Solution:

The required number is 499449.

The maximum sum of a number under 5 lakh will be of the number 499999 i.e. 49.
Thus the required number must be close to 499999.
The root of 499999 ~ 707.106
By calculating the square of 707, we get 499849 which is the answer.

Solution:

Stand up comedy (stand up comma D)

Solution:

Mayank took birth on Sunday.

Mayank was born 25 days before Rohit and thus the birth date of Mayank will be 8 Feb 1970.
Republic Day fell on Monday.
Number of days if counted from 26 January to 8 February will be 13.

After 13 days of Monday, it will be Sunday.

Solution:

There are 56 triangles add up to in the Snowflake plan.

There are 5 in the big equilateral triangle part into littler equilateral triangles.

There are 3 inside the focal little equilateral triangle utilizing the core vertex.

There are 18 (3 * 6) with the additional hexagonal sides around the little equilateral triangle.

There are 30 (3 * 10) with the additional hexagonal sides around the huge equilateral triangle.

Solution:

The word is Energy.
Nobody said anything about the order of 'g', 'r' and 'y' at the end of the word.
Also, we use energy every day.

Solution:

Yes, you should switch the envelope. In the beginning when you picked up the envelope, you had a 1/3 probability of finding an offer letter in the envelope. There was 2/3 chance that the letter was there in the two envelopes on the table.

If you keep your selected envelope, you still have a 1/3 chance of finding an offer letter in that. However, since the interviewer has removed one empty envelope from the table, if you switch, you have a probability of 2/3 that the offer letter is inside that.

Solution:

Actutally, the name of that boy is "Shut Up," and he is playing hide-and-seek with two of his friends who are named "Manners" and "Trouble". "Trouble" is the one who counted and he is looking for the other two boys. "Manners" is hiding up in the tree.

Solution:

276

Explanation:
6 = 1^1 + 2^1 + 3^1
14 = 1^2 + 2^2 + 3^2
36 = 1^3 + 2^3 + 3^3
98 = 1^4 + 2^4 + 3^4

Thus the next number will be
1^5 + 2^5 + 3^5 = 276

Solution:

6/(1 - 3/4) = 24

Solution:

The integer with the special property is -1.

To test the property, let us subtract any digit from it, let's say 5.

-1 - 5 = -6

The succeeding digit of 5 is 6.

When (-6) is divided by 6, it is completely divided.

For all other numbers as well, this stands true.