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MATHS Assertion (A) & Reason (B) MCQ

Operations on Algebraic Expressions · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 8 questions.

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Assertion (A) & Reason (B) MCQ

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8 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): $(p+1)(p-1)\left(p^2+1\right)\left(p^4+1\right)=\left(p^{16}-1\right)$
Reason (R): $(a+b)(a-b)=a^2-b^2$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
$
\begin{array}{l}
(p+1)(p-1)\left(p^2+1\right)\left(p^4+1\right) \\
=[(p+1)(p-1)]\left(p^2+1\right)\left(p^4+1\right) \\
=\left[\left(p^2-1\right)\left(p^2+1\right)\right]\left(p^4+1\right)
\end{array}
$
$
\left[\because \quad(a-b)(a+b)=a^2-b^2\right]
$
$\begin{array}{l}=\left[\left(p^2\right)^2-1^2\right]\left(p^4+1\right)=\left(p^4-1\right)\left(p^4+1\right) \\ =\left[\left(p^4\right)^2-1^2\right]=\left(p^8-1\right) .\end{array}$
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MCQ 21 Mark
Assertion (A): If we add $(-a+b-c)$ to $(a-b+c)$, we get $(2 a+2 b+2 c)$.
Reason (R): While adding algebraic expressions we add the like terms.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
$(a-b+c)+(-a+b-c)=a-b+c-a+b-c=(a-a)+(-b+b)+(c-c)=0$
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MCQ 31 Mark
Assertion (A): $\frac{-30 x^3 y^2 z}{-6 x y^2 z^3}=\frac{-5 x^2}{z^2}$
Reason (R): Quotient of two monomials $=$ (quotient of their numerical coefficients) $\times$ (quotient of their variables).
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
$\frac{-30 x^3 y^2 z}{-6 x y^2 z^3}=\left(\frac{-30}{-6}\right) \times\left(\frac{x^3}{x}\right) \times\left(\frac{y^2}{y^2}\right) \times\left(\frac{z}{z^3}\right)=5 \times x^{(3-1)} \times z^{(1-3)}=5 x^2 z^{-2}=\frac{5 x^2}{z^2}.$
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MCQ 41 Mark
Assertion (A): If we add two monomials, we always get a binomial as the sum.
Reason (R): A monomial has only one term while a binomial has two terms.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
If we add two monomials with like terms, we get a monomial as the sum,
e.g. $3 x^2 y+5 x^2 y=8 x^2 y$.
So, $A$ is false.
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MCQ 51 Mark
Assertion (A): If we subtract $(-a-b)$ from $(2 a-b)$, we get $3 a$.
Reason (R): For subtraction, we change the sign of each term to be subtracted and then add.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$(2 a-b)-(-a-b)=2 a-b+a+b=3 a$.
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MCQ 61 Mark
Assertion (A): $\left(\frac{1}{x+y}\right)\left(\frac{1}{x-y}\right)=\frac{1}{x^2}-\frac{1}{y^2}$.
Reason (R): $(a+b)(a-b)=a^2-b^2$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
$\left(\frac{1}{x+y}\right)\left(\frac{1}{x-y}\right)=\frac{1}{(x+y)(x-y)}=\frac{1}{\left(x^2-y^2\right)}$
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MCQ 71 Mark
Assertion (A): If $\left(x+\frac{1}{x}\right)=4$ then $x^2+\frac{1}{x^2}=16$.
Reason (R): $\left(x+\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}+2$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
$\left(x+\frac{1}{x}\right)=4 \Rightarrow\left(x+\frac{1}{x}\right)^2=4^2=16 \Rightarrow x^2+\frac{1}{x^2}+2 \cdot x \cdot \frac{1}{x}=16$
$\Rightarrow x^2+\frac{1}{x^2}+2=16 \Rightarrow x^2+\frac{1}{x^2}=16-2=14$
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MCQ 81 Mark
Assertion (A): $\left(x^6-1\right)\left(x^6+1\right)=x^{12}-1$.
Reason (R) : $(a-b)(a+b)=a^2-b^2$
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$\left(x^6-1\right)\left(x^6+1\right)=\left(x^6\right)^2-1^2=\left(x^{12}-1\right) \quad\left[\because \quad(a-b)(a+b)=a^2-b^2\right]$
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Assertion (A) & Reason (B) MCQ - MATHS STD 8 Questions - Vidyadip