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IIT JEE 2006 Paper : MATHEMATICS Section IV - Subjective Problems

This section contains 4 numerical problems. The answer to each of the questions would lie between 0 and 9999. You have to simply write the correct numerical value in the input box provided. You will be awarded 6 marks for correct numerical value and 0 for an incorrect value.
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A function  f (x) is a twice differentiable function such that  f (a) = 0,  f (b) = 2,  f (c) −1,  f (d) = 2 and  f (e) = 0; where a < b < c < d < e are real numbers. Then at least how many times the function g (x) = ( f '(x)) 2 + f (x).f "(x)   must vanish in the interval [a, e]?

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