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Questions  

Let F(x)=ex2x5dx

Statement-1: If F(0) = 0, then F(1)=152e1

Statement-2F increases on (0,)

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a
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
b
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation forSTATEMENT-1
c
STATEMENT-1 is True, STATEMENT-2 is False
d
STATEMENT-1 is False, STATEMENT-2 is True

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detailed solution

Correct option is B

Put  x2=t,∫e−x2x5dx=12∫e−tt2dt=C−12e−x2x4+2x2+2F(0)=0 ⇒ C=1Hence F(x)=1−12e−x2x4+2x2+2F′(x)=e−x2x5>0x∈(0,∞)


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