Question

Assertion (A) : A function $y=f(x)$ defined by $x^2-co{t}^{-1}y=\pi$ then domain of $f(x)=R$.
Reason (R) : $co{t}^{-1}y\in (0,\pi )$

• A. Both (A) & (R) are individually true & (R) is correct 3. explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (D)

From given, $x^2-co{t}^{-1}y=\pi$
$\Rightarrow x^2-\pi =co{t}^{-1}y$
$\Rightarrow 0<x^2-\pi <\pi (\because co{t}^{-1}y\in (0,\pi ))$
$\Rightarrow \pi <x^2<2\pi$
$\Rightarrow x\in (-\sqrt{2\pi },-\sqrt{\pi })\cup (\sqrt{\pi },\sqrt{2\pi })$
$\Rightarrow$ Assertion (A) is false but Reason (R) is true.