Instructions

Let $$f(x) = (1 - x)^2 \sin^2 x + x^2$$ for all $$x \in IR$$ and let $$g(x) = \int_{1}^{x}\left(\frac{2(t - 1)}{t + 1} - \ln t\right)f(t) dt$$ for all $$x \in (1, \infty)$$.

Question 50

Consider the statements :
P : There exists some $$x \in IR$$ such that $$f(x) + 2x = 2(1 + x^2)$$
Q : There exists some $$x \in IR$$ such that $$2f(x) + 1 = 2x(1 + x)$$ Then

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JEE (Advanced) 2012 Paper-2

Consider the statements :P : There exists some $$x \in IR$$ such that $$f(x) + 2x = 2(1 + x^2)$$Q : There exists some $$x \in IR$$ such that $$2f(x) + 1 = 2x(1 + x)$$ Then

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Consider the statements :
P : There exists some $$x \in IR$$ such that $$f(x) + 2x = 2(1 + x^2)$$
Q : There exists some $$x \in IR$$ such that $$2f(x) + 1 = 2x(1 + x)$$ Then