Question

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

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