If a natural number $\text{'}a\text{'}$ is divided by $7$, the remainder is $5$. If a natural number $\text{'}b\text{'}$ is divided by $7$, the remainder is $3$. The remainder is $\text{'}r\text{'}$ if $a+b$ is divided by $7$. Find the value of $\frac{3r+5}{4}$.

What will be the HCF of $\frac{2}{3}, \frac{8}{9}$ and $\frac{64}{81}$?

Find the G.C.F and L.C.M of $20$and $28$.

1. $20, 280$
2. $5, 280$
3. $10, 140$
4. $4, 140$

The LCM of two numbers is $210$. If their HCF is $35$ and one of the numbers is $105$, find the other number:

Let $N$ be the number of ways of choosing a subset of $5$ distinct numbers from the set $\left\{10a+b:1\le a\le 5,1\le b\le 5\right\}$, where $a, b$ are integers, such that no two of the selected numbers have the same unit's digit and no two have the same ten's digit. What is the remainder when $N$ is divided by $73$?

Find the ratio of the LCM and the HCF of 5, 25 and 30. 

(A) 1 : 6 

(B) 30 : 1 

(C) 1 : 30 

(D) 6 : 1 

B has $32$ pens,$24$pencils and $16$ erasers. How many sets of these three items can B make without any left over? 

1.$6$
2.$7$
3. $8$
4. $9$