Sets, Relations and Function: Let mathbbR be the set of real numbers and ' * ' be a binary… | JEE Main 2021

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 1

Let $\mathbb{R}$ be the set of real numbers and '$*$' be a binary operation on $\mathbb{R}-\{0\}$ defined by $a*b=a+2b+\frac{a}{b}$. Then the operation '$*$' is

Sets, Relations and Function

associative and commutativecommutative but not associativeassociative but not commutativeneither associative nor commutative.✓ Correct answer

Solution

$1*2=1+4+\tfrac12=5.5$ but $2*1=2+2+2=6$, so not commutative. $(1*1)*1=4*1=10$ but $1*(1*1)=1*4=9.25$, so not associative. Option (D).

Sets, Relations and Function - JEE Mathematics question (JEE Main 2021 (Online) 3rd August Evening Shift)

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