Question 1 :
If the range of a set of observations on a variable $X$ is known to be $2%$ and if $y=40+3X$, then what is the range of the set of corresponding observations of $Y$ ?

Question 2 :
<span>Write a linear equation in two variables to represent the following statement.</span><div>Two numbers are such that $2$ times of one <span>is same as $3$ times of the other.</span></div>

Question 4 :
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

Question 5 :
<span>Write the following equation in the form of ax + by + c = 0 </span><div>2x = y</div>

Question 6 :
In how many ways can $ 5$ pounds be paid in half-crowns and florins?

Question 7 :
A lady has $25p$ and $50p$ coins in her purse. If in all she has $40$ coins totalling $Rs. 12.50$, find the number of coins of each type she has.

Question 8 :
Which of the following is not a linear equation in two variables?<br/>

Question 9 :
The number of integral values of $m$, for which the x-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer is

Question 10 :
The length, in inches, of a box is $3$ inches less than twice its width in inches. Which of the following gives the length, $l$ inches, in terms of the width, $w$, inches of the box?

Question 12 :
<span>A machine takes 2 litres of petrol to start and then 3 litres per hour while running. <br/></span><span>If the equation thus formed is of the form ax+by+c=0.</span>What is the value of $\displaystyle a+b+c$ ?

Question 13 :
In a dart throwing game, points are calculated in such a manner that if dart lands in blue ring, then it is worth $5$ points, if it lands in red ring, then it is worth of $10$ points. Now, Joe has a total of $6$ darts to throw. If $x$ of his darts land in a blue ring and the rest land in a red ring, then which expression represents his total score?

Question 14 :
If $a$ and $b$ are positive integers such that $a + b = 9$, then what is the value of $\dfrac {b - 9}{4a}$?

Question 15 :
Solve the following equations:<br>$x^{2} + xy + y^{2} = 84$,<br>$x - \sqrt {xy} + y = 6$.

Question 17 :
A man buys $m$ articles at Rs. $x$ each and another $n$ articles for Rs. $y$. If he sells all the articles at Rs. $z$ per article. Frame an equation to find his profit.