**Rule**: The **Simple Present Tense** of the verb 'to be' ('is') is used to describe a current state or condition. **Correct Usage**: 'is thin' correctly describes the current condition of the ice. **Incorrect Options**: (a) 'is being' would imply the ice is temporarily behaving in a thin way, which is illogical. (b) 'has been' would need a duration (e.g., 'has been thin for a week'). (d) 'be' is the base form.

**Rule**: Both clauses describe actions happening at the same time, in the present moment. Therefore, the **Present Continuous Tense** is used for both. **Correct Usage**: 'is wagging' describes the dog's current action, and 'is coming' describes the owner's simultaneous action that is causing the dog's excitement. **Incorrect Options**: The other options create a mismatch of tenses for two simultaneous, ongoing actions.

**Rule**: The **Simple Present Tense** is used for habits and daily routines. The phrase 'every morning' indicates a repeated action. **Correct Usage**: 'works' correctly describes the old man's daily habit. The subject 'The old man' is singular. **Incorrect Options**: (a) 'is working' (Present Continuous) means he is working there now. (b) 'has worked' (Present Perfect) is for past experience. (d) 'work' is a plural verb.

**Rule**: The **Present Perfect Tense** is used to talk about past events that have happened multiple times ('several times') up to the present, showing a pattern of experience. **Correct Usage**: 'has burst' correctly refers to the repeated past occurrences that are part of the river's history. **Incorrect Options**: (a) 'bursts' (Simple Present) would imply it happens regularly. (b) 'is bursting' (Present Continuous) is for an action now. (d) 'burst' (base form) is grammatically incorrect.

**Rule**: **Subject-Verb Agreement** combined with **Present Perfect Tense**. The subject is 'The number', which is singular. The phrase 'since last year' indicates a period of time from the past to the present, which calls for the Present Perfect. **Correct Usage**: The singular verb 'has increased' agrees with the subject 'The number' and fits the time frame. **Incorrect Options**: (a) 'increase' and (d) 'have increased' are plural verbs. (b) 'increases' (Simple Present) is the wrong tense for the time frame 'since last year'.

**Rule**: The **Present Perfect Tense** is used with expressions of repetition like 'the first/second/fifth time' to count actions that have happened within an unfinished time period ('tonight'). **Correct Usage**: 'has woken' is the correct verb form to follow 'This is the fifth time' within a current time frame. **Incorrect Options**: (a) 'wakes' (Simple Present), (b) 'is waking' (Present Continuous), and (d) 'woke' (Simple Past) are grammatically incorrect in this specific structure.

**Rule**: The **Present Perfect Continuous Tense** is used for a repeated action (promising) that has been happening over a period of time ('for the last two years') without a final result yet. **Correct Usage**: 'has been promising' suggests that the promises have been made repeatedly over the period and the issue is still ongoing. **Incorrect Options**: (a) 'promises' (Simple Present) is a habit. (b) 'is promising' (Present Continuous) is for now. (d) 'has promised' (Present Perfect) implies a single, completed promise.

**Rule**: The **Present Perfect Tense** is used to describe a recently completed action with a present or future relevance. **Correct Usage**: 'has written' indicates that the action of writing is finished, and the result is a new book that is ready for release. 'has been writing' would imply he is still in the process of writing it. **Incorrect Options**: (a) 'writes' (Simple Present) is a habit. (b) 'is writing' (Present Continuous) means he is writing it now. (d) 'has been writing' suggests the process is not yet complete.

**Rule**: The **Present Perfect Continuous Tense** is used to describe a continuous action over a recent period ('all week') that leads to a present feeling or situation ('we are looking forward to the weekend'). **Correct Usage**: 'have been working' emphasizes the continuous effort that has just finished or is about to finish, causing the present feeling. **Incorrect Options**: (a) 'work' (Simple Present) is a habit. (b) 'are working' (Present Continuous) is for right now. (d) 'worked' (Simple Past) disconnects the action from the present feeling.

**Rule**: **Stative Verbs**. 'Weigh' is a stative verb when it refers to the state of having a certain weight. It is not used in continuous tenses. **Correct Usage**: 'weighs' correctly describes a factual characteristic of the box. The subject 'This box' is singular. **Incorrect Options**: (b) 'is weighing' would only be used for the action of measuring weight (e.g., 'He is weighing the ingredients'). (c) 'has weighed' is the wrong tense. (d) 'weigh' is a plural verb.