GATE ECE 2015 Set 1 | GA | Question: 4

Question

Operators $\square,$ $\Diamond$ and $\rightarrow$ are defined by: $a\,\square\,b=\frac{a-b}{a+b};\, a\,\Diamond\, b=\frac{a+b}{a-b};$ $a\,\rightarrow\, b=ab.$

Find the value of $(66\,\square\, 6)\rightarrow(66\,\Diamond\, 6).$

• A. $-2$
• B. $-1$
• C. $1$
• D. $2$

Comments

independent for value of real value of a and b answer =1

Answer 1

$\require {cancel}(66\,\square\, 6)\rightarrow(66\,\Diamond\; 6) = \frac{\cancel{66-6}}{\cancel{66+6}} \times \frac{\cancel{66+6}}{\cancel{66-6}} = 1.$

Comments

If they asked find the value of $(P\,\square\, Q)\rightarrow(P\,\Diamond\; Q)?$

Then $(P\,\square\, Q)\rightarrow(P\,\Diamond\; Q) = \dfrac{P-Q}{P+Q} \times \dfrac{P+Q}{P-Q} = 1$

Answer 2

option C as (60/52)*(52/60)=1