JEE Advance - Mathematics (2002 - No. 6)
Let $$f\left( x \right) = \int\limits_1^x {\sqrt {2 - {t^2}} \,dt.} $$ Then the real roots of the equation
$${x^2} - f'\left( x \right) = 0$$ are
$${x^2} - f'\left( x \right) = 0$$ are
$$ \pm 1$$
$$ \pm {1 \over {\sqrt 2 }}$$
$$ \pm {1 \over 2}$$
$$0$$ and $$1$$