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GATE 2016 ME (ME2) – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

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 .

  1. 0
  2. 1
  3. 2
  4. 10

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Correct answer: (A) 0

Explanation

For identity x, require ax+a+x=a for every real a. This simplifies to x(a+1)=0 for every a, forcing x=0. Substitution confirms a square0=0+a+0=a. Thus **0, A**.