Question 1 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 2 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 3 :
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 4 :
Assem went to a stationary shop and purchased $3$ pens and $5$ pencils for $Rs.40$. His cousin Manik bought $4$ pencils and $5$ pens for $Rs. 58$. If cost of $1$ pen is $Rs.x$, then which of the following represents the situation algebraically?
Question 5 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 7 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 8 :
Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:
Question 9 :
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 11 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 12 :
If x and y are positive with $x-y=2$ and $xy=24$ , then $ \displaystyle \frac{1}{x}+\frac{1}{y}$   is equal to
Question 13 :
Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the coordinates of the intersection of other line with the cordinate axes.
Question 14 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 15 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 16 :
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 17 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 
Question 18 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 19 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 21 :
In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solution. In case there is a unique solution, find it.<br>$2x+3y=7$<br>$6x+5y=11$<br>
Question 22 :
The sum of the digits of a two-digit number is 5. The digit obtained by increasing the digit in tens' place by unity is one-eighth of the number. Then the number is
Question 23 :
Solve the equations using elimination method:<br>$x - y = 2$ and $-x y = -10$
Question 24 :
The simultaneous equations, $\displaystyle y = x + 2|x| $ & $y = 4 + x - |x|$ have the solution set 
Question 25 :
Solve the equations using elimination method:<br/>$x + y = 2$ and $2x- y = 7$
Question 27 :
Find the value of x and y using cross multiplication method: <br>$x + y = 15$ and $x - y = 3$
Question 28 :
If the product of two numbers is $10$ and their sum is $7$, which is the greatest of the two numbers?
Question 29 :
Solve the following simultaneous equations by the method of equating coefficients.$\displaystyle \frac{x}{3}+\frac{y}{4}=4; \, \, \frac{5x}{6}-\frac{y}{8}=4$
Question 30 :
Solve the following pairs of equations by reducing them to a pair of linear equations.<br/>$\displaystyle \frac{3}{x+1}-\frac{1}{y+1}=2$ and $\dfrac{6}{x+1}-\dfrac{1}{y+1}=5$