KVPY SX SB Exam 2016 Question Paper

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Question : 15 of 120

Marks: +1, -0

The number of continuous function f : [0, 1] → [0, 1] such that

f(x) < x^2

for all x and

∫↖{1}↙{0}f(x) dx=1/3

is :

0
1
2
infinite

Solution:

∴ f(x) is always positive for x ∈ [0, 1]

∴\f(\x) < x^2⇒∫↖{1}↙{0}f(x)dx < ∫↖{1}↙{0}x^2

I ≤ 1/3

But it is given that

I = 1/3

which is not possible

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