Question

If $\ast$ is defined by $a\ast b=a-b^2$ and $\oplus$ is defined by $a\oplus b=a^2+b$, 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)

$-12$

Given, $a\ast b=a-b^2$ .... (i)

and $a\oplus b=a^2+b$ .... (ii)

where, $a$ and $b$ are integers

Then, $(3\oplus 4)\ast 5=\left\{\right(3{)}^2+4\}\ast 5$

$=(9+4)\ast 5=13\ast 5$

$=13-(5{)}^2=13-25=-12$