Question 1 / 17
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Answered 0/17
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Time 08:30
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\(x^2+7x+10\) और \(x^2+5x+6\) के गुणनखंडों में कौन सा सामान्य गुणनखंड है?
Which common factor is present in the factorisations of \(x^2+7x+10\) and \(x^2+5x+6\)?
Explanation opens after your attempt
Step 1
Concept
The first is ((x+5)(x+2)) and the second is ((x+2)(x+3)). So the common factor is ((x+2)).
Step 2
Why this answer is correct
The correct answer is C. (x+2). The first is ((x+5)(x+2)) and the second is ((x+2)(x+3)). So the common factor is ((x+2)).
Step 3
Exam Tip
पहला ((x+5)(x+2)) और दूसरा ((x+2)(x+3)) है। इसलिए सामान्य गुणनखंड ((x+2)) है।
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\(2x^2+11x+15\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(2x^2+11x+15\)?
Explanation opens after your attempt
Correct Answer
C. ((2x+3)(x+5))
Step 1
Concept
Check multiplication carefully: ((2x+5)(x+3)=2x-2+11x+15). So the correct factorisation is ((2x+5)(x+3)).
Step 2
Why this answer is correct
The correct answer is C. ((2x+3)(x+5)). Check multiplication carefully: ((2x+5)(x+3)=2x-2+11x+15). So the correct factorisation is ((2x+5)(x+3)).
Step 3
Exam Tip
((2x+5)(x+3)) से \(2x^2+11x+15\) नहीं बल्कि \(2x^2+11x+15\) ही मिलता है? गुणा जांचें और सही विकल्प ((2x+5)(x+3)) है।
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\(3x^2+10x+8\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(3x^2+10x+8\)?
Explanation opens after your attempt
Correct Answer
A. ((3x+4)(x+2))
Step 1
Concept
((3x+4)(x+2)=3x-2+6x+4x+8). The middle term becomes (10x).
Step 2
Why this answer is correct
The correct answer is A. ((3x+4)(x+2)). ((3x+4)(x+2)=3x-2+6x+4x+8). The middle term becomes (10x).
Step 3
Exam Tip
((3x+4)(x+2)=3x-2+6x+4x+8) है। मध्य पद (10x) बनता है।
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\(6x^2+13x+6\) का गुणनखंडन चुनिए।
Choose the factorisation of \(6x^2+13x+6\).
Explanation opens after your attempt
Correct Answer
B. ((2x+3)(3x+2))
Step 1
Concept
Expanding ((2x+3)(3x+2)) gives \(6x^2+4x+9x+6\). The middle term is (13x).
Step 2
Why this answer is correct
The correct answer is B. ((2x+3)(3x+2)). Expanding ((2x+3)(3x+2)) gives \(6x^2+4x+9x+6\). The middle term is (13x).
Step 3
Exam Tip
((2x+3)(3x+2)) फैलाने पर \(6x^2+4x+9x+6\) मिलता है। मध्य पद (13x) है।
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\(5x^2+16x+3\) का गुणनखंडन क्या होगा?
What will be the factorisation of \(5x^2+16x+3\)?
Explanation opens after your attempt
Correct Answer
A. ((5x+1)(x+3))
Step 1
Concept
((5x+1)(x+3)=5x-2+15x+x+3). Therefore the middle term is (16x).
Step 2
Why this answer is correct
The correct answer is A. ((5x+1)(x+3)). ((5x+1)(x+3)=5x-2+15x+x+3). Therefore the middle term is (16x).
Step 3
Exam Tip
((5x+1)(x+3)=5x-2+15x+x+3) है। इसलिए मध्य पद (16x) मिलता है।
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\(6x^2-x-12\) का गुणनखंडन चुनिए।
Choose the factorisation of \(6x^2-x-12\).
Explanation opens after your attempt
Correct Answer
D. ((3x-4)(2x+3))
Step 1
Concept
((3x-4)(2x+3)=6x-2+9x-8x-12). The middle term becomes (x), so signs must be checked carefully.
Step 2
Why this answer is correct
The correct answer is D. ((3x-4)(2x+3)). ((3x-4)(2x+3)=6x-2+9x-8x-12). The middle term becomes (x), so signs must be checked carefully.
Step 3
Exam Tip
((3x-4)(2x+3)=6x-2+9x-8x-12) है। मध्य पद (x) नहीं बल्कि (x) बनेगा इसलिए चिह्न जांचना जरूरी है।
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\(6x^2-x-12\) के लिए सही गुणनखंड वास्तव में कौन से हैं?
For \(6x^2-x-12\), what are the actually correct factors?
Explanation opens after your attempt
Correct Answer
A. ((3x+4)(2x-3))
Step 1
Concept
((3x+4)(2x-3)=6x-2-9x+8x-12=6x-2-x-12). Exam tip: expand to check signs.
Step 2
Why this answer is correct
The correct answer is A. ((3x+4)(2x-3)). ((3x+4)(2x-3)=6x-2-9x+8x-12=6x-2-x-12). Exam tip: expand to check signs.
Step 3
Exam Tip
((3x+4)(2x-3)=6x-2-9x+8x-12=6x-2-x-12) है। परीक्षा में विस्तार करके संकेत जांचें।
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\(2x^2-5x-3\) का सही गुणनखंडन कौन सा है?
Which is the correct factorisation of \(2x^2-5x-3\)?
Explanation opens after your attempt
Correct Answer
B. ((2x+1)(x-3))
Step 1
Concept
( (2x+1)(x-3)=2x-2-6x+x-3=2x-2-5x-3). Exam tip: check the sum of opposite-sign terms.
Step 2
Why this answer is correct
The correct answer is B. ((2x+1)(x-3)). ( (2x+1)(x-3)=2x-2-6x+x-3=2x-2-5x-3). Exam tip: check the sum of opposite-sign terms.
Step 3
Exam Tip
((2x+1)(x-3)=2x-2-6x+x-3=2x-2-5x-3) है। परीक्षा में विपरीत चिह्न वाले पदों का योग जांचें।
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\(3x^2-14x-5\) का गुणनखंडन चुनिए।
Choose the factorisation of \(3x^2-14x-5\).
Explanation opens after your attempt
Correct Answer
A. ((3x+1)(x-5))
Step 1
Concept
((3x+1)(x-5)=3x-2-15x+x-5=3x-2-14x-5). Exam tip: confirm by expansion.
Step 2
Why this answer is correct
The correct answer is A. ((3x+1)(x-5)). ((3x+1)(x-5)=3x-2-15x+x-5=3x-2-14x-5). Exam tip: confirm by expansion.
Step 3
Exam Tip
((3x+1)(x-5)=3x-2-15x+x-5=3x-2-14x-5) है। परीक्षा में विस्तार से उत्तर पक्का करें।
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\(4x^2-4x-15\) के गुणनखंड कौन से हैं?
What are the factors of \(4x^2-4x-15\)?
Explanation opens after your attempt
Correct Answer
C. ((2x-5)(2x+3))
Step 1
Concept
((2x-5)(2x+3)=4x-2+6x-10x-15=4x-2-4x-15). Exam tip: check the sum of cross terms.
Step 2
Why this answer is correct
The correct answer is C. ((2x-5)(2x+3)). ((2x-5)(2x+3)=4x-2+6x-10x-15=4x-2-4x-15). Exam tip: check the sum of cross terms.
Step 3
Exam Tip
((2x-5)(2x+3)=4x-2+6x-10x-15=4x-2-4x-15) है। परीक्षा में क्रॉस पदों का योग देखें।
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\(15x^2+2x-8\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(15x^2+2x-8\)?
Explanation opens after your attempt
Correct Answer
D. ((3x-2)(5x+4))
Step 1
Concept
((3x-2)(5x+4)=15x-2+12x-10x-8). The middle term becomes (2x).
Step 2
Why this answer is correct
The correct answer is D. ((3x-2)(5x+4)). ((3x-2)(5x+4)=15x-2+12x-10x-8). The middle term becomes (2x).
Step 3
Exam Tip
((3x-2)(5x+4)=15x-2+12x-10x-8) है। मध्य पद (2x) बनता है।
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\(x^2-11x+30\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2-11x+30\)?
Explanation opens after your attempt
Correct Answer
A. ((x-5)(x-6))
Step 1
Concept
(-5+(-6)=-11) and ((-5)(-6)=30). Exam tip: for a positive last term use same-sign factors.
Step 2
Why this answer is correct
The correct answer is A. ((x-5)(x-6)). (-5+(-6)=-11) and ((-5)(-6)=30). Exam tip: for a positive last term use same-sign factors.
Step 3
Exam Tip
(-5+(-6)=-11) और ((-5)(-6)=30) है। परीक्षा में धन अंतिम पद के लिए समान चिह्न वाले कारक देखें।
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\(x^2-x-20\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(x^2-x-20\).
Explanation opens after your attempt
Correct Answer
A. ((x-5)(x+4))
Step 1
Concept
(-5+4=-1) and \(-5\cdot4=-20\). Therefore ((x-5)(x+4)) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((x-5)(x+4)). (-5+4=-1) and \(-5\cdot4=-20\). Therefore ((x-5)(x+4)) is correct.
Step 3
Exam Tip
(-5+4=-1) और \(-5\cdot4=-20\) है। इसलिए ((x-5)(x+4)) सही है।
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\(x^2+2x-24\) का गुणनखंडन क्या होगा?
What will be the factorisation of \(x^2+2x-24\)?
Explanation opens after your attempt
Correct Answer
A. ((x+6)(x-4))
Step 1
Concept
(6+(-4)=2) and (6\cdot(-4)=-24). Exam tip: check the sum of opposite-sign factors.
Step 2
Why this answer is correct
The correct answer is A. ((x+6)(x-4)). (6+(-4)=2) and (6\cdot(-4)=-24). Exam tip: check the sum of opposite-sign factors.
Step 3
Exam Tip
(6+(-4)=2) और (6\cdot(-4)=-24) है। परीक्षा में विपरीत चिह्न वाले कारकों का योग देखें।
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\(x^2-8x+15\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2-8x+15\)?
Explanation opens after your attempt
Correct Answer
A. ((x-3)(x-5))
Step 1
Concept
(-3+(-5)=-8) and ((-3)(-5)=15). Exam tip: two negative factors make the middle term negative.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)(x-5)). (-3+(-5)=-8) and ((-3)(-5)=15). Exam tip: two negative factors make the middle term negative.
Step 3
Exam Tip
(-3+(-5)=-8) और ((-3)(-5)=15) है। परीक्षा में दोनों ऋण कारक मध्य पद ऋण बनाते हैं।
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\(2x^2+9x+10\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(2x^2+9x+10\)?
Explanation opens after your attempt
Correct Answer
A. ((2x+5)(x+2))
Step 1
Concept
((2x+5)(x+2)=2x-2+4x+5x+10). The middle term becomes (9x).
Step 2
Why this answer is correct
The correct answer is A. ((2x+5)(x+2)). ((2x+5)(x+2)=2x-2+4x+5x+10). The middle term becomes (9x).
Step 3
Exam Tip
((2x+5)(x+2)=2x-2+4x+5x+10) है। मध्य पद (9x) बनता है।
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\(8x^2+14x+3\) का गुणनखंडन चुनिए।
Choose the factorisation of \(8x^2+14x+3\).
Explanation opens after your attempt
Correct Answer
A. ((4x+1)(2x+3))
Step 1
Concept
((4x+1)(2x+3)=8x-2+12x+2x+3). Therefore the middle term is (14x).
Step 2
Why this answer is correct
The correct answer is A. ((4x+1)(2x+3)). ((4x+1)(2x+3)=8x-2+12x+2x+3). Therefore the middle term is (14x).
Step 3
Exam Tip
((4x+1)(2x+3)=8x-2+12x+2x+3) है। इसलिए मध्य पद (14x) मिलता है।
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