Another way to solve it...
Implication $A\to B$ is not tautology if $B$ is false and $A$ is true.
For b option Let RHS ie. $b\to (a\wedge c)$ be false ie $b$ is false and $(a\wedge c)$ is false.
Now, $a$ AND $c$ is false if both $a$ and $c$ are false or one of them is true and other is false.
Now, if $a$ and $c$ both are false then $a\to c$ is true. Now ,LHS is $\text{true}$ and RHS is $\text{false}.$
So option b is not tautology..