The simplified switching circuit for the following circuit is

The logical statement $(p \vee q) \wedge [(\sim p \wedge q) \vee (p \wedge \sim q)] \wedge \sim q$ is logically equivalent to ...

Which of the following logical statements is a tautology?

In $\triangle ABC$, with usual notations, if the sides $a$, $b$ and $c$ are in the ratio $18 : 17 : 7$, then $\cot\dfrac{A}{2} : \cot\dfrac{B}{2} : \cot\dfrac{C}{2} =$