Bihar Board 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. In the expansion of $(2x+3y)^3$ using the identity $(a+b)^3=a^3+3a^2b+3ab^2+b^3$, what is the coefficient of $x^2y$?

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

   • A. $36$
   • B. $12$
   • C. $54$
   • D. $18$
   Solution

   Taking $a=2x,b=3y$, the term with $x^2y$ is $3(2x)^2(3y)=36x^2y$, so its coefficient is $36$.

   $a=2x,b=3y$ लेने पर, $x^2y$ वाला पद $3(2x)^2(3y)=36x^2y$ है, इसलिए इसका गुणांक $36$ है।

2. Q2. If $x=2$, $y=-3$ and $z=1$, what is the value of $x^2+y^2+z^2+2xy+2yz+2zx$?

   यदि $x=2$, $y=-3$ और $z=1$ है, तो $x^2+y^2+z^2+2xy+2yz+2zx$ का मान क्या है?

   • A. $4$
   • B. $0$
   • C. $-14$
   • D. $14$
   Solution

   This expression equals $(x+y+z)^2$. Since $x+y+z=2-3+1=0$, the value is $0^2=0$.

   यह व्यंजक $(x+y+z)^2$ के बराबर है। चूँकि $x+y+z=2-3+1=0$ है, इसलिए मान $0^2=0$ है।

3. Q3. Using the identity $x^2-y^2=(x+y)(x-y)$, find the value of $55^2-45^2$.

   सर्वसमिका $x^2-y^2=(x+y)(x-y)$ का उपयोग करते हुए, $55^2-45^2$ का मान ज्ञात कीजिए।

   • A. $100$
   • B. $10000$
   • C. $1000$
   • D. $-1000$
   Solution

   $55^2-45^2=(55+45)(55-45)=100\times10=1000$.

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