Browse Questions

# In the set of integers with operation $^{\ast}$ defined by $a ^{\ast} b=a+b-ab,$ the value of $3^{\ast}(4^{\ast} 5)$ is

$\begin{array}{1 1}(1)25&(2)15\\(3)10&(4)5\end{array}$

$a+b =a+b-ab$
$3 *(4*5) =3 * (4+5-4(5))$
$\qquad= 3 *(9-20)$
$\qquad= 3 * (-11)$
$\qquad =3 +(-11) -3(-11)$
$\qquad= 3-11+33$
$\qquad= -8+33=25$
Hence 1 is the correct answer.