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JEE Advanced 2017 Paper 1

Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three columns for the following table
Let f(x)=x+logex−xlogex,x∊(0,∞)
• Column 1 contains information about zeros of f(x),f′(x) and f′′(x)
• Column 2 contains information about the limiting behavior of f(x),f′(x) and f′′(x) at infinity
• Column 3 contains information about increasing/decreasing nature of f(x) and f′(x).

Column 1	Column 2	Column 3
(I) f(x)=0 for some x∊(1,e2)	(i) limx→∞f(x)=0	f is increasing in (0,1)
(II) f′(x)=0 for some x∊(1,e)	(ii) limx→∞f(x)=−∞	(Q) f is decreasing in (e.e2)
(III) f′(x)=0 for some x∊(0,1)	(iii)limx→∞f′(x)=−∞	f′ increasing in (0,1)
(IV) f′′(x)=0 for some x∊(1,e)	(iv) limx→∞f′′(x)=0	(S) f′ decresing in (e,e2)

Question : 54

Total: 54

Which of the following options is the only CORRECT combination ?

[JEE Adv 2017 P1]

(I) (ii) (R)
(II) (iii) (S)
(III) (iv) (P)
(IV) (i) (S)

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