Mohan correctly remembers that his father's birthday is before 20th January but after 16th January whereas his sister correctly remembers that their father's birthday is after 18th January but before 23rd January. On which date in January is definitely their father's birthday?

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.

Days by Pratap - [20,21 or 22] in April
Days by his sister, not on or after 22 April
Clearly, the answer is [20 or 21] in April.

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.

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.

Ascending order 1 2 3 4 5 7 8 9
? Required difference = 5 - 3 = 2

After interchanging the first and the last digit, numbers are 984, 145, 456, 359, 387
Hence, second highest number = 456 means 654.