Question 1 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 2 :
The  linear equation, such that each point on its graph has an ordinate $3$ times its abscissa is $y=mx$. Then the value of $m$ is<br/>
Question 4 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 5 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 6 :
The simultaneous equations, $\displaystyle y = x + 2|x| $ & $y = 4 + x - |x|$ have the solution set 
Question 7 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\,  \displaystyle \frac{8}{y}\, =\, 14$<br/>Hence, find 'a' if $y\, =\, ax\, -\, 2$
Question 8 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, =\, 5\,;\, \frac{1}{x}\, -\, \frac{1}{y}\, =\, 1$
Question 9 :
With Rs. $1000$ a rancher is to buy steers at Rs. $25$ each and cows at Rs. $26$ each. If the number of steers $s$ and the number of cows $c$ are both positive integers, then:
Question 10 :
Find the fraction such that it becomes $\displaystyle \frac{1}{2}$ if 1 is added to the numerator, and $\displaystyle \frac{1}{3}$ if 1 is added to the denominator.
Question 11 :
The equation of the straight line which passes through $(1, 1)$ and making angle $60^o$ with the line $x+ \sqrt 3y +2 \sqrt 3=0$ is/are.
Question 12 :
Equations of the two straight lines passing through the point $(3, 2)$ and making an angle of $45 ^ { \circ }$ with the line $x - 2 y = 3$, are
Question 13 :
Equations $\displaystyle \left ( b-c \right )x+\left ( c-a \right )y+\left ( a-b \right )=0$ and $\displaystyle \left ( b^{3}-c^{3} \right )x+\left ( c^{3}-a^{3} \right )y+a^{3}-b^{3}=0$ will represent the same line if<br>
Question 14 :
Based on equations reducible to linear equations<br/>Solve for x and y: $\dfrac {16}{x+3}+\dfrac {3}{y-2}=5; \dfrac {8}{x+3}-\dfrac {1}{y-2}=0$<br/>
Question 15 :
If the equations $y = mx + c$ and $x  \cos  \alpha + y \sin  \alpha = p$ represent the same straight line, then
Question 16 :
A straight line L through the point $(3, - 2)$ is inclined at an angle of 60$^o$ to the line $\sqrt 3 x + y = 1$. If $L$ also intersects the $x-$axis, then the equation of $L$ is
