Subject Experts Solutions for Chapter: Number Systems, Exercise 2: PRACTICE QUESTIONS (COMPETITION WING)

If $x=(-23)+22+(-23)+22 ....$ ($40$ terms) and $y=11+(-10)+11+(-10)+ .....$ ($40$ terms), then $y-x$ is _____.

Ram went to a shop to purchase an article. But, he had an amount which is equal to $\left[\frac{13}{27}\right]$ of the cost of the article. If the cost of the article was $₹540$, then find the amount with him.

If $x$ and $y$ are the smallest and the greatest four-digit numbers formed by using $1, 3, 5$ and $9$, then find $y-x$.

If $x=(-1{)}^1+(-1{)}^2+\dots +(-1{)}^{2009}$ and $y=(-1{)}^1-(-1{)}^2+(-1{)}^3-(-1{)}^4+\dots +(-1{)}^{2009}$, then find $x-y$.

Raj went to a market to buy a radio. But he had an amount which is equal to $\left[\frac{15}{28}\right]$ of the cost of the radio. If the cost of the radio is $₹560$, then find the amount with him.

Four persons $A, B, C,$ and $D$ start jogging from a point around a circular track simultaneously at $6 \mathrm{am}$. If they complete one round in $120$ seconds, $150$ seconds, $100$ seconds, and $160$ seconds respectively, after how much time will they meet at the starting point for the first time after $6 \mathrm{am}$?

In a tank, one-third of the capacity is filled with water. If $50$ litres is drawn from it, the remaining is just two-nineth of the capacity. What is the total capacity of the tank?

The breadth of a cuboid is twice the height of the cuboid and the length is thrice of its breadth. If the volume of the cuboid is $2592 {\mathrm{cm}}^3$, find the length of the cuboid.