Fundamental Concepts of Algebra — Assertion Reason Type Questions

Assertion (A): Since, 2 − 5 + 8 = 5

$\Rightarrow 2x − 5y + 8z = 5xyz$

Reason (R): Only the like terms can be added or subtracted together.

$\therefore 2x − 5y + 8z$ can not be added to get the single term.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

In $2x - 5y + 8z$, the terms $2x, -5y$ and $8z$ are unlike terms, so they cannot be combined into a single term. Thus, $2x - 5y + 8z \neq 5xyz$ and Assertion (A) is false.

As only like terms (terms having the same literal coefficients) can be added or subtracted to get a single term, and so $2x - 5y + 8z$ cannot be added to get a single term. So, Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): $(5x^2 − 7x) − (x^2 + x) + (−3x^2 + 5x)$ is equal to $x^2 − 3x$.

Reason (R): Given expression

$= 5x^2 − 7x − x^2 − x − 3x^2 + 5x$

$= (5 − 1 − 3)x^2 + (−7 − 1 + 5)x$

$= x^2 − 3x$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Solving,

$\Rightarrow (5x^2 - 7x) - (x^2 + x) + (-3x^2 + 5x) \\[1em] \Rightarrow 5x^2 - 7x - x^2 - x - 3x^2 + 5x \\[1em] \Rightarrow (5 - 1 - 3)x^2 + (-7 - 1 + 5)x \\[1em] \Rightarrow x^2 - 3x$

So, Assertion (A) is true.

The steps shown in Reason (R) are correct, so Reason (R) is true.

Hence, option 3 is the correct option.