A) 5
B) 10
C) 0
D) 15
Correct Answer: A
Solution :
[a] \[F'(x)=\left[ f\left( \frac{x}{2} \right).f'\left( \frac{x}{2} \right)+g\left( \frac{x}{2} \right)g'\left( \frac{x}{2} \right) \right]\] Here, \[g(x)=f'(x)\] and \[g'(x)=f''(x)=-f(x)\] so \[F'(x)=f\left( \frac{x}{2} \right)g\left( \frac{x}{2} \right)-f\left( \frac{x}{2} \right)g\left( \frac{x}{2} \right)=0\] \[\Rightarrow F(x)\] is constant function so \[F(10)=5\]
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