Download App

Operations on Algebraic Expressions — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSOperations on Algebraic Expressions1 Mark
MCQ
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]
$
$\begin{array}{l}=\left[\left(p^2\right)^2-1^2\right]\left(p^4+1\right)=\left(p^4-1\right)\left(p^4+1\right) \\ =\left[\left(p^4\right)^2-1^2\right]=\left(p^8-1\right) .\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion (A) & Reason (B) MCQ" from Operations on Algebraic Expressions→Operations on Algebraic Expressions — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): $10$ men can dig a trench in $15$ days. Then in $55$ days $3$ men take to dig a trench
Reasons (R): A direct proportion shows the direct the relation between two quantities. An inverse proportion shows inverse or indirect relation between two quantities
→
Assertion (A): The ratio 4 : 25 converted to percentage is 18%.
Reasons (R): A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.
→
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ Rational numbers are closed under subtraction
Reason $(R):$ A rational number is a number that is in the form of $\frac{\text{p}}{\text{q}}$ where $p$ and $q$ are integers, and $q$ is not equal to $0.$
→
Assertion (A): The sum of the internal angles of a polygon is 10 right angles. Then the number of sides is 7
Reason (R): Quadrilaterals are composed of two triangles. Seeing as we know the sum of the interior angles of a triangle is 180°, it follows that the sum of the interior angles of a quadrilateral is 360°.
→
Assertion (A): 10000 is not a cube number.
Reasons (R): A cube number is a number multiplied by itself 3 times.
→
Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The coefficient in the term $-20$bc is $20.$
Reasons $(R)$: A coefficient is a number multiplied by a variable
→
Assertion (A): $8^{-2}$ is the same as $2^{-8}$.
Reason (R): If $\frac{a}{b}$ be a rational number and $n$ be a positive integer then $\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^n$.
→
Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): A boy runs $1k\ m$ in $10$ minutes. Then He will take $6$ minutes to ran $600\ m$
Reasons (R): A direct proportion shows the direct the relation between two quantities.
→
Assertions (A): Hindi have maximum books.
Observe the figure as reasons for the following assertions:
→
Assertion (A): The degree of the equation x2 - 2x + 1 = x2 - 3 is 2
Reason (R): Standard form for linear equation in one variable is ax + b = 0. where x is variable and a, b are arbitrary constants.
→