RD Sharma 2020 solution class 9 chapter 7 Linear Equations In Two Variables MCQS

MCQS

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Question 1:

Mark the correct alternative in each of the following:

If (4, 19) is a solution of the equation y = ax + 3, then a=

(a) 3

(b) 4

(c) 5

(d) 6

Answer 1:

We are given (4, 19)as the solution of equation

Substituting x = 4 and y = 19, we get

Therefore, the correct answer is (b).

Question 2:

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

(a) 3

(b) 1

(c) 3

(d) 4

Answer 2:

We are given (a, 4) lies on the graph of linear equation 3x + y = 10.
So, the given co-ordinates are the solution of the equation 3x + y = 10.
Therefore, we can calculate the value of a by substituting the value of given co-ordinates in equation 3x + y = 10.
Substituting x = a and y = 4 in equation 3x + y = 10, we get

No option is correct.

Question 3:

The graph of the linear equation 2x − y = 4 cuts x- axis at

(a) (2, 0)

(b) (−2, 0)

(c) (0, −4)

(d) (0, 4)

Answer 3:

We are given,

we get,

We will substitute in to get the co-ordinates for the graph of at x axis

Co-ordinates for the graph of are .
Therefore, the correct answer is (a).

Question 4:

How many linear equations are satisfied by x = 2  and y = −3?

(a) Only one

(b) Two

(c) Three

(d) Infinitely many

Answer 4:

There are infinite numbers of linear equations that are satisfied by as
(i) Every solution of the linear equation represent a point on the line.
(ii) Every point on the line is the solution of the linear equation.
Therefore, the correct answer is (d).

Question 5:

The equation x − 2 = 0 on number line is represented by

(a) a line

(b) a point

(c) infinitely many lines

(d) two lines

Answer 5:

The equation is represented by a point on the number line.
Therefore, the correct answer is (b).

Question 6:

x = 2, y = −1 is a solution of the linear equation

(a) x + 2y = 0

(b) x + 2y = 4

(c) 2x + y = 0

(d) 2x + y = 5

Answer 6:

We are given as the solution of linear equation, which we have to find?
The equation is which can be proved by
Substituting in the equation, we get

Therefore, the correct answer is (a).

Question 7:

If (2k − 1, k) is a solution of the equation 10x − 9y = 12, then k =

(a) 1

(b) 2

(c) 3

(d) 4

Answer 7:

We are given as the solution of equation

Substituting, we get

Therefore, the correct answer is (b).

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Question 8:

The distance between the graph of the equations x = −3 and x = 2 is

(a) 1

(b) 2

(c) 3

(d) 5

Answer 8:

Distance between the graph of equations, say D
D = Distance of co-ordinate on negative side of x axis + Distance of co-ordinate on positive side of x axis
Distance of co-ordinate on negative side of x axis = x = 3 units
Distance of co-ordinate on positive side of x axis = x = 2 units

Therefore, the correct answer is (d).

Question 9:

The distance between the graphs of the equations y = −1 and y = 3 is

(a) 2

(b) 4

(c) 3

(d) 1

Answer 9:

Distance between the graph of equations, say D
D = Distance of co-ordinate on negative side of y axis + Distance of co-ordinate on positive side of y axis
Distance of co-ordinate on negative side of y axis = y = 1 units
Distance of co-ordinate on positive side of y axis = y = 3 units

Therefore, the correct answer is (b).

Question 10:

If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length

(a) 4 units

(b) 3 units

(c) 5 units

(d) none of these

Answer 10:

(i) We are given,

We get,

Now, substituting in, we get

Substituting in,we get

Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation

x	0	3
y	4	0

We are given that the graph of equation cuts the co-ordinate axes and and forms the right angle triangle AOB.
Length of AB in right angled triangle AOB

The length of hypotenuse AB of triangle AOB is 5 units.
Therefore, the correct answer is (c).