Q1. The pair of equations $x = -4$ and $y = -5$ graphically represents lines which are:
Q2. For what value of $k$, do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?
Q3. The area of the triangle formed by the line $x + y = 10$ and the coordinate axes is:
Q4. Assertion (A): The value of $q = \pm 2$, if $x=3, y=1$ is the solution of the line $2x + y - q^2 - 3 = 0$. Reason (R): The solution of the line satisfies the equation of the line.
Q5. Solve for $x$ and $y$: $152x - 378y = -74$ $-378x + 152y = -604$.
Solve on white paper.
Q6. Find the values of $\alpha$ and $\beta$ for which the following pair of linear equations has infinite number of solutions: $2x + 3y = 7$ $2\alpha x + (\alpha + \beta)y = 28$.
Q7. The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2:3. Determine the fraction.
Q8. 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Q9. The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Q10. Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Q11. Case Study: Geometry & Area
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units.
(i) Form the pair of linear equations representing the situation.
(ii) Find the dimensions (length and breadth) of the rectangle.
(iii) Find the area of the rectangle.