Question

If $*$ is defined by $a*b$ = $a - b^2$ and $\oplus$ is defined by $\oplus$ = $a^2 + b$, where a and b are integers, then ($3 \oplus 4) * 5$ is equal to

• A. 164
• B. 38
• C. -12
• D. -28

Answer 1

Answer: (C)

-12

Answer 2

Given, $a^{*}b =a-b^{2}\,\,\,\,\,\dots(i)$
and $a \oplus b=a^{2}+b \,\,\,\,\,\dots(ii)$
where, $a$ and $b$ are integers.
Then, (3 \oplus 4)^{*} 5 =\left\\{(3)^{2}+4\right\\}^{*} 5
$=(9+4)^{*} 5=13^{*} 5$
$=13-(5)^{2}=13-25=-12$