Number Systems and Series

The number name for the numeral 9651 is nine thousand six hundred fifty one. Hence, this option is not matched correctly.

Solution: The greatest 3-digit number = 999 The smallest 3-digit number = 100 The sum = 999 + 100                 = 1099 Its successor = 1099 + 1                         = 1100

This sequence of numbers is correctly written in ascending order.

It is the greatest number in the given numerals.

Solution: The greatest 4-digit number = 9999 Its successor = 9999+1 = 10000 The smallest 4-digit number = 1000 The difference = 10000 - 1000                            = 9000

Multiples of 9 = 9, 18, 27, 36, 45 Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45 Least common multiple = 45 Factors of 77 = 1, 7, 11, 77 Factors of 33 = 1, 3, 11, 33 Greatest common factor = 11 11 + 45 = 56 56 × 3 = 168

This is not a number system.

Octal number system's base is 8.

Digit at tens place in 23418 = 1

Correct.

The answer is the GCD (Greatest Common Divisor) of the respective numbers subtracted by values of remainder 

i.e GCD of (398 - 7), (436 - 11), (542 - 15) .

Which is 17.

This is the correct answer.e The successor of the largest 5 digit ( 99999) number is 100000 which is a smallest 6 digit number.

This is a correct answer. As 7689 will be the smallest number lying in between the 7500 and 9500.

This is the right answer. If we look the series given in the question. The next number is having the difference of 8 like 21 + 8 = 29, 29 + 8 = 37 and so on, So if we add 8 to 45, we will get he answer45 + 8 = 53

This is a right answer. 5000 cannot be rearranged to get another four digit number as it has 3 zeros. If we rearrange 5000, we may get 3 digit or 2 digit numbers but not a 4 digit number.

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.