H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Number System, Exercise 1: EXERCISE

If the HCF of $210 \mathrm{and} 55$ is expressible in the form of $210\times 5+55\times A$, then find the value of $\left[2-A\right]$.

Find HCF of $81 \mathrm{and} 237$. Express the HCF in the form of $237\times p+81\times q$. Find the value of $\left(3p+q\right)$.

Show that $247$ and $187$ are co-prime [Relatively prime].

Show the numbers of form $4m$ and $4m+2$ cannot be co-prime. 

There are $120$ boys and $114$ girls in class $\mathrm{X}$ of a school. Principal of the school decided as a policy matter to have a maximum number of mixed sections, each section has to accommodate equal number of boys and equal number of girls. What is the maximum number of such sections?

Length, breadth and height of a cuboidal room are $6.15 \mathrm{m}, 4.25 \mathrm{m} \mathrm{and} 3.15 \mathrm{m}$. Find the length of the longest rod required to measure each of length, breadth and height of the room completely [exactly]. Also find how many times we will use this rod of the longest length to measure length, breadth and height. 

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is $14.5 \mathrm{ft}$ by $12.5 \mathrm{ft}$. What would be the size of tiles in inches? How many such tiles are required?

A bookseller purchased $117$ books out of which $45$ books are of mathematics and the remaining $72$ are of physics. Each book has same size. Mathematics and physics books are to be packed in separate bundles and each bundle must contain same number of books. Find the least number of bundles which can be made for these $117$ books.