Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Choose the factorised form of \(x^2+7x+12-y^2\).
C. ( (x+3-y)(x+4+y) )
\(x^2+7x+12\) को ((x+3)(x+4)) तोड़ना पर्याप्त नहीं है। दिए गए विकल्प को फैलाने पर सही पद \( -y^2 \) भी मिलता है। / Factoring \(x^2+7x+12\) as ((x+3)(x+4)) alone is not enough. Expanding the given option also gives the term \(-y^2\).
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What is the factorised form of \(a^2+b^2+c^2+2ab-2ac-2bc\)?
D. ( (a+b-c)2 )
यह (a), (b), (-c) का पूर्ण वर्ग है। परीक्षा में (2ab), (-2ac), (-2bc) से चिन्ह तय करें। / This is the perfect square of (a), (b), and (-c). Exam tip: decide signs from (2ab), (-2ac), and (-2bc).
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What is the factorised form of \(x^4+2x^2y^2+y^4-16z^4\)?
A. ( \(x^2+y^2-4z^2\)\(x^2+y^2+4z^2\) )
पहले \(x^4+2x^2y^2+y^4\) को (\(x^2+y^2\)2) बनाएं। परीक्षा में बड़े पदों को एक संयुक्त वर्ग मानें। / First write \(x^4+2x^2y^2+y^4\) as (\(x^2+y^2\)2). Exam tip: treat larger expressions as one combined square.
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Which is one complete factorised form of \(a^6-b^6\)?
B. ( (a-b)(a+b)\(a^2+ab+b^2\)\(a^2-ab+b^2\) )
\(a^6-b^6\) को घन और वर्ग दोनों पहचान से पूर्ण रूप में तोड़ा जा सकता है। परीक्षा में \(a^3-b^3\) और \(a^3+b^3\) दोनों को आगे तोड़ें। / \(a^6-b^6\) can be fully factored using both cube and square identities. Exam tip: factor both \(a^3-b^3\) and \(a^3+b^3\) further.
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Choose the correct factorisation of \(3x^2+2xy-8y^2\).
C. ( (3x-4y)(x+2y) )
(6xy-4xy) से (2xy) बनता है। परीक्षा में ऋणात्मक अंतिम पद के कारण चिन्ह विपरीत होंगे। / The split (6xy-4xy) gives (2xy). Exam tip: the signs are opposite because the last term is negative.
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What is the factorised form of \(10p^2-23pq+12q^2\)?
D. ( (5p-4q)(2p-3q) )
फैलाने पर \(10p^2-15pq-8pq+12q^2\) मिलता है। परीक्षा में (-15pq) और (-8pq) का योग (-23pq) जांचें। / Expanding gives \(10p^2-15pq-8pq+12q^2\). Exam tip: check that (-15pq) and (-8pq) add to (-23pq).
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What is the factorised form of (x-3+27y-3-9xy(x+3y))?
A. ( (x+3y)(x-3y)2 )
\(x^3+27y^3\) में ((x+3y)) गुणनखंड आता है। अंदर \(x^2-12xy+9y^2\) बनकर ((x-3y)2) देता है। / The expression \(x^3+27y^3\) has factor ((x+3y)). The inside becomes \(x^2-12xy+9y^2\), giving ((x-3y)2).
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Which is the correct factorisation of \(4a^2-4ab+b^2-25c^2\)?
B. ( (2a-b-5c)(2a-b+5c) )
\(4a^2-4ab+b^2\) को ((2a-b)2) लिखें। परीक्षा में फिर (25c-2=(5c)2) लगाकर अंतर वर्ग करें। / Write \(4a^2-4ab+b^2\) as ((2a-b)2). Exam tip: then use (25c-2=(5c)2) for difference of squares.
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What is the factorised form of \(9x^4-30x^2+25\)?
C. ( \(3x^2-5\)2 )
यह (\(3x^2\)2-2\cdot3x-2\cdot5+52) है। परीक्षा में \(x^4\) वाले पूर्ण वर्ग को भी पहचानें। / It is (\(3x^2\)2-2\cdot3x-2\cdot5+52). Exam tip: identify perfect squares involving \(x^4\) too.
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Choose the simplified factorised form of \(x^2+6x+9-4y^2+12y-9\).
B. ( (x-2y+6)(x+2y) )
इसे ((x+3)2-(2y-3)2) लिखने पर सरल रूप ((x-2y+6)(x+2y)) आता है। परीक्षा में अंतिम उत्तर को सरल करें। / Writing it as ((x+3)2-(2y-3)2) gives the simplified form ((x-2y+6)(x+2y)). Exam tip: simplify the final answer.
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