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Q.

Statement-1: The function x2(ex+e-x) is increasing for all x>0.

Statement-2: The functions x2ex and x2e-x are increasing for all x>0 
and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b).

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a

Statement-1 is false and the Statement-2 is true

b

Statement -1 is true and the Statement-2 is false

c

Statement-1 is true, Statement-2 is true and the Statement 2 is not the correct explanation of the Statement 1.

d

Statement-1 is true, Statement-2 is true and the Statement-2 is true explanation of the Statement-1.

answer is D.

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Detailed Solution

f(x)=x2(ex+e-x) f'(x)=x2(ex-e-x)+2x(ex+e-x)   =x(x(ex-e-x)+2(ex+e-x)) f(x) is increasing  f'(x)>0x>0

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