+71x^2+15x+105\) / पद उलटे
Explanation opens after your attempt
Correct Answer
A. \(x^3+15x^2+71x+105\) / सही विस्तार
Step 1
Concept
Expand two factors first and then multiply by the third. Exam tip: combine like terms in order.
Step 2
Why this answer is correct
The correct answer is A. \(x^3+15x^2+71x+105\) / सही विस्तार. Expand two factors first and then multiply by the third. Exam tip: combine like terms in order.
Step 3
Exam Tip
पहले दो गुणनखंडों को फैलाकर तीसरे से गुणा करें। परीक्षा में समान पदों को क्रम से जोड़ें।
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यदि (x+y+z=10) और (xy+yz+zx=28) हो तो \(x^2+y^2+z^2\) क्या है?
If (x+y+z=10) and (xy+yz+zx=28), what is \(x^2+y^2+z^2\)?
#three term identity
#given values
#sum of squares
A (44) / सही मान
B (100) / केवल योग का वर्ग
C (56) / केवल दोहरा गुणन
D (72) / घटाव गलत
Explanation opens after your attempt
Correct Answer
A. (44) / सही मान
Step 1
Concept
(100=x-2 +y-2 +z-2 +2(28)). Therefore \(x^2+y^2+z^2=44\).
Step 2
Why this answer is correct
The correct answer is A. (44) / सही मान. (100=x-2 +y-2 +z-2 +2(28)). Therefore \(x^2+y^2+z^2=44\).
Step 3
Exam Tip
(100=x-2 +y-2 +z-2 +2(28)) है। इसलिए \(x^2+y^2+z^2=44\) मिलता है।
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यदि (a+b=18) और (a-b=6) हो तो (ab) का मान क्या है?
If (a+b=18) and (a-b=6), what is the value of (ab)?
#given values
#ab
#square difference
A (72) / सही मान
B (36) / आधा मान
C (108) / योग और अंतर का गुणन
D (144) / वर्ग गलती
Explanation opens after your attempt
Correct Answer
A. (72) / सही मान
Step 1
Concept
From ( (a+b)2 -(a-b)2 =4ab ), (324-36=288=4ab), so (ab=72).
Step 2
Why this answer is correct
The correct answer is A. (72) / सही मान. From ( (a+b)2 -(a-b)2 =4ab ), (324-36=288=4ab), so (ab=72).
Step 3
Exam Tip
( (a+b)2 -(a-b)2 =4ab ) से (324-36=288=4ab), इसलिए (ab=72)।
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यदि (m+n=14) और \(m^2+n^2=100\) हो तो (mn) क्या होगा?
If (m+n=14) and \(m^2+n^2=100\), what is (mn)?
#given values
#mn
#identity application
A (48) / सही मान
B (96) / (2mn) का मान
C (100) / वर्गों का योग
D (14) / केवल योग
Explanation opens after your attempt
Correct Answer
A. (48) / सही मान
Step 1
Concept
Using ( (m+n)2 =m-2 +2mn+n-2 ), (196=100+2mn), so (mn=48). Exam tip: find (2mn) first.
Step 2
Why this answer is correct
The correct answer is A. (48) / सही मान. Using ( (m+n)2 =m-2 +2mn+n-2 ), (196=100+2mn), so (mn=48). Exam tip: find (2mn) first.
Step 3
Exam Tip
( (m+n)2 =m-2 +2mn+n-2 ) से (196=100+2mn), इसलिए (mn=48)। परीक्षा में पहले (2mn) निकालें।
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यदि (p-q=9) और (pq=22) हो तो \(p^2+q^2\) कितना होगा?
If (p-q=9) and (pq=22), what is \(p^2+q^2\)?
#given values
#p square plus q square
#identity
A (81) / केवल अंतर का वर्ग
B (103) / गलत जोड़
C (125) / सही मान
D (44) / केवल (2pq)
Explanation opens after your attempt
Correct Answer
C. (125) / सही मान
Step 1
Concept
(p-2 +q-2 =(p-q)2 +2pq=81+44=125). Exam tip: do not forget to add (2pq).
Step 2
Why this answer is correct
The correct answer is C. (125) / सही मान. (p-2 +q-2 =(p-q)2 +2pq=81+44=125). Exam tip: do not forget to add (2pq).
Step 3
Exam Tip
(p-2 +q-2 =(p-q)2 +2pq=81+44=125)। परीक्षा में (2pq) जोड़ना न भूलें।
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यदि (x+y=17) और (xy=60) हो तो \(x^2+y^2\) का मान क्या है?
If (x+y=17) and (xy=60), what is the value of \(x^2+y^2\)?
#given values
#sum of squares
#identity application
A (169) / केवल योग का वर्ग
B (120) / केवल (2xy)
C (229) / (xy) जोड़ा
D (169) / गलत दोहराव
Explanation opens after your attempt
Correct Answer
A. (169) / केवल योग का वर्ग
Step 1
Concept
(x-2 +y-2 =(x+y)2 -2xy=289-120=169). Exam tip: subtract (2xy) from the square of the sum.
Step 2
Why this answer is correct
The correct answer is A. (169) / केवल योग का वर्ग. (x-2 +y-2 =(x+y)2 -2xy=289-120=169). Exam tip: subtract (2xy) from the square of the sum.
Step 3
Exam Tip
(x-2 +y-2 =(x+y)2 -2xy=289-120=169)। परीक्षा में योग के वर्ग से (2xy) घटाएँ।
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( (a+b)3 -\(a^3+b^3\) ) का गुणनखंड रूप क्या है?
What is the factor form of ( (a+b)3 -\(a^3+b^3\) )?
#cube expansion
#factor form
#3ab
A (3ab(a+b)) / सही रूप
B (3ab(a-b)) / चिह्न गलत
C \(a^2+b^2\) / अधूरा
D (0) / मध्य पद बचते हैं
Explanation opens after your attempt
Correct Answer
A. (3ab(a+b)) / सही रूप
Step 1
Concept
The middle terms in the cube expansion are \(3a^2b+3ab^2\). They are written as (3ab(a+b)).
Step 2
Why this answer is correct
The correct answer is A. (3ab(a+b)) / सही रूप. The middle terms in the cube expansion are \(3a^2b+3ab^2\). They are written as (3ab(a+b)).
Step 3
Exam Tip
घन विस्तार के मध्य पद \(3a^2b+3ab^2\) हैं। इन्हें (3ab(a+b)) के रूप में लिखा जाता है।
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\( 27p^3-64q^3 \) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(27p^3-64q^3\).
#difference of cubes
#factorisation
#27p cube
A ( (3p+4q)\(9p^2-12pq+16q^2\) ) / योग का घन
B ( (27p-64q)\(p^2+pq+q^2\) ) / घनमूल गलत
C ( (3p-4q)3 ) / अलग पहचान
D ( (3p-4q)\(9p^2+12pq+16q^2\) ) / सही रूप
Explanation opens after your attempt
Correct Answer
D. ( (3p-4q)\(9p^2+12pq+16q^2\) ) / सही रूप
Step 1
Concept
This is ( (3p)3 -(4q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.
Step 2
Why this answer is correct
The correct answer is D. ( (3p-4q)\(9p^2+12pq+16q^2\) ) / सही रूप. This is ( (3p)3 -(4q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.
Step 3
Exam Tip
यह ( (3p)3 -(4q)3 ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड धन पदों वाला रखें।
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\( a^3+216b^3 \) का गुणनखंडन क्या है?
What is the factorisation of \(a^3+216b^3\)?
#sum of cubes
#factorisation
#a cube 216b cube
A ( (a-6b)\(a^2+6ab+36b^2\) ) / अंतर का घन
B ( (a+6b)3 ) / अलग विस्तार
C ( (a+6b)\(a^2-6ab+36b^2\) ) / सही रूप
D ( (a+216b)\(a^2-ab+b^2\) ) / घनमूल गलत
Explanation opens after your attempt
Correct Answer
C. ( (a+6b)\(a^2-6ab+36b^2\) ) / सही रूप
Step 1
Concept
This is (a-3 +(6b)3 ). In sum of cubes, the second factor is \(a^2-6ab+36b^2\).
Step 2
Why this answer is correct
The correct answer is C. ( (a+6b)\(a^2-6ab+36b^2\) ) / सही रूप. This is (a-3 +(6b)3 ). In sum of cubes, the second factor is \(a^2-6ab+36b^2\).
Step 3
Exam Tip
यह (a-3 +(6b)3 ) है। घनों के योग में दूसरा गुणनखंड \(a^2-6ab+36b^2\) होता है।
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( (x+6)3 -(x-6)3 ) का पूरा सरल रूप क्या है?
What is the complete simplified form of ( (x+6)3 -(x-6)3 )?
#cube simplification
#x plus 6
#x minus 6
A \(36x^2+432\) / सही रूप
B \(18x^2+432\) / आधा \(x^2\) पद
C \(12x^3+432\) / घन पद बचा
D \(36x^2+216x\) / गलत पद
Explanation opens after your attempt
Correct Answer
A. \(36x^2+432\) / सही रूप
Step 1
Concept
In cube expansion, the \(x^3\) and (x) terms cancel. Exam tip: change signs while subtracting.
Step 2
Why this answer is correct
The correct answer is A. \(36x^2+432\) / सही रूप. In cube expansion, the \(x^3\) and (x) terms cancel. Exam tip: change signs while subtracting.
Step 3
Exam Tip
घन विस्तार में \(x^3\) और (x) वाले पद कट जाते हैं। परीक्षा में घटाव करते समय चिह्न बदलें।
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( (4a-b)3 ) में \(a^2b\) वाले पद का गुणांक क्या है?
What is the coefficient of the term containing \(a^2b\) in ( (4a-b)3 )?
#cube identity
#coefficient
#4a minus b
A - (48) / सही गुणांक
B (48) / चिह्न गलत
C - (12) / कम मान
D (64) / पहला घन
Explanation opens after your attempt
Correct Answer
A. - (48) / सही गुणांक
Step 1
Concept
In the cube of a difference, ( -3(4a)2 b=-48a-2 b ) appears. Exam tip: check sign and coefficient together.
Step 2
Why this answer is correct
The correct answer is A. - (48) / सही गुणांक. In the cube of a difference, ( -3(4a)2 b=-48a-2 b ) appears. Exam tip: check sign and coefficient together.
Step 3
Exam Tip
घटाव के घन में ( -3(4a)2 b=-48a-2 b ) आता है। परीक्षा में चिह्न और गुणांक साथ जाँचें।
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( (3x+2y)3 ) में \(x^2y\) का गुणांक क्या होगा?
What is the coefficient of \(x^2y\) in ( (3x+2y)3 )?
#cube expansion
#coefficient
#x square y
A (18) / आधा मान
B (54) / सही गुणांक
C (27) / पहले पद का घन
D (12) / कम मान
Explanation opens after your attempt
Correct Answer
B. (54) / सही गुणांक
Step 1
Concept
(3(3x)2 (2y)=54x-2 y). Exam tip: square the complete term (3x).
Step 2
Why this answer is correct
The correct answer is B. (54) / सही गुणांक. (3(3x)2 (2y)=54x-2 y). Exam tip: square the complete term (3x).
Step 3
Exam Tip
(3(3x)2 (2y)=54x-2 y) है। परीक्षा में पूरे (3x) का वर्ग करें।
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( (6x+5)2 +(6x-5)2 -72x-2 ) का मान क्या है?
What is the value of ( (6x+5)2 +(6x-5)2 -72x-2 )?
#sum identity
#constant value
#6x 5
A (25) / आधा स्थिर भाग
B (60x) / मध्य पद
C (50) / सही मान
D (0) / स्थिर पद बचता है
Explanation opens after your attempt
Correct Answer
C. (50) / सही मान
Step 1
Concept
The sum of the first two squares is \(72x^2+50\). After subtracting \(72x^2\), (50) remains.
Step 2
Why this answer is correct
The correct answer is C. (50) / सही मान. The sum of the first two squares is \(72x^2+50\). After subtracting \(72x^2\), (50) remains.
Step 3
Exam Tip
पहले दो वर्गों का योग \(72x^2+50\) है। \(72x^2\) घटाने पर (50) बचता है।
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( (8x+1)2 -(8x-1)2 ) का सरल रूप क्या है?
What is the simplified form of ( (8x+1)2 -(8x-1)2 )?
#square difference
#8x
#32x
A (16x) / आधा मान
B (32x) / सही मान
C \(64x^2-1\) / वर्गों का अंतर
D \(128x^2+2\) / योग पहचान
Explanation opens after your attempt
Correct Answer
B. (32x) / सही मान
Step 1
Concept
This is (4ab), where (a=8x) and (b=1), so (32x) is obtained. Exam tip: take the full term for (a).
Step 2
Why this answer is correct
The correct answer is B. (32x) / सही मान. This is (4ab), where (a=8x) and (b=1), so (32x) is obtained. Exam tip: take the full term for (a).
Step 3
Exam Tip
यह (4ab) है जहाँ (a=8x) और (b=1), इसलिए (32x) मिलता है। परीक्षा में (a) का पूरा पद लें।
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\( 305^2 \) को पहचान से निकालने पर सही मान क्या है?
What is the correct value of \(305^2\) using an identity?
#mental calculation
#305 square
#identity
A (93025) / सही मान
B (90025) / मध्य पद नहीं
C (91525) / मध्य पद कम
D (93500) / अंतिम पद गलत
Explanation opens after your attempt
Correct Answer
A. (93025) / सही मान
Step 1
Concept
(3052 =(300+5)2 =90000+3000+25=93025). Exam tip: add both (2ab) and \(b^2\).
Step 2
Why this answer is correct
The correct answer is A. (93025) / सही मान. (3052 =(300+5)2 =90000+3000+25=93025). Exam tip: add both (2ab) and \(b^2\).
Step 3
Exam Tip
(3052 =(300+5)2 =90000+3000+25=93025) होता है। परीक्षा में (2ab) और \(b^2\) दोनों जोड़ें।
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\( 1006^2-994^2 \) का मान क्या है?
What is the value of \(1006^2-994^2\)?
#difference of squares
#numerical identity
#large numbers
A (12000) / आधा मान
B (24000) / सही मान
C (2000) / केवल योग
D (12) / केवल अंतर
Explanation opens after your attempt
Correct Answer
B. (24000) / सही मान
Step 1
Concept
By difference of squares, ( (1006+994)(1006-994)=2000\cdot12=24000 ). Exam tip: multiply the sum and difference.
Step 2
Why this answer is correct
The correct answer is B. (24000) / सही मान. By difference of squares, ( (1006+994)(1006-994)=2000\cdot12=24000 ). Exam tip: multiply the sum and difference.
Step 3
Exam Tip
वर्गों के अंतर से ( (1006+994)(1006-994)=2000\cdot12=24000 )। परीक्षा में योग और अंतर का गुणन करें।
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\(998^2\) का सही मान क्या है?
What is the correct value of \(998^2\)?
#large square
#mental calculation
#identity
A (996004) / सही मान
B (998004) / मध्य पद गलत
C (1000004) / चिह्न गलत
D (996000) / अंतिम वर्ग नहीं
Explanation opens after your attempt
Correct Answer
A. (996004) / सही मान
Step 1
Concept
\(998^2=1000000-4000+4=996004\). Exam tip: subtract \(2\cdot1000\cdot2\).
Step 2
Why this answer is correct
The correct answer is A. (996004) / सही मान. \(998^2=1000000-4000+4=996004\). Exam tip: subtract \(2\cdot1000\cdot2\).
Step 3
Exam Tip
\(998^2=1000000-4000+4=996004\) है। परीक्षा में \(2\cdot1000\cdot2\) घटाएँ।
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\( 998^2 \) को पहचान से निकालने के लिए सबसे उपयुक्त रूप कौन-सा है?
Which form is most suitable for finding \(998^2\) using an identity?
#mental math
#998 square
#square identity
A ( (998+2)2 ) / मान बदलता है
B ( (1000-2)2 ) / सही रूप
C ( (1000+2)2 ) / गलत संख्या
D ( (998+2)(998-2) ) / वर्ग नहीं
Explanation opens after your attempt
Correct Answer
B. ( (1000-2)2 ) / सही रूप
Step 1
Concept
Since (998=1000-2), the square of difference identity is easiest. Exam tip: choose a nearby base.
Step 2
Why this answer is correct
The correct answer is B. ( (1000-2)2 ) / सही रूप. Since (998=1000-2), the square of difference identity is easiest. Exam tip: choose a nearby base.
Step 3
Exam Tip
(998=1000-2) इसलिए घटाव के वर्ग की पहचान सबसे आसान है। परीक्षा में निकट आधार चुनें।
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( (x+3y+4z)2 ) में (xy), (yz), और (xz) वाले पदों का योग क्या है?
What is the sum of the terms containing (xy), (yz), and (xz) in ( (x+3y+4z)2 )?
#three term identity
#pair terms
#xy yz xz
A (6xy+24yz+8xz) / सही योग
B (3xy+12yz+4xz) / आधा परिणाम
C (12xyz) / तीनों का गुणन
D \(x^2+9y^2+16z^2\) / वर्ग पद
Explanation opens after your attempt
Correct Answer
A. (6xy+24yz+8xz) / सही योग
Step 1
Concept
The (xy), (yz), and (xz) terms are (6xy), (24yz), and (8xz). Exam tip: find each pair separately.
Step 2
Why this answer is correct
The correct answer is A. (6xy+24yz+8xz) / सही योग. The (xy), (yz), and (xz) terms are (6xy), (24yz), and (8xz). Exam tip: find each pair separately.
Step 3
Exam Tip
(xy), (yz), और (xz) पद क्रमशः (6xy), (24yz), और (8xz) हैं। परीक्षा में प्रत्येक जोड़ी अलग निकालें।
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( (3a+b+c)2 -\(9a^2+b^2+c^2\) ) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying ( (3a+b+c)2 -\(9a^2+b^2+c^2\) )?
#three term square
#remaining terms
#expert
A (3ab+3ac+bc) / आधा परिणाम
B (6ab+6ac+2bc) / सही रूप
C (9abc) / तीनों का गुणन
D (0) / गुणन पद बचते हैं
Explanation opens after your attempt
Correct Answer
B. (6ab+6ac+2bc) / सही रूप
Step 1
Concept
The pair terms in the square are (6ab), (6ac), and (2bc). Exam tip: take the double product of every pair.
Step 2
Why this answer is correct
The correct answer is B. (6ab+6ac+2bc) / सही रूप. The pair terms in the square are (6ab), (6ac), and (2bc). Exam tip: take the double product of every pair.
Step 3
Exam Tip
तीन पदों के वर्ग में जोड़ी पद (6ab), (6ac), और (2bc) आते हैं। परीक्षा में हर जोड़ी का दोहरा गुणन करें।
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( (x+4)(x+10)-(x+6)(x+8) ) का मान क्या है?
What is the value of ( (x+4)(x+10)-(x+6)(x+8) )?
#linear products
#subtraction
#simplification
A (-8) / सही मान
B (8) / चिह्न गलत
C (2x) / चर पद नहीं बचेगा
D (0) / स्थिर पद अलग हैं
Explanation opens after your attempt
Correct Answer
A. (-8) / सही मान
Step 1
Concept
Both expansions have the same \(x^2+14x\), and constants give (40-48=-8). Exam tip: cancel like terms and subtract constants.
Step 2
Why this answer is correct
The correct answer is A. (-8) / सही मान. Both expansions have the same \(x^2+14x\), and constants give (40-48=-8). Exam tip: cancel like terms and subtract constants.
Step 3
Exam Tip
दोनों विस्तारों में \(x^2+14x\) समान है और स्थिर पद (40-48=-8) देता है। परीक्षा में समान पद काटकर स्थिर पद घटाएँ।
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( (a+b)2 +(a-b)2 -2a-2 -2b-2 ) का मान क्या है?
What is the value of ( (a+b)2 +(a-b)2 -2a-2 -2b-2 )?
#identity verification
#sum identity
#zero
A (4ab) / अंतर पहचान
B (2ab) / मध्य पद
C \(a^2-b^2\) / गलत पहचान
D (0) / सही मान
Explanation opens after your attempt
Correct Answer
D. (0) / सही मान
Step 1
Concept
The sum of the first two squares is \(2a^2+2b^2\). Subtracting the same expression gives zero.
Step 2
Why this answer is correct
The correct answer is D. (0) / सही मान. The sum of the first two squares is \(2a^2+2b^2\). Subtracting the same expression gives zero.
Step 3
Exam Tip
पहले दो वर्गों का योग \(2a^2+2b^2\) होता है। वही घटाने पर शून्य मिलता है।
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( (4m-3n)2 -\(16m^2+9n^2\) ) का मान क्या होगा?
What is the value of ( (4m-3n)2 -\(16m^2+9n^2\) )?
#negative middle term
#minus square
#simplification
A (24mn) / चिह्न गलत
B \(16m^2-9n^2\) / अलग पहचान
C (-24mn) / सही मान
D (0) / मध्य पद नहीं कटता
Explanation opens after your attempt
Correct Answer
C. (-24mn) / सही मान
Step 1
Concept
( (4m-3n)2 =16m-2 -24mn+9n-2 ). After square terms are removed, (-24mn) remains.
Step 2
Why this answer is correct
The correct answer is C. (-24mn) / सही मान. ( (4m-3n)2 =16m-2 -24mn+9n-2 ). After square terms are removed, (-24mn) remains.
Step 3
Exam Tip
( (4m-3n)2 =16m-2 -24mn+9n-2 ) है। वर्ग पद हटने पर (-24mn) बचता है।
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( (2x+5)2 -\(4x^2+25\) ) का सरल रूप क्या है?
What is the simplified form of ( (2x+5)2 -\(4x^2+25\) )?
#middle term
#simplification
#binomial square
A (10x) / आधा मध्य पद
B (20x) / सही उत्तर
C \(4x^2-25\) / वर्गों का अंतर
D (0) / मध्य पद बचता है
Explanation opens after your attempt
Correct Answer
B. (20x) / सही उत्तर
Step 1
Concept
( (2x+5)2 =4x-2 +20x+25 ). After subtracting the given square and constant terms, (20x) remains.
Step 2
Why this answer is correct
The correct answer is B. (20x) / सही उत्तर. ( (2x+5)2 =4x-2 +20x+25 ). After subtracting the given square and constant terms, (20x) remains.
Step 3
Exam Tip
( (2x+5)2 =4x-2 +20x+25 ) है। दिए गए वर्ग पद और स्थिर पद घटाने पर (20x) बचता है।
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( (x+12)(x-5) ) में (x) का गुणांक और स्थिर पद कौन-से हैं?
What are the coefficient of (x) and the constant term in ( (x+12)(x-5) )?
#linear factors
#coefficient
#constant term
A (17) और (-60) / गुणांक गलत
B (7) और (60) / स्थिर पद गलत
C (7) और (-60) / सही जोड़ा
D - (7) और (-60) / चिह्न गलत
Explanation opens after your attempt
Correct Answer
C. (7) और (-60) / सही जोड़ा
Step 1
Concept
The sum of constants is (12+(-5)=7) and the product is (-60). Exam tip: check sum and product separately with mixed signs.
Step 2
Why this answer is correct
The correct answer is C. (7) और (-60) / सही जोड़ा. The sum of constants is (12+(-5)=7) and the product is (-60). Exam tip: check sum and product separately with mixed signs.
Step 3
Exam Tip
स्थिर पदों का योग (12+(-5)=7) और गुणन (-60) है। परीक्षा में मिश्रित चिह्नों में योग और गुणन अलग जाँचें।
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\(81a^2-49b^2\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(81a^2-49b^2\)?
#difference of squares
#factorisation
#81a square
A ( (9a+7b)(9a-7b) ) / सही रूप
B ( (9a-7b)2 ) / पूर्ण वर्ग नहीं
C ( (81a+49b)(a-b) ) / वर्गमूल गलत
D ( (9a+7b)2 ) / योग का वर्ग
Explanation opens after your attempt
Correct Answer
A. ( (9a+7b)(9a-7b) ) / सही रूप
Step 1
Concept
This is ( (9a)2 -(7b)2 ). Exam tip: take both square roots correctly in difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ( (9a+7b)(9a-7b) ) / सही रूप. This is ( (9a)2 -(7b)2 ). Exam tip: take both square roots correctly in difference of squares.
Step 3
Exam Tip
यह ( (9a)2 -(7b)2 ) है। परीक्षा में वर्गों के अंतर में दोनों वर्गमूल सही लें।
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\(16x^2-40xy+25y^2\) किसका पूर्ण वर्ग है?
\(16x^2-40xy+25y^2\) is the perfect square of what?
#perfect square
#recognition
#factorisation
A ( (4x+5y)2 ) / चिह्न गलत
B ( (16x-25y)2 ) / वर्गमूल गलत
C ( (4x+5y)(4x-5y) ) / वर्गों का अंतर
D ( (4x-5y)2 ) / सही पूर्ण वर्ग
Explanation opens after your attempt
Correct Answer
D. ( (4x-5y)2 ) / सही पूर्ण वर्ग
Step 1
Concept
This is ( (4x)2 -2\cdot4x\cdot5y+(5y)2 ). Exam tip: identify a minus square from the negative middle term.
Step 2
Why this answer is correct
The correct answer is D. ( (4x-5y)2 ) / सही पूर्ण वर्ग. This is ( (4x)2 -2\cdot4x\cdot5y+(5y)2 ). Exam tip: identify a minus square from the negative middle term.
Step 3
Exam Tip
यह ( (4x)2 -2\cdot4x\cdot5y+(5y)2 ) है। परीक्षा में ऋण मध्य पद से घटाव वाला वर्ग पहचानें।
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( (3p+2q+r)2 ) में (pq), (pr) और (qr) वाले पदों का योग क्या होगा?
What is the sum of the terms containing (pq), (pr), and (qr) in ( (3p+2q+r)2 )?
#three term square
#double products
#pair terms
A (6pq+3pr+2qr) / आधा परिणाम
B (12pq+6pr+4qr) / सही योग
C (6pqr) / तीनों का गुणन
D \(9p^2+4q^2+r^2\) / वर्ग पद
Explanation opens after your attempt
Correct Answer
B. (12pq+6pr+4qr) / सही योग
Step 1
Concept
A three-term square has double products of every pair. Here the (pq), (pr), and (qr) terms are (12pq), (6pr), and (4qr).
Step 2
Why this answer is correct
The correct answer is B. (12pq+6pr+4qr) / सही योग. A three-term square has double products of every pair. Here the (pq), (pr), and (qr) terms are (12pq), (6pr), and (4qr).
Step 3
Exam Tip
तीन पदों के वर्ग में हर जोड़ी का दोहरा गुणन आता है। यहाँ (pq), (pr), (qr) पद क्रमशः (12pq), (6pr), (4qr) हैं।
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( (x+y+z)2 -(x-y+z)2 ) का सही सरल रूप कौन-सा है?
Which is the correct simplified form of ( (x+y+z)2 -(x-y+z)2 )?
#grouping identity
#three terms
#square difference
A (4y(x+z)) / सही रूप
B (2y(x+z)) / आधा मान
C (4xz) / गलत जोड़ी
D \(x^2-y^2+z^2\) / गलत पहचान
Explanation opens after your attempt
Correct Answer
A. (4y(x+z)) / सही रूप
Step 1
Concept
Take (A=x+z) and apply ( (A+y)2 -(A-y)2 =4Ay ). Exam tip: group terms before applying the identity.
Step 2
Why this answer is correct
The correct answer is A. (4y(x+z)) / सही रूप. Take (A=x+z) and apply ( (A+y)2 -(A-y)2 =4Ay ). Exam tip: group terms before applying the identity.
Step 3
Exam Tip
इसे (A=x+z) मानकर ( (A+y)2 -(A-y)2 =4Ay ) लगाएँ। परीक्षा में समूह बनाकर पहचान लगाएँ।
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( (5a-4b)2 +(5a+4b)2 ) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying ( (5a-4b)2 +(5a+4b)2 )?
#sum identity
#binomial square
#expert
A \(25a^2+16b^2\) / आधा परिणाम
B (40ab) / मध्य पद
C \(50a^2+32b^2\) / सही परिणाम
D \(50a^2-32b^2\) / गलत चिह्न
Explanation opens after your attempt
Correct Answer
C. \(50a^2+32b^2\) / सही परिणाम
Step 1
Concept
The sum identity gives (2(5a)2 +2(4b)2 =50a-2 +32b-2 ). Exam tip: notice the cancellation of middle terms.
Step 2
Why this answer is correct
The correct answer is C. \(50a^2+32b^2\) / सही परिणाम. The sum identity gives (2(5a)2 +2(4b)2 =50a-2 +32b-2 ). Exam tip: notice the cancellation of middle terms.
Step 3
Exam Tip
योग पहचान से (2(5a)2 +2(4b)2 =50a-2 +32b-2 ) मिलता है। परीक्षा में मध्य पदों के कटने को पहचानें।
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( (x+4)2 -(x-6)2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+4)2 -(x-6)2 )?
#difference of expressions
#algebraic identities
#simplification
A (20x-20)
B (10x-20)
C (20x+20)
D (10x+20)
Explanation opens after your attempt
Correct Answer
A. (20x-20)
Step 1
Concept
Apply (A-2 -B-2 =(A+B)(A-B)). Here (A+B=2x-2) and (A-B=10), so it is (20x-20).
Step 2
Why this answer is correct
The correct answer is A. (20x-20). Apply (A-2 -B-2 =(A+B)(A-B)). Here (A+B=2x-2) and (A-B=10), so it is (20x-20).
Step 3
Exam Tip
(A-2 -B-2 =(A+B)(A-B)) लगाएँ। यहाँ (A+B=2x-2) और (A-B=10), इसलिए (20x-20) है।
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( (2x+1)(2x+9)-(2x+5)2 ) का मान क्या है?
What is the value of ( (2x+1)(2x+9)-(2x+5)2 )?
#comparison
#binomial product
#simplification
A (4)
B (8)
C (-8)
D (-16)
Explanation opens after your attempt
Step 1
Concept
The first product is \(4x^2+20x+9\) and the second is \(4x^2+20x+25\). Exam tip: cancel like terms and compare constants.
Step 2
Why this answer is correct
The correct answer is D. (-16). The first product is \(4x^2+20x+9\) and the second is \(4x^2+20x+25\). Exam tip: cancel like terms and compare constants.
Step 3
Exam Tip
पहला गुणनफल \(4x^2+20x+9\) और दूसरा \(4x^2+20x+25\) है। परीक्षा में समान पद काटकर स्थिर पदों का अंतर लें।
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( (x+3)2 -(x-1)(x+7) ) का सरल रूप क्या है?
What is the simplified form of ( (x+3)2 -(x-1)(x+7) )?
#error check
#identity comparison
#simplification
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The first is \(x^2+6x+9\) and the second is \(x^2+6x-7\). Subtracting gives (9-(-7)=16), so the correct option should be (16).
Step 2
Why this answer is correct
The correct answer is B. (4). The first is \(x^2+6x+9\) and the second is \(x^2+6x-7\). Subtracting gives (9-(-7)=16), so the correct option should be (16).
Step 3
Exam Tip
पहला \(x^2+6x+9\) और दूसरा \(x^2+6x-7\) है। घटाने पर (16) नहीं बल्कि (9-(-7)=16) होगा इसलिए सही विकल्प (16) होना चाहिए।
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यदि ( (x-4)(x+k)=x-2 +3x-28 ) है तो (k) का मान क्या है?
If ( (x-4)(x+k)=x-2 +3x-28 ), what is the value of (k)?
#unknown constant
#product expansion
#verification
A (4)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
The constant term (-4k=-28) gives (k=7), and the middle term also becomes (3x). Exam tip: verify using both conditions.
Step 2
Why this answer is correct
The correct answer is C. (7). The constant term (-4k=-28) gives (k=7), and the middle term also becomes (3x). Exam tip: verify using both conditions.
Step 3
Exam Tip
स्थिर पद (-4k=-28) से (k=7) मिलता है और मध्य पद भी (3x) बनता है। परीक्षा में दोनों शर्तों से जाँच करें।
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यदि ( (x+2)(x+5)=x-2 +kx+10 ) है तो (k) का मान क्या है?
If ( (x+2)(x+5)=x-2 +kx+10 ), what is the value of (k)?
#unknown coefficient
#product identity
#binomial
A (5)
B (7)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (2+5=7). Exam tip: in ((x+a)(x+b)), the coefficient of (x) is (a+b).
Step 2
Why this answer is correct
The correct answer is B. (7). The coefficient of (x) is (2+5=7). Exam tip: in ((x+a)(x+b)), the coefficient of (x) is (a+b).
Step 3
Exam Tip
(x) का गुणांक (2+5=7) है। परीक्षा में ((x+a)(x+b)) में (x) का गुणांक (a+b) होता है।
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( (2x-3y+z)2 ) में (xz) वाला पद क्या है?
What is the term containing (xz) in ( (2x-3y+z)2 )?
#three term square
#xz term
#coefficients
A (2xz)
B (4xz)
C (-6xz)
D (6xz)
Explanation opens after your attempt
Step 1
Concept
\(2\times2x\times z=4xz\). Exam tip: find the mixed term for the required pair only.
Step 2
Why this answer is correct
The correct answer is B. (4xz). \(2\times2x\times z=4xz\). Exam tip: find the mixed term for the required pair only.
Step 3
Exam Tip
\(2\times2x\times z=4xz\) मिलता है। परीक्षा में जिस जोड़ी की बात हो वही मिश्र पद निकालें।
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( (a+2b-c)2 ) में (bc) वाला पद कौन सा होगा?
Which term containing (bc) appears in ( (a+2b-c)2 )?
#three term square
#negative mixed term
#bc
A (2bc)
B (-2bc)
C (-4bc)
D (4bc)
Explanation opens after your attempt
Step 1
Concept
\(2\times2b\times(-c)=-4bc\). Exam tip: handle signs carefully in squares of three terms.
Step 2
Why this answer is correct
The correct answer is C. (-4bc). \(2\times2b\times(-c)=-4bc\). Exam tip: handle signs carefully in squares of three terms.
Step 3
Exam Tip
\(2\times2b\times(-c)=-4bc\) है। परीक्षा में तीन पदों के वर्ग में चिन्हों को ध्यान से रखें।
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यदि \(u^2+v^2=29\) और (uv=10) है तो ( (u-v)2 ) का मान क्या है?
If \(u^2+v^2=29\) and (uv=10), what is the value of ( (u-v)2 )?
#given values
#difference square
#expert
A (9)
B (19)
C (39)
D (49)
Explanation opens after your attempt
Step 1
Concept
( (u-v)2 =u-2 +v-2 -2uv=29-20=9). Exam tip: subtract (2uv) in the square of difference.
Step 2
Why this answer is correct
The correct answer is A. (9). ( (u-v)2 =u-2 +v-2 -2uv=29-20=9). Exam tip: subtract (2uv) in the square of difference.
Step 3
Exam Tip
( (u-v)2 =u-2 +v-2 -2uv=29-20=9)। परीक्षा में अंतर के वर्ग में (2uv) घटता है।
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यदि \(x^2+y^2=50\) और (xy=7) है तो ( (x+y)2 ) कितना होगा?
If \(x^2+y^2=50\) and (xy=7), what is ( (x+y)2 )?
#given values
#sum square
#xy
A (57)
B (64)
C (43)
D (14)
Explanation opens after your attempt
Step 1
Concept
( (x+y)2 =x-2 +y-2 +2xy=50+14=64). Exam tip: remember to add (2xy).
Step 2
Why this answer is correct
The correct answer is B. (64). ( (x+y)2 =x-2 +y-2 +2xy=50+14=64). Exam tip: remember to add (2xy).
Step 3
Exam Tip
( (x+y)2 =x-2 +y-2 +2xy=50+14=64)। परीक्षा में (2xy) जोड़ना याद रखें।
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( \(x^2+3\)2 -\(x^2-3\)2 ) का सरल रूप क्या है?
What is the simplified form of ( \(x^2+3\)2 -\(x^2-3\)2 )?
#higher power
#square difference
#shortcut
A \(6x^2\)
B \(9x^2\)
C \(12x^2\)
D \(18x^2\)
Explanation opens after your attempt
Correct Answer
C. \(12x^2\)
Step 1
Concept
This is (4AB) where \(A=x^2\) and (B=3). Exam tip: treat \(x^2\) as one whole term.
Step 2
Why this answer is correct
The correct answer is C. \(12x^2\). This is (4AB) where \(A=x^2\) and (B=3). Exam tip: treat \(x^2\) as one whole term.
Step 3
Exam Tip
यह (4AB) है जहाँ \(A=x^2\) और (B=3)। परीक्षा में \(x^2\) को एक पूरा पद मानें।
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\( 16x^4-81y^4 \) का गुणनखंडों में सही पहला चरण क्या है?
What is the correct first factorization step for \( 16x^4-81y^4 \)?
#higher powers
#difference of squares
#factorization
A ( \(4x^2-9y^2\)\(4x^2+9y^2\) )
B ( (4x-9y)(4x+9y) )
C ( \(2x^2-3y^2\)\(2x^2+3y^2\) )
D ( \(16x^2-81y^2\)\(x^2+y^2\) )
Explanation opens after your attempt
Correct Answer
A. ( \(4x^2-9y^2\)\(4x^2+9y^2\) )
Step 1
Concept
(16x-4 =\(4x^2\)2 ) and (81y-4 =\(9y^2\)2 ). Exam tip: identify larger squares first.
Step 2
Why this answer is correct
The correct answer is A. ( \(4x^2-9y^2\)\(4x^2+9y^2\) ). (16x-4 =\(4x^2\)2 ) and (81y-4 =\(9y^2\)2 ). Exam tip: identify larger squares first.
Step 3
Exam Tip
(16x-4 =\(4x^2\)2 ) और (81y-4 =\(9y^2\)2 ) है। परीक्षा में पहले बड़े वर्ग पहचानें।
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( (x-2)(x+2)\(x^2+4\) ) का सरल रूप क्या है?
What is the simplified form of ( (x-2)(x+2)\(x^2+4\) )?
#nested identity
#difference of squares
#quartic
A \(x^4+16\)
B \(x^4-8\)
C \(x^4-16\)
D \(x^4+8x^2+16\)
Explanation opens after your attempt
Correct Answer
C. \(x^4-16\)
Step 1
Concept
First ( (x-2)(x+2)=x-2 -4 ), then (\(x^2-4\)\(x^2+4\)=x-4 -16). Exam tip: apply difference of squares twice.
Step 2
Why this answer is correct
The correct answer is C. \(x^4-16\). First ( (x-2)(x+2)=x-2 -4 ), then (\(x^2-4\)\(x^2+4\)=x-4 -16). Exam tip: apply difference of squares twice.
Step 3
Exam Tip
पहले ( (x-2)(x+2)=x-2 -4 ) और फिर (\(x^2-4\)\(x^2+4\)=x-4 -16)। परीक्षा में दो बार अंतर वर्ग लगाएँ।
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( \(x+\frac{1}{x}\)2 -\(x-\frac{1}{x}\)2 ) का मान क्या है?
What is the value of ( \(x+\frac{1}{x}\)2 -\(x-\frac{1}{x}\)2 )?
#reciprocal identity
#difference
#expert
A (2)
B (4)
C \(x^2+\frac{1}{x^2}\)
D (0)
Explanation opens after your attempt
Step 1
Concept
This is (4AB) where (A=x) and \(B=\frac{1}{x}\), so the value is (4). Exam tip: reciprocal terms multiply to (1).
Step 2
Why this answer is correct
The correct answer is B. (4). This is (4AB) where (A=x) and \(B=\frac{1}{x}\), so the value is (4). Exam tip: reciprocal terms multiply to (1).
Step 3
Exam Tip
यह (4AB) है जहाँ (A=x) और \(B=\frac{1}{x}\), इसलिए मान (4) है। परीक्षा में reciprocal terms का गुणन (1) होता है।
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यदि \(t-\frac{1}{t}=6\) है तो \(t^2+\frac{1}{t^2}\) कितना होगा?
If \(t-\frac{1}{t}=6\), what is \(t^2+\frac{1}{t^2}\)?
#reciprocal expression
#minus square
#identity
A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
On squaring, \(t^2-2+\frac{1}{t^2}=36\), so the value is (38). Exam tip: the square of a difference gives (-2).
Step 2
Why this answer is correct
The correct answer is C. (38). On squaring, \(t^2-2+\frac{1}{t^2}=36\), so the value is (38). Exam tip: the square of a difference gives (-2).
Step 3
Exam Tip
वर्ग करने पर \(t^2-2+\frac{1}{t^2}=36\) इसलिए मान (38) है। परीक्षा में अंतर के वर्ग में (-2) आता है।
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यदि \(x+\frac{1}{x}=5\) है तो \(x^2+\frac{1}{x^2}\) का मान क्या होगा?
If \(x+\frac{1}{x}=5\), what is the value of \(x^2+\frac{1}{x^2}\)?
#reciprocal identity
#square relation
#expert
A (23)
B (25)
C (27)
D (20)
Explanation opens after your attempt
Step 1
Concept
On squaring, \(x^2+2+\frac{1}{x^2}=25\). Exam tip: do not forget to subtract (2).
Step 2
Why this answer is correct
The correct answer is A. (23). On squaring, \(x^2+2+\frac{1}{x^2}=25\). Exam tip: do not forget to subtract (2).
Step 3
Exam Tip
वर्ग करने पर \(x^2+2+\frac{1}{x^2}=25\) मिलता है। परीक्षा में (2) घटाना न भूलें।
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( (a-b)2 -\(a^2+b^2\) ) किसके बराबर है?
What is ( (a-b)2 -\(a^2+b^2\) ) equal to?
#minus square
#middle term
#identity
A (2ab)
B (-2ab)
C \(a^2-b^2\)
D \(-b^2\)
Explanation opens after your attempt
Step 1
Concept
( (a-b)2 =a-2 -2ab+b-2 ), so subtracting leaves (-2ab). Exam tip: remember the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. (-2ab). ( (a-b)2 =a-2 -2ab+b-2 ), so subtracting leaves (-2ab). Exam tip: remember the negative middle term.
Step 3
Exam Tip
( (a-b)2 =a-2 -2ab+b-2 ) है इसलिए घटाने पर (-2ab) बचता है। परीक्षा में नकारात्मक मध्य पद याद रखें।
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( (a+b)2 -\(a^2-b^2\) ) का सरल रूप क्या है?
What is the simplified form of ( (a+b)2 -\(a^2-b^2\) )?
#identity comparison
#sign handling
#simplification
A \(2ab+2b^2\)
B (2ab)
C \(a^2+2ab\)
D \(b^2\)
Explanation opens after your attempt
Correct Answer
A. \(2ab+2b^2\)
Step 1
Concept
\(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Exam tip: apply the minus sign to the whole second expression.
Step 2
Why this answer is correct
The correct answer is A. \(2ab+2b^2\). \(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Exam tip: apply the minus sign to the whole second expression.
Step 3
Exam Tip
\(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\)। परीक्षा में ऋण चिन्ह को पूरे दूसरे पद पर लगाएँ।
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( (x+2)3 +(x-2)3 ) का सरल रूप क्या है?
What is the simplified form of ( (x+2)3 +(x-2)3 )?
#cube identity
#symmetric expression
#simplification
A \(2x^3+24x\)
B \(2x^3+12x\)
C \(x^3+8\)
D \(2x^3+16\)
Explanation opens after your attempt
Correct Answer
A. \(2x^3+24x\)
Step 1
Concept
In the sum, constant cube terms cancel and \(2x^3+6x\cdot4=2x^3+24x\) remains. Exam tip: understand symmetric cube expansion.
Step 2
Why this answer is correct
The correct answer is A. \(2x^3+24x\). In the sum, constant cube terms cancel and \(2x^3+6x\cdot4=2x^3+24x\) remains. Exam tip: understand symmetric cube expansion.
Step 3
Exam Tip
योग में स्थिर घन कटते हैं और \(2x^3+6x\cdot4=2x^3+24x\) बचता है। परीक्षा में सममित घन विस्तार समझें।
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( (x+4)3 -(x-4)3 ) में \(x^2\) वाला पद क्या होगा?
What will be the term containing \(x^2\) in ( (x+4)3 -(x-4)3 )?
#cube expansion
#term identification
#expert
A \(12x^2\)
B \(24x^2\)
C \(48x^2\)
D \(96x^2\)
Explanation opens after your attempt
Correct Answer
B. \(24x^2\)
Step 1
Concept
The difference gives \(6x^2\cdot4=24x^2\). Exam tip: identify the \(x^2\) term quickly in cube differences.
Step 2
Why this answer is correct
The correct answer is B. \(24x^2\). The difference gives \(6x^2\cdot4=24x^2\). Exam tip: identify the \(x^2\) term quickly in cube differences.
Step 3
Exam Tip
अंतर में \(6x^2\cdot4=24x^2\) मिलता है। परीक्षा में घन अंतर में \(x^2\) वाला पद जल्दी पहचानें।
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( (2x+3)2 -(2x+3)(2x-3) ) का सरल रूप क्या है?
What is the simplified form of ( (2x+3)2 -(2x+3)(2x-3) )?
#common factor
#combined identity
#simplification
A (12x+18)
B (6x+9)
C (18)
D \(4x^2+9\)
Explanation opens after your attempt
Correct Answer
A. (12x+18)
Step 1
Concept
((2x+3)) is common, giving ((2x+3)[(2x+3)-(2x-3)]). Exam tip: taking common factors makes work easier.
Step 2
Why this answer is correct
The correct answer is A. (12x+18). ((2x+3)) is common, giving ((2x+3)[(2x+3)-(2x-3)]). Exam tip: taking common factors makes work easier.
Step 3
Exam Tip
((2x+3)) सामान्य लेकर ((2x+3)[(2x+3)-(2x-3)]) मिलता है। परीक्षा में common factor लेने से काम आसान होता है।
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( (x+y+z)2 ) में \(x^2+y^2+z^2\) हटाने पर क्या बचेगा?
What remains when \(x^2+y^2+z^2\) is removed from ( (x+y+z)2 )?
#three term square
#mixed terms
#identity
A (xy+yz+zx)
B (2xy+2yz+2zx)
C (xyz)
D (x+y+z)
Explanation opens after your attempt
Correct Answer
B. (2xy+2yz+2zx)
Step 1
Concept
The extra mixed terms in the square of three terms are (2xy+2yz+2zx). Exam tip: write all three mixed terms.
Step 2
Why this answer is correct
The correct answer is B. (2xy+2yz+2zx). The extra mixed terms in the square of three terms are (2xy+2yz+2zx). Exam tip: write all three mixed terms.
Step 3
Exam Tip
तीन पदों के वर्ग में अतिरिक्त मिश्र पद (2xy+2yz+2zx) होते हैं। परीक्षा में सभी तीन मिश्र पद लिखें।
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यदि (x+y+z=6) और (xy+yz+zx=11) है तो \(x^2+y^2+z^2\) कितना है?
If (x+y+z=6) and (xy+yz+zx=11), what is \(x^2+y^2+z^2\)?
#three term square
#given values
#sum of squares
A (14)
B (25)
C (36)
D (47)
Explanation opens after your attempt
Step 1
Concept
(x-2 +y-2 +z-2 =(x+y+z)2 -2(xy+yz+zx)=36-22=14). Exam tip: use the three-term identity.
Step 2
Why this answer is correct
The correct answer is A. (14). (x-2 +y-2 +z-2 =(x+y+z)2 -2(xy+yz+zx)=36-22=14). Exam tip: use the three-term identity.
Step 3
Exam Tip
(x-2 +y-2 +z-2 =(x+y+z)2 -2(xy+yz+zx)=36-22=14)। परीक्षा में तीन पदों की पहचान उपयोग करें।
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\( x^3+y^3+z^3-3xyz \) में यदि (x+y+z=0) हो तो मान क्या होगा?
If (x+y+z=0), what is the value of \( x^3+y^3+z^3-3xyz \)?
#three variable identity
#zero condition
#cube
A (xyz)
B (3xyz)
C \(x^2+y^2+z^2\)
D (0)
Explanation opens after your attempt
Step 1
Concept
In the identity, this expression is multiplied by (x+y+z), so the value is (0). Exam tip: check the condition first.
Step 2
Why this answer is correct
The correct answer is D. (0). In the identity, this expression is multiplied by (x+y+z), so the value is (0). Exam tip: check the condition first.
Step 3
Exam Tip
पहचान में यह पद (x+y+z) से गुणा होता है इसलिए मान (0) होगा। परीक्षा में शर्त को पहले जाँचें।
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यदि (a+b+c=0) है तो \(a^3+b^3+c^3\) किसके बराबर होगा?
If (a+b+c=0), what is \(a^3+b^3+c^3\) equal to?
#three variable identity
#cube relation
#expert
A (ab+bc+ca)
B (abc)
C (3abc)
D (0)
Explanation opens after your attempt
Step 1
Concept
By identity, (a-3 +b-3 +c-3 -3abc=(a+b+c)\(\cdots\)). Exam tip: if (a+b+c=0), remember \(a^3+b^3+c^3=3abc\).
Step 2
Why this answer is correct
The correct answer is C. (3abc). By identity, (a-3 +b-3 +c-3 -3abc=(a+b+c)\(\cdots\)). Exam tip: if (a+b+c=0), remember \(a^3+b^3+c^3=3abc\).
Step 3
Exam Tip
पहचान के अनुसार (a-3 +b-3 +c-3 -3abc=(a+b+c)\(\cdots\)) है। परीक्षा में (a+b+c=0) होने पर \(a^3+b^3+c^3=3abc\) याद रखें।
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\( 8x^3-125 \) का गुणनखंड रूप कौन सा है?
Which is the factor form of \( 8x^3-125 \)?
#difference of cubes
#factorization
#expert identity
A ( (2x-5)\(4x^2+10x+25\) )
B ( (2x+5)\(4x^2-10x+25\) )
C ( (2x-5)3 )
D ( (8x-5)\(x^2+5x+25\) )
Explanation opens after your attempt
Correct Answer
A. ( (2x-5)\(4x^2+10x+25\) )
Step 1
Concept
(8x-3 =(2x)3 ) and \(125=5^3\). Exam tip: apply the \(a^3-b^3\) formula correctly.
Step 2
Why this answer is correct
The correct answer is A. ( (2x-5)\(4x^2+10x+25\) ). (8x-3 =(2x)3 ) and \(125=5^3\). Exam tip: apply the \(a^3-b^3\) formula correctly.
Step 3
Exam Tip
(8x-3 =(2x)3 ) और \(125=5^3\) है। परीक्षा में \(a^3-b^3\) का सूत्र सही लगाएँ।
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\( x^3+27 \) का गुणनखंड रूप क्या है?
What is the factor form of \( x^3+27 \)?
#sum of cubes
#factorization
#cube identity
A ( (x+3)\(x^2-3x+9\) )
B ( (x-3)\(x^2+3x+9\) )
C ( (x+3)3 )
D ( (x+9)\(x^2-9x+9\) )
Explanation opens after your attempt
Correct Answer
A. ( (x+3)\(x^2-3x+9\) )
Step 1
Concept
This is the form (a-3 +b-3 =(a+b)\(a^2-ab+b^2\)). Exam tip: identify \(27=3^3\).
Step 2
Why this answer is correct
The correct answer is A. ( (x+3)\(x^2-3x+9\) ). This is the form (a-3 +b-3 =(a+b)\(a^2-ab+b^2\)). Exam tip: identify \(27=3^3\).
Step 3
Exam Tip
यह (a-3 +b-3 =(a+b)\(a^2-ab+b^2\)) का रूप है। परीक्षा में \(27=3^3\) पहचानें।
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