'Although' and 'but' are both conjunctions of contrast and should not be used in the same sentence structure. Use 'Although... (yet)' or simply a comma. Remove 'but'.

When an infinitive is used as an adjective to qualify a noun, the appropriate preposition must be used if the verb is intransitive. It should be 'to live in'.

When 'enter' means to go into a physical place, it is not followed by a preposition. 'Into' is redundant. It should be 'I entered the room'.

The verb 'resembles' takes a direct object and is not followed by a preposition. 'With' is incorrect. It should be 'She resembles her mother'.

Names of subjects ending in 's' like Mathematics, Physics, and Economics are singular and take a singular verb. It should be 'Mathematics is...'.

The correct correlative conjunction is 'No sooner... than'. 'When' is used with 'Hardly/Scarcely'. The correct phrase is 'than the train left'.

'Hardly' means 'scarcely' or 'almost not', which contradicts the intended meaning. The adverb meaning 'with great effort' is 'hard'. He works 'hard'.

'Cattle' is a collective noun that is plural in meaning and requires a plural verb. It should be 'The cattle are grazing...'.

The correct preposition for the phrase meaning proficient or skilled is 'good at', not 'good in'. The sentence should be 'She is good at English'.

The Present Perfect tense ('have seen') cannot be used with a specific past time marker like 'yesterday'. Simple Past tense must be used. Correct: 'I saw him yesterday'.