Question

Assertion: $x+y=5$ is the equation of a line passing through the origin.

Reason: $y=mx$ is the equation of a line passing through the origin.

Which of the following is correct?

• A. Both Assertion and Reason are true and Reason is correct explanation of Assertion.
• B. Both Assertion and Reason are true but reason is not a correct explanation of Assertion.
• C. Assertion is true and Reason is false.
• D. Assertion is false and Reason is true.

Answer 1

The correct option is D

Assertion is false and Reason is true.

Step 1: Explanation for assertion

If the equation passes through the origin then it will have $(0,0)$ as its solution.

Substituting $(0,0)$ in the equation $x+y=5$,

$$\begin{gathered} x+y=5 \\ \Rightarrow RHS=5 \\ \Rightarrow LHS=0+0=0 \\ \Rightarrow LHS\ne RHS \end{gathered}$$

Hence, Assertion is false.

Step 2: Explanation for reason

Given, $y=mx$

It can be rewritten as: $y-mx=0$

If this line passes through the origin then it will have $(0,0)$ as its solution.

Substituting $(0,0)$ in the equation ,

$$\begin{gathered} y-mx=0 \\ \Rightarrow RHS=0 \\ \Rightarrow LHS=0-m\times 0=0 \\ \Rightarrow LHS=RHS \end{gathered}$$

Hence, Reason is true.

Step 3: Checking if Assertion and Reason are related.

Since Assertion is false they can't be related to each other anyway.

Thus, Assertion is false and Reason is true and they are not related to each other.

Hence, the correct answer is option D.