Question

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

• A. 164
• B. 38
• C. -12
• D. -28
• E. 144

Answer 1

Answer: (C)

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