Number of days between 22 January 2000 & 23 January 2005 

365*3 + 366*2 – 22 + 23 = 1828

261 weeks and 1 days

Since 23 January 2005 was given to be Thrusday.

22 January 2000 will be Thursday - 1 = Wednesday

Days left in April = 30 – 27 = 3 

Days in September to count = 28 

Thus total number of days from Aarush's birthday to Mitul’s birthday = 3 + 31 + 30 + 31 + 31 + 28 = 154 

Thus number of odd days = 154 | 7 = 0 

As Aarush's birthday is on Thursday, Mitul’s birthday will on Thursday + 0 days = Thursday.

According to Akshar Date of match may be one of 27/4, 28/4, 29/4, 

According to Suresh Date of match may be one of 23/4, 24/4, 25/4, 26/4, 27/4, 

Common date is 27/4. 

Thus option C is the correct answer.

Number of hours in a year = 365*24 = 8760 

Hours in a day = 30 

Number of hours in a week = 30*12 = 360 

Number of weeks in a year = 8760/360 = 24.33

Since, A clock gains five minutes every hour i.e. 65 minutes instead of 60 minutes. 

Now, hour hand = 65/60 = 13/12

Therefore, the second hand will traverse 13/12 * 360^o = 390^o

Hence, option C is correct.

At 6’o clock the hour hand is at 6 and minute hand is at 12 so they are 30 min apart 

Now to be together minute hand has to gain minutes over the hour hand 

Time taken to gain 55 minutes = 60 minute 

Time taken to gain 1 minute = 60/55min 

Time taken to gain 30 min = 60/55 × 30 = 360/11 

So the hands will coincide at 32 

Hence, the correct option is A.

Clearly 1^st, 8^th, 15^th 22^nd and 29^th October are Sundays. 

So, 31^st October is Tuesday. 

1^st November will be Wednesday

29th February comes in a Leap Year. Therefore, his birthday will come once in four years. Hence, option C is the right answer. 

According to Hari, his father’s birthday may be on 14^th or 15^th June. 

According to Hari’s sister, their father’s birthday may be on 15^th, 16^th or 17^th June.

Common Date ⇒ 15^th June