RD Sharma MCQs: Linear Equations in Two Variables | Mathematics (Maths) Class 9 PDF Download

 Page 1


         
              
         
         
                
     
Question:47
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
Solution:
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:48
If (a, 4) lies on the graph of 3x + y = 10, then the value of a is
a
3
b
Page 2


         
              
         
         
                
     
Question:47
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
Solution:
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:48
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
Solution:
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:49
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
Solution:
We are given,
we get,
We will substitute  in  to get the co-ordinates for the graph of  at x axis
Page 3


         
              
         
         
                
     
Question:47
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
Solution:
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:48
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
Solution:
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:49
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
Solution:
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:50
How many linear equations are satisfied by x = 2  and y = -3?
a
Only one
b
Two
c
Three
d
Infinitely many
Solution:
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.
i i Every point on the line is the solution of the linear equation.
Therefore, the correct answer is
d.
Question:51
The equation x - 2 = 0 on number line is represented by
a
a line
b
a point
c
infinitely many lines
d
two lines
Solution:
The equation  is represented by a point on the number line.
Therefore, the correct answer is
b.
Question:52
x = 2, y = -1 is a solution of the linear equation
a
x + 2y = 0
Page 4


         
              
         
         
                
     
Question:47
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
Solution:
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:48
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
Solution:
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:49
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
Solution:
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:50
How many linear equations are satisfied by x = 2  and y = -3?
a
Only one
b
Two
c
Three
d
Infinitely many
Solution:
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.
i i Every point on the line is the solution of the linear equation.
Therefore, the correct answer is
d.
Question:51
The equation x - 2 = 0 on number line is represented by
a
a line
b
a point
c
infinitely many lines
d
two lines
Solution:
The equation  is represented by a point on the number line.
Therefore, the correct answer is
b.
Question:52
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
Solution:
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:53
If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =
a
1
b
2
c
3
d
4
Solution:
We are given as the solution of equation
Substituting , we get
Therefore, the correct answer is
b.
Page 5


         
              
         
         
                
     
Question:47
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
Solution:
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:48
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
Solution:
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:49
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
Solution:
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:50
How many linear equations are satisfied by x = 2  and y = -3?
a
Only one
b
Two
c
Three
d
Infinitely many
Solution:
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.
i i Every point on the line is the solution of the linear equation.
Therefore, the correct answer is
d.
Question:51
The equation x - 2 = 0 on number line is represented by
a
a line
b
a point
c
infinitely many lines
d
two lines
Solution:
The equation  is represented by a point on the number line.
Therefore, the correct answer is
b.
Question:52
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
Solution:
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:53
If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =
a
1
b
2
c
3
d
4
Solution:
We are given as the solution of equation
Substituting , we get
Therefore, the correct answer is
b.
Question:54
The distance between the graph of the equations x = -3 and x = 2 is
a
1
b
2
c
3
d
5
Solution:
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:55
The distance between the graphs of the equations y = -1 and y = 3 is
a
2
b
4
c
3
d
1
Solution:
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.