If in an election to a State Legislative Assembly, the candidate who is declared elected loses his deposit, it means that Option 4: a very large number of candidates contested the election.

In elections, candidates are often required to deposit a certain amount of money as security. If a candidate fails to secure a minimum percentage of votes (usually a specific threshold, such as one-sixth or one-eighth of the total valid votes), their deposit is forfeited. This deposit serves as a deterrent for frivolous candidates and helps in maintaining the integrity of the election process.

Losing the deposit suggests that the candidate did not receive a significant number of votes. When there is a large number of candidates contesting the election, the votes are likely to be divided among them. As a result, individual candidates may not receive a substantial share of votes, leading to a situation where even the elected candidate may lose their deposit.

Let`s consider the other options and explain why they are not the correct choices:

Option 1: the polling was very poor

The phrase "polling was very poor" generally refers to low voter turnout. However, low voter turnout alone does not necessarily indicate that the winning candidate will lose their deposit. Voter turnout does not directly affect the financial standing of the candidates.

Option 2: the election was for a multi-member constituency

In a multi-member constituency, multiple candidates are elected to represent the constituency. In such cases, the elected candidates are typically the ones who receive the highest number of votes, regardless of whether they lose their deposit. The loss of deposit is not directly related to the type of constituency.

Option 3: the elected candidate`s victory over his nearest rival was very marginal

The margin of victory between the elected candidate and their nearest rival does not determine whether the winning candidate loses their deposit. The deposit is forfeited based on the candidate`s share of the total votes, not the margin by which they won.

Therefore, based on the explanation provided above, Option 4 is the correct answer, indicating that a very large number of candidates contested the election.