In the following sentence on success in life, identify which part contains a grammatical error: Progress in life depends (1) a good deal under crossing (2) one threshold after another. (3) No error (4).

Introduction / Context:
This error spotting question checks your knowledge of fixed prepositional patterns after verbs such as "depend". Many English verbs are followed by particular prepositions, and using the wrong one makes the sentence sound unnatural or incorrect. Here, you must find which numbered portion of the sentence contains the mistake, or decide that the sentence is fully correct.

Given Data / Assumptions:

• Part (1): Progress in life depends.
• Part (2): a good deal under crossing.
• Part (3): one threshold after another.
• Part (4): No error.
• The common collocation is "depends on", not "depends under".

Concept / Approach:
In standard English, the verb "depend" is normally followed by the preposition "on" (or sometimes "upon"), not by "under". Phrases like "depends on effort" or "depends on circumstances" are examples of this fixed pattern. The chunk "a good deal under crossing" is therefore wrong because "under" does not collocate with "depends". The rest of the sentence, which uses the metaphor "crossing one threshold after another" to describe progress through life, is grammatically acceptable and coherent.

Step-by-Step Solution:
Step 1: Examine part (1): "Progress in life depends." This is correct so far and prepares for a following prepositional phrase. Step 2: Look at part (2): "a good deal under crossing." The important sequence is "depends a good deal under". Step 3: Recall that the standard expression is "depends a good deal on", not "under". The preposition is wrong here. Step 4: Recognise that the correct phrase should be "depends a good deal on crossing". Step 5: Check part (3): "one threshold after another." This is a clear and correct phrase extending the idea of continuous advancement. Step 6: Therefore, the only error lies in the choice of preposition in part (2).

Verification / Alternative check:
Rewrite the sentence correctly: "Progress in life depends a good deal on crossing one threshold after another." This version reads smoothly and follows the widely used pattern "depends on something". If we kept "under" instead of "on", the phrase "depends under crossing" would not match any recognised English structure. The rest of the sentence does not require modification, confirming that part (2) is the sole source of error.

Why Other Options Are Wrong:
Part (1) is correctly formed; "Progress in life depends" is a natural starting clause. Part (3) uses the metaphor "one threshold after another" appropriately, so it contains no grammatical problem. Part (4), "No error", is incorrect because there is a clear error in part (2). Thus, none of the other labelled parts can be selected as containing the grammatical mistake.

Common Pitfalls:
Learners may overlook errors in small function words like prepositions, focusing instead on nouns and verbs. Some may imagine that "under" adds an extra nuance, but in this case it simply breaks the fixed collocation. To avoid such mistakes, it is helpful to memorise common verb preposition pairs such as "depend on", "insist on", "agree with", and "apologise for". Awareness of these patterns makes it easier to spot when an exam question deliberately uses a wrong preposition.

Final Answer:
The incorrect portion is Part (2), because "under" should be replaced with "on" in the expression "depends a good deal on crossing".