Question

Assertion :The range of $\log \left(\frac{1}{1+x^2}\right)$ is $(-\infty ,\infty )$ Reason: When $0<x\le 1$, $\log x\in (-\infty ,0]$

• A. Assertion is true, Reason is also true; Reason is the correct explanation of Assertion
• B. Assertion is true, Reason is also true; Reason is not the correct explanation of Assertion
• C. Assertion is true, Reason is false
• D. Assertion is false, Reason is true

Answer 1

The correct option is D Assertion is false, Reason is true

Statement II is true

Statement I is false as

Range of $\frac{1}{1+x^2}$is $(0,1)$, domain $R$

$\therefore \log \left(\frac{1}{1+x^2}\right)\in (-\infty ,0)$