Question

Assertion :Let $f\left(x\right)=\tan x$ and $g\left(x\right)=x^2$ then $f\left(x\right)+g\left(x\right)$ is neither even nor odd function. Reason: If $h\left(x\right)=f\left(x\right)+g\left(x\right)$, then $h\left(x\right)$ does not satisfy the condition $h(-x)=h\left(x\right)$ and $h(-x)=-h\left(x\right)$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$h\left(x\right)=\tan x+x^2$
$\therefore h(-x)=\tan (-x)+(-x^2)=-\tan x+x^2$
$\Rightarrow -\tan x+x^2\ne h\left(x\right)$
$\Rightarrow h(-x)\ne h\left(x\right)$
and $-(\tan x-x^2)\ne h\left(x\right)$ and $h(-x)\ne -h\left(x\right)$
$\Rightarrow h\left(x\right)$ is neither even nor odd
Both Assertion $\left(A\right)$ and Reason $\left(R\right)$ are correct & Reason is the correct explanation of Assertion.
'A' is correct