The elements $\mathrm{p}\in \mathrm{P}$ and $\mathrm{q}\in \mathrm{Q}$ are found in two sets $\mathrm{P}$ and $\mathrm{Q}.$ When translated to base $6, \mathrm{p}$ is a four-digit decimal integer with at least three trailing zeroes, and $\mathrm{q}$ is a four-digit perfect square. What is the total number of items in the set $\mathrm{PUQ}?$

Twice the difference between two numbers is equal to their sum. If one number is $15$, Find the other number.

1. $15$
2. $10$
3. $5$
4. $20$

The population of Patna city is $96000$, the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$, the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?

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. $9$

The sum of three consecutive numbers is $126$. Find the highest number-

1. $41$
2. $42$
3. $43$
4. $44$

1 USD = Rs. 67.89. A money changer adds a margin of Rs. 1.11. What will be the cost of 150 USD ? 

1. Rs. 10,183
2. Rs. 10,350
3. Rs. 10,330
4. Rs. 10,450

How many times does the number $3$ occur in unit's place for numbers ranging from $1$ to $100$?

1. $20$
2. $11$
3. $10$
4. $19$