Correct In octal number system, we have 8 digits 0, 1, 2, 3, 4, 5, 6 and 7. So, 168 cannot be an octal number. 8 is not a digit in octal number system.

Hexadecimal number system has 16 distinct digits. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

The positional weight of digits in a number in a number system with base n are given by 1, n, n² ....... etc. starting from rightmost place moving one place leftward. So, 11 = n + 1 in decimal system where n is the base of the number system of 11. Thus, n + 1 = 6 as per the question. Hence, n = 5

Correct 111 is the highest 3 digit number in binary system. So the next number will be 1000.

At each of the 4 places in a 4 digit number in octal number system, we have 8 options. So, we can have 8 * 8 * 8 * 8 = 8⁴ combinations of 4 octal digits. Hence, these many numbers can be there.

77 in octal system is equivalent to 8*7 + 7 = 63 in decimal number system. 62 in decimal can be written as sum of powers of 2 as 32 + 16 + 8 + 4 + 2 + 1. So, the required binary number is 111111.

In octal number system, we have 8 digits from 0 to 7 ony. Hence, 578 is not an octal number.

0.75 + 0.25 = 1.00

0.11 in binary number system is equal to 0.5 + 0.25 = 0.75 in decimal number system.

1101 + 101 = 1202 in any number system where digits upto 2 are present. This is so in all the number systems with base 3 or more.

If one is subtracted from the lowest 4 digit number 1000, we get the highest 3 digit number in that number system. In octal, it is 777.

With 8 binary digits, we can have 2*2*2*2*2*2*2*2 = 256 distinct combinations of 0s and 1s. Each combination can represent a character. Thus, the right answer is 256.

F is equivalent to 15 in decimal. Hexadecimal FF will be equal to 16*15 + 15 = 255 in decimal number system.

While converting a hexadecimal number to binary, we can convert each digit to a 4 digit binary number and write them in order of the hexadecimal digits. Thus, the resulting binary number will be of 16 digits. If the leftmost hexadecimal digit is less than 8, we will have zeroes on the left in the binary equivalent of such numbers. In any case the number of digits will not be more than 16.

If one is added to the greatest number of any number of digits, it gives the least number of next number of digits in that number system.