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TIFR-2014-Maths-B-1

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Let $f : [0, 1] \rightarrow [0, \infty)$ be continuous. Suppose

$\int_{0}^{x} f(t) \text{d}t \geq f(x)$, for all $x \in [0, 1]$. Then 

  1. No such function exists 
  2. There are infinitely many such functions 
  3. There is only one such function 
  4. There are exactly two such functions
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