If S is a set of \[P(x)\] is polynomial of degree \[\le 2\] such that \[P(0)=0,\]\[P(1)=1\],\[P'(x)>0\text{ }\forall x\in (0,\,1)\], then [IIT Screening 2005]

\[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in (0,\infty )\]

\[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in R\]

\[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in (0,2)\]

If S is a set of \[P(x)\] is polynomial of degree \[\le 2\] such that

1.	If S is a set of \[P(x)\] is polynomial of degree \[\le 2\] such that \[P(0)=0,\]\[P(1)=1\],\[P'(x)>0\text{ }\forall x\in (0,\,1)\], then [IIT Screening 2005]
A.	\[S=0\]
B.	\[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in (0,\infty )\]
C.	\[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in R\]
D.	\[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in (0,2)\]
Answer» E.

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If S is a set of \[P(x)\] is polynomial of degree \[\le 2\] such that \[P(0)=0,\]\[P(1)=1\],\[P'(x)>0\text{ }\forall x\in (0,\,1)\], then [IIT Screening 2005]

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