4 Marks Questions

Question 14 Marks

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is:

5ms^-2
6ms^-2

Answer

Given that, the force (F) is directly proportional to the the acceleration (a) i.e. $\text{F}\propto\text{a}$

$\Rightarrow\text{F}=\text{ma}$ [where m = arbitary constant and take value 6kg of mass]

$\therefore\text{F}=6\text{a}$

If $\text{a}=5\frac{\text{m}}{\text{s}}^2$ then from Eq (i), we get

F = 6 × 5 = 30N

If $\text{a}=6\frac{\text{m}}{\text{s}}^2$ then from Eq (i), we get

F = 6 × 6 = 36N

Here, we find two points A(5, 30) and B(6, 36).

So draw the graph by plotting the point and joining the line AB.

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Question 24 Marks

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

Answer

As per question, the sum of the coordinates is 10 units.
Let x and y be two coordinates, then we get x + y = 10.

For x = 5, y = 5, therefore, (5, 5) lies on the graph of x + y = 10.
For x = 3, y = 7, therefore, (3, 7) lies on the graph of x + y = 10.
Now, plotting the points (5, 5) and (3, 7) on the graph paper and joining them by a line, we get graph of the linear equation x + y = 10.

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Question 34 Marks

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.

Answer

Let the abscissa of the point be x,
According to the question, Ordinate (y) = 3 x Abscissa ⇒ y= 3x When x = 1, then y = 3 × 1 = 3 and when x = 2, then y = 3 × 2 = 6.

x	1	2
y	3	6

Here, we find two points A(1, 3) and B(2, 6).
So, draw the graph by plotting the points and joining the line AB.

Hence, y = 3x is the required equation such that each point on its graph has an ordinate 3 times its abscissa.

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Maths 4 Marks Questions

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