Question 1 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is

Question 2 :
Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is

Question 3 :
What is the nature of the graphs of a system of linear equations with exactly one solution?

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 :
What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point ?

Question 6 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is

Question 7 :
The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two. 

Question 8 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is

Question 9 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point

Question 10 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be

Question 11 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$

Question 12 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at

Question 13 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is

Question 14 :
If the system of equation, ${a}^{2}x-ay=1-a$ & $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:

Question 17 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is

Question 18 :
Equation of a straight line passing through the origin and making an acute angle with $x-$axis twice the size of the angle made by the line $y=(0.2)\ x$ with the $x-$axis, is:

Question 19 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 

Question 20 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.