Select the option that is related to the third number in the same way as the second number is related to the first number.
2 : 32 ∷ 4 : ?

Given: 2 : 32 :: 4 : ?

Logic: For each pair, multiply the first number by itself 5 times to get the second number.

2 : 32 $$\rightarrow$$ 2 $$\times$$ 2 $$\times$$ 2 $$\times$$ 2 $$\times$$​ 2 = (2)$$^5$$ = 32

Similarly, follow the same pattern for 4 : ? $$\rightarrow$$ 4 $$\times$$ 4 $$\times$$ 4 $$\times$$ 4 $$\times$$ 4 = (4)$$^5$$ = 1024

So, the correct answer is (b).