Let T(n) be the function defined by $$T(1) =1, \: T(n) = 2T (\lfloor \frac{n}{2} \rfloor ) + \sqrt{n}$$
Which of the following statements is true?

In the following grammar:

$$\eqalign{ & X:: = X \oplus {Y \over Y} \cr & Y:: = Z*{Y \over Z} \cr & Z:: = id \cr} $$

Which of the following is true?

The correct matching for the following pairs is

An $$N$$-bit carry look ahead adder, where $$N$$ is a multiple of $$4,$$ employs $${\rm I}cs$$ $$74181$$ ($$4$$bit $$ALU$$) and $$74182$$ ($$4$$ bit carry look ahead generator). The minimum addition time using the best architecture for this adder is