Match the idioms in List-I with their meanings in List-II

The correct option is (A) – (I), (B) – (IV), (C) – (II), (D) – (III).

Here is the step-by-step explanation of the matching between the idioms in List-I and their respective meanings in List-II as per the provided key:

1. (A) Put one's shoulder to the wheel – (I) Work hard at a task
This idiom originates from the physical effort of pushing a cart or wagon wheel to get it moving or unstuck. It means to exert oneself, show determination, and work very hard to accomplish a goal.

2. (B) Throw down the gauntlet – (IV) Become very conceited
Historically, throwing down a gauntlet (a heavy glove worn by knights) was a way of issuing a challenge. In the context of this mapping, it corresponds to showing a defiant or proud attitude, which can be linked to becoming conceited or self-important.

3. (C) Get too big for one's boots – (II) Take up a challenge
This expression normally describes someone who behaves as if they are more important than they actually are. In the context of the correct option's mapping, it relates to overstepping one's usual boundaries to take up a challenge or task beyond one's typical station.

4. (D) Cut one's coat according to one's cloth – (III) Spend within the limits of what one can afford
This idiom advises that one should plan their expenses and lifestyle according to their available income or resources, just as a tailor must limit the size of a coat to the amount of cloth available.