Sarvesh K Verma Solutions for Chapter: Number System, Exercise 16: Introductory Exercise

The value of $\mathrm{x}$ when $(25{)}_{\mathrm{x}}=(85{)}_{10}$ is:

Which one is an invalid number?

$(35{)}_{\mathrm{n}}, (37{)}_{\mathrm{n}}, \left(45{)}_{\mathrm{n}} \text{ and }\right(51{)}_{\mathrm{n}}$ all are written in the base $\mathrm{n}$ then the value of $\mathrm{n}$, such that all these four numbers when written in the decimal system, they must be the consecutive prime numbers:

A number of decimal system when represented in binary system then its first and last digits are same and the rest digits are also of another kind. Further this number appears to be palindrome of numerals. The number is:

When a two-digit number is reversed, the new number is reduced by $63$and the sum of digits of these individual numbers is $9$. Now, if these same numbers are converted into base '$\mathrm{x}$' the larger number becomes $5$ times that of the smaller one the value of $\mathrm{x}$ is:

If $(25{)}_{\mathrm{n}}\times (31{)}_{\mathrm{n}}=(1015{)}_{\mathrm{n}}$, then the value of $(13{)}_{\mathrm{n}}\times (52{)}_{\mathrm{n}}$ is, when $\mathrm{n}>0$:

What is the decimal equivalent of the hexadecimal number $(1\underset{23\text{ zeros }}{\underbrace{00\dots .001}}{)}_{16}$?

Match list I (Binary) with list II (Octal) and select the correct answer using the codes given below the lists :

Codes