Question 1 :
A line which passes through (5, 6) and (-3. -4) has an equation of

Question 2 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.

Question 3 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.

Question 4 :
In a zoo there are some pigeons and some rabbits. If their heads are counted these are $300$ and if their legs are counted these are $750$ How many pigeons are there?

Question 5 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is

Question 6 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is

Question 7 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 

Question 8 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<br/>$6x - ay = 8$<br/>In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$

Question 9 :
State whether the given statement is true or false:The graph of a linear equation in two variables need not be a line.<br/>

Question 11 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$

Question 12 :
If $2^{2x - y} = 32$ and $2^{x + y} = 16$ then $x^{2} + y^{2}$ is equal to<br>

Question 13 :
If$\displaystyle \frac{x+y}{x-y}=\frac{5}{3}\: and\: \frac{x}{\left ( y+2 \right )}=2$ the value of (x , y) is

Question 15 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$2x+7y= 39$<br/>$3x+5y= 31$

Question 16 :
One pendulum ticks $57$ times in $58$ seconds and another $608$ times in $609$ seconds. If they start simultaneously, find the time after which will they tick together?

Question 20 :
The cost of an article $A$ is $15$% less than that of article $B.$ If their total cost is $2,775\:Rs\:;$ find the cost of each article$.$ <br>

Question 21 :
The ratio between the number of passangers travelling by $1^{st}$ and $2^{nd}$ class between the two railway stations is 1 : 50, whereas the ratio of$1^{st}$ and $2^{nd}$ class fares between the same stations is 3 : 1. If on a particular day, Rs. 1325 were collected from the passangers travelling between these stations by these classes, then what was the amount collected from the $2^{nd}$ class passangers ?

Question 22 :
The sum of three numbers is $92$. The second number is three times the first and the third exceeds the second by $8$. The three numbers are:&#160;