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  4. If * is defined by a*b = a - b2 and ⊕ is defined by ⊕ = a2 + b, where a and b are integers, then (3 ⊕ 4) * 5 is equal to

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Q. 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

KEAMKEAM 2013Relations and Functions - Part 2

Solution:

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