CBSE Class 9 Mathematics · Ch 4: Exploring Algebraic Identities

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Difficulty: 7 medium · 23 hard

Exploring Algebraic Identities MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

1. Q1. The expression $x^3+8y^3+6xy(x+2y)$ can be written in factorised form as

   व्यंजक $x^3+8y^3+6xy(x+2y)$ को गुणनखंडित रूप में इस प्रकार लिखा जा सकता है

   • A. $(x+y)^3$
   • B. $(x+2y)^3$
   • C. $(2x+y)^3$
   • D. $(x-2y)^3$
   Solution

   Taking $a=x$ and $b=2y$ in $(a+b)^3=a^3+b^3+3ab(a+b)$, the expression matches $(x+2y)^3$ exactly.

   $(a+b)^3=a^3+b^3+3ab(a+b)$ में $a=x$ और $b=2y$ लेने पर, व्यंजक ठीक $(x+2y)^3$ से मेल खाता है।

2. Q2. In the expansion of $(2x-3y)^3$ using the identity $(a-b)^3=a^3-3a^2b+3ab^2-b^3$, the coefficient of the term containing $xy^2$ is

   सर्वसमिका $(a-b)^3=a^3-3a^2b+3ab^2-b^3$ का उपयोग करते हुए $(2x-3y)^3$ के विस्तार में, $xy^2$ वाले पद का गुणांक है

   • A. $36$
   • B. $-54$
   • C. $18$
   • D. $54$
   Solution

   $(2x-3y)^3=8x^3-36x^2y+54xy^2-27y^3$, so the term with $xy^2$ has coefficient $54$.

   $(2x-3y)^3=8x^3-36x^2y+54xy^2-27y^3$, इसलिए $xy^2$ वाले पद का गुणांक $54$ है।

3. Q3. If $a^2+b^2+c^2=50$ and $a+b+c=12$, then the value of $ab+bc+ca$ is

   यदि $a^2+b^2+c^2=50$ और $a+b+c=12$ है, तो $ab+bc+ca$ का मान है

   • A. $47$
   • B. $94$
   • C. $188$
   • D. $-47$
   Solution

   From $(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$, $144=50+2(ab+bc+ca)$, so $ab+bc+ca=47$.

   $(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$ से, $144=50+2(ab+bc+ca)$, इसलिए $ab+bc+ca=47$।

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