M L Aggarwal Solutions for Chapter: Real Numbers, Exercise 2: Exercise 1.2

Find the largest number which on dividing $1251, 9377 and 15628$ leaves remainders $1, 2 and 3$ respectively.

Three bells toll at intervals of $9, 12, 15$ minutes respectively. If they start tolling together, after what time (in hours) will they next toll together?

The length, breadth and height of a room are $\text{8 m 50 cm, 6 m 25 cm and 4 m 75 cm}$ respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.

Explain why $11\times 13\times 15\times 17+17$ is a composite number?

Explain why $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ is a composite number?

Explain why $17\times 5\times 11\times 3\times 2+2\times 11$ is a composite number?

Show that $6^n$cannot end with the digit $0$ for any natural number $n$.

Show that ${12}^n$ cannot end with the digits $0 and 5$ for any natural number $n$