Direct speech : - Direct speech is used to report or rather repeat the words spoken by the speaker or writer in the way it is told by the speaker .

Indirect speech : - Indirect speech is the way in which you convey what someone said to another person, not necessarily using the exact words of the speaker.

The auxiliary verbs such as had, should , would, could, might, must and ought do not change in the reported speech:

• "The police could not prove that the man had been murdered", said Raveena, (Direct Speech)
• Raveena said the police could not prove that the man had been murdered. (Indirect Speech)

In the question : -

1. He said, "you must take responsibility of your own life."

The Indirect speech of the above sentence is :

He said I must/had to take responsibility of my own life .

While converting into indirect speech ,  the inverted commas converted into that , then the pronoun I is converted into you , then the modal verb must remains same and we can also use had here , then the objective part your own life .

2. She said , " I may wash my shirt ."

The Indirect speech of the above sentence is :

She said that she might take wash her shirt .

While converting into indirect speech ,  the inverted commas converted into that , then the pronoun I is converted into she , then the modal verb may is converted into might , then the objective part my shirt .

Thus , the Correct Option is A  , which is  1. He said I must/had to take responsibility of my own life . 2. She said that she might take wash her shirt .

Direct speech : - Direct speech is used to report or rather repeat the words spoken by the speaker or writer in the way it is told by the speaker .

Indirect speech : - Indirect speech is the way in which you convey what someone said to another person, not necessarily using the exact words of the speaker.

The auxiliary verbs such as had, should , would, could, might, must and ought do not change in the reported speech:

• "The police could not prove that the man had been murdered", said Raveena, (Direct Speech)
• Raveena said the police could not prove that the man had been murdered. (Indirect Speech)

In the question : -

1. Mania said, "I may go to the party now."

The Indirect speech of the above sentence is :

Mania said she might go to the party then.

While converting into indirect speech , the inverted commas converted into that , then the pronoun I is converted into he , then the modal verb will is converted into would , then the objective part my house .

2. You asked, " May I use the bathroom?"

The Indirect speech of the above sentence is :

You asked if you could use the bathroom.

While converting into indirect speech , the inverted commas converted into that , then the pronoun I is converted into he , then the modal verb will is converted into would , then the objective part my house .

Thus , the Correct Option is C  , which is

Direct speech : - Direct speech is used to report or rather repeat the words spoken by the speaker or writer in the way it is told by the speaker .

Indirect speech : - Indirect speech is the way in which you convey what someone said to another person, not necessarily using the exact words of the speaker.

The auxiliary verbs such as had, should , would, could, might, must and ought do not change in the reported speech:

• "The police could not prove that the man had been murdered", said Raveena, (Direct Speech)
• Raveena said the police could not prove that the man had been murdered. (Indirect Speech)

In the question : -

He said, "shall I pick you up?"

The Indirect speech of the above sentence is :

He asked if he should pick me up.

While converting into indirect speech in question sentence , said is converted into asked , the use if or whether , then  the inverted commas converted into that , then the pronoun I is converted into he , then the modal verb shall is converted into should , then the objective part pick me up  .

Thus , the Correct Option is A  , which is He asked if he should pick me up.