H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Number System, Exercise 2: EXERCISE

Check whether the following number is prime or composite.

$3\times 7+2$

Check whether the following number is Prime Number / Composite Number

$13\times 17\times 19+23\times 28$

A rectangular field is $150 \mathrm{m}\times 60 \mathrm{m}$. Two cyclists Karan and Vijay start together and can cycle at speed of $21 \mathrm{m}/\min \mathrm{and} 28 \mathrm{m}/\min$, respectively. They cycle along the rectangular track, around the field from the same point and at the same moment. After how many minutes will they meet again at the starting point?

Radius of a circular track is $63 \mathrm{m}$. Two cyclists Amit and Ajit start together from the same position, at the same time and in the same direction with speeds $33 \mathrm{m}/\min \mathrm{and} 44 \mathrm{m}/\min$. After how many minutes they meet again at the starting point? Take $\mathrm{\pi }=\frac{22}{7}$.

On a morning walk, three persons step off together and their steps measure $40 \mathrm{cm}, 42 \mathrm{cm} \mathrm{and} 45 \mathrm{cm}$, respectively. If the minimum distance each should walk so that each can cover the same distance in complete steps is equal to $k cm$, then find the value of $k$.

An army contingent of $455$ members is to march behind an army band of $42$ members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same. The number of English books is $96,$ the number of Hindi books is $240$ and the number of Mathematics books is $336$. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

In a delegation of students there are $60$ Indian, $84$ Chinese and $108$ British. They all want to stay in the same hotel. The number of students stay in each same room is same and will also stay with their own country students. Find the minimum number of rooms required for stay of these students.