Mathematics Class IX

Question 1 of 20

1. Question
Find the value of $ k $ if the point (7,3) lies on the line $ 2x-3y=k $.
- 5
- 4
- -4
- -5
Correct

Incorrect

Hint

Substitute the point (7,3) in the given equation.

(1) $\begin{equation*}\begin{split} 2(7)-3(3)=k \\ 5 &= k \end{split}\end{equation*}$
Question 2 of 20

2. Question
Find the value of $ k $ if the point (1,5) lies on the line $ a^{2}x-3y=1 $.
- 2
- Only 4
- Only -4
- 4, -4
Correct

Incorrect

Hint

Substitute the point (1,5) in the given equation.

(1) $\begin{equation*}\begin{split} a^{2}(1)-3(5)&=1 \\ a^{2} &= 16 \\ a &= 4, -4 \end{split}\end{equation*}$
Question 3 of 20

3. Question
Find the value of y-coordinate if $ x=2 $ in the equation $ x+y+\frac{x-y}{2} = 3$.
- 1
- 0
- 3
- 2
Correct

Incorrect

Hint

Substitute the value of x in the given equation.

(1) $\begin{equation*}\begin{split} 2+y+\frac{2-y}{2}&=3 \\ 3+\frac{y}{2} &= 3 \\ y &= 0 \end{split}\end{equation*}$
Question 4 of 20

4. Question
Find the area of the triangle formed by the line $ \frac{x}{11}+\frac{y}{12} = 1 $ and the coordinate axes in the first quadrant.
- 144
- 72
- 66
- 132
Correct

Incorrect

Hint

Find the points where the given line intersects the coordinate axes.

(1) $\begin{equation*}\begin{split} \frac{0}{11}+\frac{y}{12}&=1 \\ y &= 12 \\\\ \frac{x}{11}+\frac{0}{12} &= 1 \\ x &= 11 \end{split}\end{equation*}$

The triangle formed is a right angled triangle with the length of perpendicular legs as 11 and 12.

(2) $\begin{equation*}\begin{split} Area &= \frac{1}{2} \times 11 \times 12 \\ &= 66 \end{split}\end{equation*}$
Question 5 of 20

5. Question
How many solutions does the line $ 7x + 8y = -19 $ have?
- Infinitely many
- Zero
- One
- Nineteen
Correct

Incorrect

Hint

Number of solutions of a single line is just the number of points that lie on it. A line always passes through infinitely many solutions. So this line also has infinitely many solutions.
Question 6 of 20

6. Question
What are the coordinates of the point of intersection of the line $ 3x + \frac{1}{3}y = 18 $ and the x-axis?
- (8,0)
- (6,0)
- (0,6)
- (0,8)
Correct

Incorrect

Hint

Just substitute the value of y as 0.

(1) $\begin{equation*}\begin{split} 3x+\frac{1}{3}(0) = 18 \\ x &= 6 \end{split}\end{equation*}$

The coordinates are (6,0).
Question 7 of 20

7. Question
What are the coordinates of the point of intersection of the line $ 5x + 7y = 34 $ and the x-axis?
- $ (0,34) $
- $ (\frac{34}{7},0) $
- $ (0,\frac{34}{7}) $
- $ (34,0) $
Correct

Incorrect

Hint

Just substitute the value of $x$ as 0.

(1) $\begin{equation*}\begin{split} 5(0)+7y = 34 \\ y &= \frac{34}{6} \end{split}\end{equation*}$

The coordinates are $(0,\frac{34}{7})$ .
Question 8 of 20

8. Question
If the point $ (k^{2},k) $ lies on the line $ 2x-3y=20 $ then find the positive value of $ k $.
- 2
- 1
- 3
- 4
Correct

Incorrect

Hint

Just substitute the point in the given equation.

(1) $\begin{equation*}\begin{split} 2k^{2}-3k &= 20 \\ 2k^{2}-3k-20 &= 0 \\ (k-4)(2k+5) &= 0 \\ k &= 4, -\frac{5}{2} \end{split}\end{equation*}$

The positive value of $k$ is 4.
Question 9 of 20

9. Question
How many lines can pass through a particular point?
- Zero
- 2
- 1
- Infinitely many
Correct

Incorrect

Hint

Infinitely many lines can pass through a particular point.
Question 10 of 20

10. Question
For what values of $ a $ and $ b $, does the line $ ax+by+c=0 $ is a line in two variables?
- $ a \neq 0, b = 0 $
- $ a = 0, b = 0 $
- $ a \neq 0, b \neq 0 $
- $ a = 0, b \neq 0 $
Correct

Incorrect

Hint

The line $ax+by+c=0$ is a line in two variables only when the values of $a$ and $b$ are not equal to 0.
Question 11 of 20

11. Question
The cost of a pencil is Rs 7. Which of the following correctly represents the total cost $ y $ of $ x $ pencils?
- $ y=7+x $
- $ y=7x $
- $ y=7-x $
- $ y=\frac{7}{x} $
Correct

Incorrect

Hint

The total cost is represented by the equation $y=7x$ .
Question 12 of 20

12. Question
Find the equation of the line that is parallel to x-axis and that lies at distance of 7 units above the x-axis.
- $ y=7 $
- $ y=-7 $
- $ x=7 $
- $ x=-7 $
Correct

Incorrect

Hint

The equations of the line parallel to x-axis and at a distance of 7 units are $y=7$ and $y=-7$ , but it is given that the line lies above the x-axis so the required line is $y=7$ .
Question 13 of 20

13. Question
Find the equation of the line that is parallel to y-axis and that lies at distance of 15 units on the left side of the y-axis.
- $ y=15 $
- $ x=-15 $
- $ x=15 $
- $ y=-15 $
Correct

Incorrect

Hint

The equations of the line parallel to y-axis and at a distance of 15 units are $x=15$ and $x=-15$ , but it is given that the line lies on the left side of y-axis so the required line is $x=-15$ .
Question 14 of 20

14. Question
Which of the line passes through the points (4,-2) and (-3,5)?
- $ x+y=8 $
- $ x-y=2 $
- $ x-y=4 $
- $ x+y=2 $
Correct

Incorrect

Hint

The points (4,-2) and (-3,5) passes only through the line that is represented by the line $x+y=2$ .
Question 15 of 20

15. Question
Which of the following is correct?
- The line represented by $ x+8y=0 $ passes through the origin.
- $ x=5 $ is a line parallel to x-axis.
- $ y=-4 $ is a line parallel to y-axis.
- None of these
Correct

Incorrect

Hint

The point (0,0) satisfies the equation $x+8y=0$ . Therefore, the line represented by $x+8y=0$ passes through the origin.
Question 16 of 20

16. Question
The cost of making tables is represented by the equation $ y=35 + 66x $ where $ x $ is the number of tables. Find the cost of making 10 tables.
- 660
- 625
- 695
- None of these
Correct

Incorrect

Hint

Substitute the value of $x$ as 10 in the given equation and solve for the total cost.

(1) $\begin{equation*}\begin{split} y &= 35+66(10) \\ y &= 695 \end{split}\end{equation*}$
Question 17 of 20

17. Question
The length of a rectangular metal sheet is 3 metres more than the width. If the perimeter of the sheet is 34 metre, find the length and width of the sheet.
- width = 7 m, length = 10 m
- width = 6 m, length = 9 m
- width = 6 m, length = 11 m
- width = 8 m, length = 11 m
Correct

Incorrect

Hint

Let the width be $x$ and then the length can be written as $x+3$ .

(1) $\begin{equation*}\begin{split} x+x+3+x+x+3 &= 34 \\ 4x &= 28 \\ x &= 7 \end{split}\end{equation*}$

Width of the sheet is 7 m and its length is 10 m.
Question 18 of 20

18. Question
Which of the following equation passes through the point (4,-9)?
- $ 2x-y=-1 $
- $ 2x+y=-1 $
- $ 2x+y=1 $
- $ 2x-y=1 $
Correct

Incorrect

Hint

The point (4,-9) passes only through the equation $2x+y=-1$ .
Question 19 of 20

19. Question
Find the value of $ p $ the point (3,10) lies on the line $ px+4y=10 $?
- 10
- 5
- -10
- -5
Correct

Incorrect

Hint

Substitute the point (3,10) in the equation $px+4y=10$ and solve for the value of $p$ .

(1) $\begin{equation*}\begin{split} p(3)+4(10) &= 10 \\ 3p+40 &= 10 \\ 3p &= -30 \\ p &= -10 \end{split}\end{equation*}$
Question 20 of 20

20. Question
Which of the following is correct?
- $ y=9 $ is a line parallel to y-axis.
- The line represented by $ x+8y=15 $ passes through the origin.
- $ x=7 $ is a line parallel to y-axis.
- None of these
Correct

Incorrect

Hint

The line $x=7$ is a vertical line passing through the point (7,0).. Therefore, the line represented by $x=7$ is parallel to y-axis.

Mathematics Class IX

Olympiad Questions – Linear Equations in two varaibles – Class IX

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