Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2016
Hard
The binary operation [] is defined as a[]b = ab+(a+b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the number x such that a[]x = a, for any a, is _____.
- 0
- B1
- C2
- D10
Explanation
Set a[]x = a: ax + (a+x) = a, which simplifies to ax + x = 0, i.e. x(a+1) = 0. For this to hold for EVERY real number a (not just a=-1), x must be 0.
Source: GATE ME 2016 Set-2 (2016)
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