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Factorization Of Algebraic Expressions [NEW] Maths - Factorization Of Algebraic Expressions [NEW]

Gujarat Board (GSEB) - STD 9 - Maths (GSEB - English Medium). 159 questions in this chapter.

Question types

Factorization Of Algebraic Expressions [NEW] question types

159 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

159
Questions
7
Question groups
5
Question types
Sample Questions

Factorization Of Algebraic Expressions [NEW] questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
$(x+y)^3-(x-y)^3$ can be factorized as
  • ✓
    $2 y\left(3 x^2+y^2\right)$
  • B
    $2 x\left(3 x^2+y^2\right)$
  • C
    $2 y\left(3 y^2+x^2\right)$
  • D
    $2 x\left(x^2+3 y^2\right)$

Answer: A.

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Q 2M.C.Q1 Mark
Which of the following is a factor of $(x+y)^3-\left(x^3+y^3\right) ?$
  • A
    $x^2+y^2+2 x y$
  • B
    $x^2+y^2-x y$
  • C
    $x y^2$
  • ✓
    $3 x y(x+y)$

Answer: D.

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Q 4M.C.Q1 Mark
The value of $\frac{(0.013)^3+(0.007)^3}{(0.013)^2-0.013 \times 0.007+(0.007)^2}$, is
  • A
    0.006
  • ✓
    0.02
  • C
    0.0091
  • D
    0.00185

Answer: B.

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Q 5M.C.Q1 Mark
The factors of $x^4+x^2+25$, are
  • ✓
    $\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$
  • B
    $\left(x^2+3 x+5\right)\left(x^2+3 x-5\right)$
  • C
    $\left(x^2+x+5\right)\left(x^2-x+5\right)$
  • D
    none of these

Answer: A.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 $(A)$ : The value of $\frac{(0.093)^3+(0.007)^3}{(0.093)^2-(0.093)(0.007)+(0.007)^2}$ is 0.1.
Statement-2 (R): $\quad a^3+b^3=(a+b)\left(a^2-a b+b^2\right)$.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The value of $\frac{(0.027)^3-(0.023)^3}{(0.027)^2-(0.027)(0.023)+(0.023)^2}$ is 0.05
Statement-2 $(R): \quad a^3-b^3=(a-b)\left(a^2-a b-b^2\right)$
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Stateme
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statemen
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.

Answer: C.

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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The value of $\frac{(0.027)^3+(0.023)^3}{(0.027)^2-(0.027)(0.023)+(0.023)^2}$ is 0.05
Statement-2 (R): $a^3-b^3=(a-b)\left(a^2-a b+b^2\right)$
  • A
    Statement- 1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement- 1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.

Answer: C.

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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): The value of $1000^3-900^3-100^3$ is $270,000,000$
Statement-2 (R): If $a+b+c=0$, then $a^3+b^3+c^3=3 a b c$
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
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Q 10Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 $(A)$ : The product of $\left(x^2+4 y^2+z^2+2 x y+x z-2 y z\right)$ and $(-z+x-2 y)$ is $x^3-8 y^3-z^3-6 x y z$
Statement-2 $(R): \quad a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-5
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
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Q 324 Marks Questions4 Marks
Factorize the following expressions:
$\Big[\frac{\text{x}}{2}+\text{y}+\frac{\text{z}}{3}\Big]^3+\Big[\frac{\text{x}}{3}-\frac{2\text{y}}{3}+\text{z}\Big]^3+\Big[-\frac{5\text{x}}{6}-\frac{\text{y}}{3}-\frac{4\text{z}}{3}\Big]^3$
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