KVPY Government Jobs Exams

Let f : R → R be a continuous function satisfying f(x) = x + ∫
x
0
f (t) dt , for all x ∈ R. Then the number of
elements in the set S = {x ∈ R ; f(x) = 0} is-

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KVPY Other Question

Let V1 be the volume of a given right circular cone with O as the centre of the base and A as its apex. Let V2
be the maximum volume of the right circular cone inscribed in the given cone whose apex is O and whose
base is parallel to the base of the given cone. Then the ratio V2/V1 is- The value of ∫
π
− π −
2
0
min{| x |, cos 1(cos x)} dx is