Number System MCQs

The distance between the house of Rajan and Raman is 900 km and the house of former is at 100^th milestone where as the house of Raman is at 1000^th milestone. There are total 901 milestone at a regular interval of 1 km each. When you go to Raman's house from the house of Rajan which are on same highway, you will find that if the last digit (i.e. unit digit) of 3 digit number on every milestone is same as the first (i.e. hundreds digit) of the number on the next milestone is same, then these milestones must be red colour and rest will be of black. Total number of red colour milestone is:

If n is an integer, then (n³ - n) is always divisible by :

When (77⁷⁷ + 77) is divided by 78, the remainder is:

If n is any positive integer, 3⁴ⁿ - 4³ⁿ is always divisible by :

Select the correct option:
Convert decimal 99 to binary.

Find the remainder when 67⁹⁹ is divided by 7.

For an integer n, n! = n(n - 1) (n - 2) ..... 3.2.1
Then, 1! + 2! + 3! +.....+ 100!, when divided by 5 leaves remainder

Thrice the square of a natural number decreased by four times the number is equal to 50 more than the number, the number is -

If a² + b² + c² = 1, what is the maximum value of abc ?