Question 1 :
Write the following equations in the form $ax + by + c = 0 $, where $a= -2,b=3$ and $c=-6$

Question 2 :
Mark the correct option in the following questions:Which of the following equations is not a linear equation?<br>

Question 5 :
If $\sqrt{x - 1} - \sqrt{x + 1} + 1 = 0$, then 4x equals

Question 8 :
If $217\ x + 131 = 913$ and $131x + 217y = 827$, then the value of $x + y$ is _______.

Question 9 :
Which of the following equations has the vertex of $(3, -3)$?

Question 10 :
Express the given information in mathematical form using two variables:One number is 5 more&#160;than seven times the other number.

Question 11 :
If$\displaystyle y-\frac{1}{3y}=\frac{1}{3}$ then the value of$\displaystyle y\left ( y-\frac{1}{3} \right )$ is

Question 14 :
At a convenience store, two candy bars and two bags of potato chips cost $\$4.00$, and three candy bars and two bags of potato chips cost $\$4.75$. What is the price of one bag of potato chips?

Question 15 :
Denominator of rational number is 4 less than its numerator if 11 is added to numerator and 1 is subtracted from denominator the new number becomes$\displaystyle \frac{7}{3}$ Find the rational number

Question 16 :
Solve the following pair of equation by reducing them to a pair of linear equations<br>$\displaystyle \frac{3}{x}+\frac{7}{y} = 14$ and $\displaystyle \frac{2}{x}+\frac{7}{y} = 21$

Question 17 :
The sales manager of a company awarded a total of $\$3000$ in bonuses to the most productive sales people. The bonuses were awarded in amounts of $\$250$ and $\$750$. If at least one $\$250$ bonus and at least one $\$750$ bonus were awarded, what is one possible number of $\$250$ bonuses awarded?

Question 18 :
Identify which of the following points satisfy the given linear equations: $x - 2y = -4; x - y = 8$

Question 19 :
If $\dfrac {3}{4}y = 6 - \dfrac {1}{3}c$, then the value of $2c + \dfrac {9}{2} y$ is

Question 20 :
In a zoo, there are rabbits and pigeons. If their heads are counted, these are $90$ while their legs are $224$. Find the number of pigeons in the zoo.

Question 21 :
The budget for the annual day function of a school was Rs. $60,000$, out of which Rs. $14,500$ was paid to the tent house, Rs. $10,400$ to the band party and Rs. $5,000$ for refreshments. How much money was left over after meeting the expenses?

Question 22 :
If the numerator of a fraction is increased by $2$ and the denominator is decreased by $4$ then it becomes $2$. If the numerator is decreased by $1$ and the denominator is increased by $2$, then it becomes $\dfrac13$. Find the sum of the numerator and denominator of the fraction.

Question 23 :
Ravi distributed the chocolates with him equally between Rajesh and Suresh. He was left with a chocolate. Rajesh distributed his share equally among three of his friends and was also left with a chocolate. One of the three distributed his share equally among four of his friends and was left with no chocolate. Which of the following could be the number of chocolates that Rajesh received?

Question 24 :
The cost of using a telephone in a hotel meeting room is $&#160;$0.20$ per minute. Which of the following equations represents the total cost $c$, in dollars, for $h$&#160;<u>hours</u>&#160;of phone use?

Question 25 :
$300$ works were engeged to finish a piece of work in a certain number pf days. $8$ workers dropped on the second day, $8$ more workersdropped the third day and so on. It takes $8$ more days to finish the work now. Find the number of days in which the work was completed.

Question 27 :
In a class the ratio of the number of boys to that of the girls is $7: 3$. Each boy is given only a $50$ paise coin and each girl is given a $75$ paise coin (assuming $75$ paise coins are available) &#160;The difference in the amount present with the boys and the girls is Rs. $3.75$. How many coins should the boys and girls exchange so that the amount with the boys becomes twice the amount with the girls?

Question 28 :
The ratio of two numbers is $5:4$ and their sum is $54$. The greater of the two numbers is&#160;

Question 29 :
Given that $\displaystyle \frac{x}{y} = 6$ and&#160;$\displaystyle 4(y+ 1)&#160;= x$<br/>If $(x, y)$ is the solution to the system of equations&#160;above, what is the value of $y$?