Let y=x2⋅e−x For increasing function, dxdy>0⇒x[(2−x)e−x]>0∵x>0,∴(2−x)e−x>0⇒(2−x)ex1>0 For 0<x<2,(2−x)<0∴ex1<0, but it is not possible Hence the statement- 2 is false.
JEE Main 2013 — Mathematics Calculus
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).
Held on 22 Apr 2013 · Verified 6 Jul 2026.
Statement-1 is false; Statement-2 is true.
Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Statement-1 is true; Statement-2 is false.
Statement-1is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.
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