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# Statement 1: If g(x) is a differentiable function, g(2)≠0, g(−2)≠0 and Rolle's theorem is not applicable to f(x) =x2−4g(x) in [−2,2], then g(x) has at least one root in (−2,2). Statement 2: If f(a)=f(b), then Rolle's theorem is applicable for x∈(a,b)

A
Only Statement 1 is true
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B
Only Statement 2 is true
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C
Both statements are true
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D
Both statements are false
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Solution

## The correct option is A Only Statement 1 is true Statement 1: Given : g(x) is a differentiable function and Rolle's theorem is not applicable to f(x) in (−2,2), but f(−2)=f(2)=0. It implies that either f(x) is discontinuous or not differentiable at atleast one point in (−2,2). So, g(x)=0 has atleast one root in (−2,2). Hence, statement 1 is correct. Statement 2: Since f(x) must be continuous in [a,b] and differentiable in (a,b) is not given. ∴ Statement 2 is wrong.

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