Pratap correctly remembers that his mother's birthday is before 23rd April but after 19th April, whereas his sister correctly remembers that their mother's birthday is not on or after 22nd April. On which day in April is definitely their's mother's birthday?

According to question,
Samant remembers that his brother's birthday is after 16th but before 20th of January
it means birthday will be on of any one date
17th, 18th, 19th January.
According to his sister remembers that her brother's birthday is after 17th but before 19th of January.
it means birthday will be on
18th January.
Her brother's birth day is on 18th of January as 18th January is common to both the groups of dates.

Days by Sameer [16,17],in February
Days by Kanika [17,18] in February
17th February is common in both the groups.
Cleary, the correct date is 17th February.

Days by Ayush, [13, 14, 15] in January
Days by Mehar, [14, 15, 16] in January

Clearly, 14th and 15th January are common in both the groups.
Hence, the correct answer is either 14th or 15th January.

Sudha read the book 4 days after Sunday. it means Sudha read the book on Thursday. Hence, Anil will read the book on Friday.

Days by Menna, 19th, 20th or 21st May.
Days by her brother, 21st , 22nd or 23rd May.
Clearly, 21st may is common in both the groups and hence it is the required day.

According to above question,
Days by Rajat, June 18 or earlier.
Days by his sister, June 18 or June 19.
Clearly, June 18 is the required day.

According to question,
Days by Mohan, [17th, 18th or 19th] January
Days by sister, [19th, 20th, 21st or 22nd] January.
Required days is 19th January as it is common in both the groups.

In the given series, there are six 9's followed by and preceded by number divisible by 2.

Total number of boys = (10 + 27 - 1)
    = 37 - 1 = 36
So, Rajan's position from the right
= (36 - 10) + 1 = 26 + 1 = 27

When Rahul was shifted by three places towards his right side, then he occupies the middle position, i.e., 13th position.