GATE Mechanical 2021 Set 2 | GA Question: 4

Question

If $\bigoplus \div \bigodot =2;\: \bigoplus \div\Delta =3;\:\bigodot +\Delta =5; \:\Delta \times \bigotimes =10$,

Then, the value of $\left ( \bigotimes - \bigoplus \right )^{2}$, is :

• A. $0$
• B. $1$
• C. $4$
• D. $16$

Comments

nice problem.

Answer 1

Let’s suppose $\bigoplus  = a,\bigodot = b,\Delta = c,$ and $\bigotimes = d.$

Then,  $a \div b =2;\: a \div c =3;\: b  + c =5; \:c \times d =10$

Now, $a = 2b = 3c,$ and  $b + c = 5 \implies c = 2,d = 5,a = 6$

$\therefore$ The value of $\left(\bigotimes \;– \;\bigoplus\right)^{2} = (d-a)^{2} = (5 – 6)^{2} = (-1)^{2} = 1.$

So, the correct answer is $(B).$