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Mathematics · 2014
JEE Main · 12 April 2014, Shift 1 · Q88
Statement I: The equation ( sin^-1 x)^3+( cos^-1 x)^3- a π^3=0 has a solution for all a ≥ 1/32. Statement II: For any x ∈ R, sin^-1 x+ cos^-1 x=(π)/2…
Statement I : The equation $\displaystyle \left(\sin ^{-1} x\right)^3+\left(\cos ^{-1} x\right)^3-\mathrm{a} \pi^3=0$ has a solution for all $\displaystyle \mathrm{a} \geqslant \frac{1}{32}$.Statement II : For any $\displaystyle x \in \mathbf{R}$, $\displaystyle \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}$ and
$$0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^2 \leq \frac{9 \pi^2}{16} .
$$
Official answer
(4)
Statement I is false and statement II is true.
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JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.