**Rule:** The phrasal verb 'set up' means to establish a new business or organization. The company has to set up a new branch, so 'up' is the correct preposition. 'Set off' means to start a journey. 'Set out' means to begin a journey or a task. 'Set in' means to begin and seem likely to continue.

**Rule:** The adjective 'essential' is followed by 'to' or 'for'. 'Essential to' is used to show the importance of something for another thing to exist or succeed. She is essential to the success of the project, so 'to' is the correct preposition. 'Essential for' is also possible. Both are correct. Options (c) and (d) are incorrect.

**Rule:** The adjective 'close' is followed by the preposition 'to'. 'Close to' doing something means to be nearly in a particular state or condition. The company is close to signing a new deal, so 'to' is the correct preposition. Options (b), (c), and (d) are incorrect.

**Rule:** The adjective 'different' is followed by the preposition 'from'. 'Different from' is the standard and most widely accepted form. He is different from his brother, so 'from' is the correct preposition. Option (b) 'than' is used in American English, but 'from' is preferred in British English and formal writing. Option (c) 'to' is also used informally in some dialects. Option (d) 'with' is grammatically incorrect.

**Rule:** The verb 'provide' is followed by the preposition 'with' when the thing provided follows the preposition. 'Provide someone with something' is the correct structure. The company has to provide its customers with reliable service, so 'with' is the correct preposition. Option (b) 'to' would be used if the sentence was 'The company has to provide reliable service to its customers'. Option (c) 'for' is incorrect. Option (d) 'of' is grammatically incorrect.

**Rule:** The verb 'invested' is followed by the preposition 'in'. 'Invested in' something means to put money, effort, or time into it to make a profit or get an advantage. The company has put money in research and development, so 'in' is the correct preposition. Option (b) 'on' is incorrect. Option (c) 'at' is incorrect. Option (d) 'with' is grammatically incorrect.

**Rule:** The phrasal verb 'cutting down' on something means to reduce the amount of it. He is cutting down on his expenses, so 'down' is the correct preposition. 'Cutting off' means to stop the supply of something. 'Cutting out' means to stop doing something. 'Cutting in' means to interrupt. Options (b), (c), and (d) are incorrect.

**Rule:** The verb 'distinguish' is followed by 'between' or 'from'. 'Distinguish between' is used to show the difference between two things. She has to distinguish between good and evil, so 'between' is the correct preposition. 'Distinguish from' is used to recognize the difference between two things. Option (b) is also possible. 'Among' is used for more than two things. Option (d) is incorrect.

**Rule:** The adjective 'proper' is followed by 'for' or 'to'. 'Proper for' is used to show that something is suitable for a particular person or purpose. It is not proper for a gentleman to behave rudely, so 'for' is the correct preposition. 'Proper to' is used to show that something belongs to a particular person or thing. Options (b), (c), and (d) are incorrect.

**Rule:** The verb 'insist' is followed by the preposition 'on'. 'Insist on' means to demand something forcefully, not accepting refusal. She has to insist on going to the party, so 'on' is the correct preposition. Option (b) 'for' is incorrect. Option (c) 'with' is incorrect. Option (d) 'to' is grammatically incorrect.