M.C.Q

MCQ 511 Mark

The equation of a line parallel to x-axis and 3 units above the origin is:

A
x = 3
B
y = 3
C
x = -3
D
y = -3

Answer

y = 3
Solution:
The equation of a line parallel to x-axis and 3 units above the origin is y = 3.
Because when a line parallel to x axis in that case equation of line is y = a where a is the co-ordinate of y-axis and 3 units above the origin value x-coordinate is 3 so required equation is y = 3.

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MCQ 521 Mark

3x + 10 = 0 will have:

A
Unique solution
B
Two solutions
C
Infinitely many solutions
D
No solutions

Answer

Unique solution
Solution:
$3\text{x}+10 = 0$
$\text{x}=\frac{-10}{3}.$
Hence, only one solution is possible.

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MCQ 531 Mark

If a linear equation has solutions (-2, 2), (0, 0) and (2, -2), then it is of the form:

A
-x + 2y = 0
B
x + y = 0
C
x - y = 0
D
-2x + y = 0

Answer

x + y = 0
Solution:
Linear equation has solutions (-2, 2), (0, 0) and (2, -2), then the equation will be x + y = 0.
As all the given three points satisfy the given equation.

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MCQ 541 Mark

The area of the triangle formed by the line 2x + 5y = 10 and the co-ordinate axis is:

A
4 sq. units.
B
10 sq. units.
C
3 sq. units.
D
5 sq. units.

Answer

5 sq. units.
Solution:
To find the area of the triangle formed by the line 2x + 5y = 10 and co-ordinate axis. We put x = 0 in given equation at x = 0, we get y = 2 at y = 0 we get x = 5. So the line cut y-axis at 2 and x-axis at 5.
So the height of the triangle is 2 units and the base is 5 units.
Area of triangle $=\frac{1}{2}$ base × heigh,
$=\frac{1}{2}\times2\times5$
= 5 sq. units.

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MCQ 551 Mark

The equation of a line parallel to x - axis and 3 units above the origin is:

A
x = -3
B
x = 3
C
y = -3
D
y = 3

Answer

y = 3

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MCQ 561 Mark

If x and y are both positive solutions of equation ax + by + c = 0, always lie in the:

A
First quadrant
B
Second quadrant
C
Third quadrant
D
Fourth quadrant

Answer

First quadrant

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MCQ 571 Mark

Any point of the form (a, -a) always lie on the graph of the equation.

A
x = -a
B
y = a
C
y = x
D
x + y = 0

Answer

x + y = 0

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MCQ 581 Mark

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is:

Answer

4
Solution:
Substitute x = 2 and y = 0 in the given equation, we get
2 (2) + 3 (0) = k
k = 4 + 0
k = 4.
Hence, the value of k is 4.
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MCQ 591 Mark

The point of the form (a, a), where a lies on:

A
The line y = x.
B
The line x + y = 0.
C
The x-axis.
D
The y-axis.

Answer

The line y = x.
Solution:
The point (a, a) lies on line x = y or x - y = 0
Here, is the verification
Put x = a in equation
x - y = 0
a - y = 0
-y = -a
y = a
Hence, it is prove that (a, a) is a solution of x - y = 0 or x = y.

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MCQ 601 Mark

A linear equation in two variables x and y is of the form ax + by + c = 0, where:

A
$\text{a}\neq0,\ \text{b}\neq0$
B
$\text{a}\neq0,\ \text{b}=0$
C
$\text{a}=0,\ \text{b}\neq0$
D
$\text{a}=0,\ \text{c}=0$

Answer

$\text{a}\neq0,\ \text{b}\neq0$
Solution:
A linear equation in tow variables x and y is of the form ax + by + c = 0, where $\text{a}\neq0$ and $\text{b}\neq0,$ since if either a or be is 0, the degree of the equation would be but it would not be a linear equation in tow variables.
If both a and b are 0, then the equation is not linear.

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MCQ 611 Mark

The linear equation 2x + 3y = 6 has:

A
Infinitely many solutions.
B
Two solutions.
C
A unique solution.
D
Three solutions.

Answer

Infinitely many solutions.
Solution:
2x + 3y = 6
2x = 6 - 3y
$\text{x}=\frac{6-3\text{y}}{2}$

x	0	3232	3
y	2	1	0

This table continues for infinite terms for different values of x and y. So for infinite value of y we have infinite value of x.
Therefore, this equation has Infinitely many solutions.

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MCQ 621 Mark

Which of the following pair is a solution of the equation 3x - 2y = 7?

A
(-2, 1)
B
(5, 1)
C
(1, -2)
D
(1, 5)

Answer

(1, -2)
Solution:
Solution of the equation 3x - 2y = 7 is (1, -2) as it satisfy the given equation,
3x - 2y = 7
⇒ 3(1) - 2(-2) = 7
⇒ 3 + 4 = 7
LHS = RHS.

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MCQ 631 Mark

Which of the following is not a solution of 2x - 3y = 12?

A
(6, 0)
B
(3, -2)
C
(0, -4)
D
(2, 3)

Answer

(2, 3)
Solution:
We have to check (2, 3) is a solution of 2x - 3y = 12 if (2, 3) satisfy the equation then (2, 3) solution of 2x - 3y = 12.
LHS = 2x - 3y
2 × 2 - 3 × 3
4 - 9 = -5
RHS = -5
LHS ≠ RHS
So (2, 3) is not a solution of 2x - 3y = 12.

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MCQ 641 Mark

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

Answer

4
Solution:
y = ax + 3
If (4, 19) is its solution, then it must satisfy the equation.
Thus, we have
19 = a × 4 + 3
i.e. 4a = 16
i.e. a = 4
Hence, correct option is (b).

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MCQ 651 Mark

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

x + 2y = 0
Solution:
Substituting x = 2 and y = -1 in the following equations:
L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 = R.H.S.
L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 ≠ 4 ≠ R.H.S.
L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 0 ≠ R.H.S.
L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 5 ≠ R.H.S.
Hence, correct option is (a).

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MCQ 661 Mark

The equation of a line parallel to y-axis and 4 units to the right of origin is:

A
x = 4
B
x = -4
C
y = -4
D
y = 4

Answer

x = 4
Solution:
The equation of a line parallel to y-axis at a distance of 4 units from it, to its right from the origin.
x = 4
Because when a line parallel toy axis in that case equation of line is x = 4
So required equation is x = 4

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MCQ 671 Mark

For what value of ‘k’, x = 2 and y = -1 is a solution of x + 3y - k = 0?

A
2
B
-2
C
-1
D
1

Answer

-1
Solution:
For finding value of ‘k’, we put x = 2 and y = -1 in a equation x + 3y - k = 0.
x + 3y - k = 0
2 + 3(-1) = k
2 - 3 = k
k = -1.

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MCQ 681 Mark

The maximum number of points that lie on the graph of a linear equation in two variables is:

A
One
B
Two
C
Three
D
Infinitely many

Answer

Infinitely many

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MCQ 691 Mark

The graph of the equation 2x + 3y = 6 cuts the x - axis at the point.

A
(0, 3)
B
(3, 0)
C
(2, 0)
D
(0, 2)

Answer

(3, 0)

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MCQ 701 Mark

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

Answer

2
Solution:
3x + y = 10
If (a, 4) lies on its graph, then it must satisfy the equation.
Thus, we have
3(a) + 4 = 10
i.e. 3a = 6
i.e. a = 2
Hence, correct option is (c).

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MCQ 711 Mark

Write the correct answer in the following:
The equation of X-axis is of the form,

A
x = 0
B
y = 0
C
x + y = 0
D
x = y

Answer

y = 0
Solution:
y = 0 is the equation of x-axis.

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MCQ 721 Mark

The graph of x = 4 is a line.

A
Making an intercept 4 on the y-axis.
B
Parallel to the y-axis at a distance of 5 units from the origin.
C
Making an intercept 4 on the x-axis.
D
Parallel to the x-axis at a distance of 4 units from the origin.

Answer

Making an intercept 4 on the x-axis.
Solution:
As, the graph of x = 4 is a line parallel to y-axis i.e. x = 0.
⇒ The line represented by the equation x = 4 is parallel to y-axis and intersects x-axis at x = 4.
So, the graph of x = 4 is parallel to y-axis at a distance of 4 units from the origin making an intercept 4 on the x-axis.

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MCQ 731 Mark

Which of the following ordered pairs is a solution of the equation x - 2y - 6?

A
(2, 4)
B
(0, 3)
C
(-4, 1)
D
(4, -1)

Answer

(4, -1)

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MCQ 741 Mark

If x = 3 and y = -2 satisfies 5x - y = k, then the value of k is:

A
3
B
-2
C
17
D
12

Answer

17
Solution:
If x = 3 and y = -2 satisfies 5x - y = k
Then
5x - y = k
5 × 3 - (-2) = k
15 + 2 = k
k = 17.

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MCQ 751 Mark

If (-2, 5) is a solution of 2x + my = 11, then the value of ‘m’ is:

A
-3
B
2
C
3
D
-2

Answer

3
Solution:
If (-2, 5) is a solution of 2x + my = 11 then it will satisfy the given equation,
2.(-2) + 5m = 11
-4 + 5m = 11
5m = 11 + 4
5m = 15
$\text{m}=\frac{15}{5}=3$
m = 3.

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MCQ 761 Mark

If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of 'k' is:

Answer

1
Solution:
If the line represented by the equation 3x + ky = 9 passes through the points (2, 3) then (2, 3) will satisy the equation 3x + ky = 9
3(2) + 3k = 9
⇒ 6 + 3k = 9
⇒ 3k - 9 - 6
⇒ 3k = 3
⇒ k = 1

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MCQ 771 Mark

The condition that the equation ax + by + c = 0 represents a linear equation in two variables is:

A
a ≠ 0, b = 0
B
b ≠ 0, a = 0
C
a = 0, b = 0
D
a ≠ 0, b ≠ 0

Answer

a ≠ 0, b ≠ 0

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MCQ 781 Mark

Any point on line x = y is of the form:

A
(k, -k)
B
(0, k)
C
(k, 0)
D
(k, k)

Answer

(k, k)

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MCQ 791 Mark

The value of k if x = 2, y = 1 is a solution of equation 2x - k = -3y is:

A
6
B
5
C
7
D
-7

Answer

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MCQ 801 Mark

If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of k is:

Answer

1
Solution:
If the line represented by the equation 3x + ky = 9 passes through the points (2, 3) then (2, 3) will satisy the equation 3x + ky = 9
3(2) + 3k = 9
⇒ 6 + 3k = 9
⇒ 3k = 9 - 6
⇒ 3k = 3
⇒ k = 1

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MCQ 811 Mark

Solutions of the equation 2x + 5y = 0 is:

A
3, 0
B
-3, 2
C
0, 0
D
0, 4

Answer

0, 0

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MCQ 821 Mark

The point of the form (a, a) always lies on:

A
On the line x + y = 0
B
On the line y = x
C
x - axis
D
y - axis

Answer

On the line y = x
Solution:
The point of the form (a, a) always lies on the line y = x.
If the point has the same x and y values, it should lie on the same line.

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MCQ 831 Mark

The graph of x = 3 is a line:

A
Parallel to x - axis at a distance of 3 units from the origin.
B
Parallel to y - axis at a distance of 3 units from the origin.
C
Makes an intercept 3 on x - axis.
D
Makes an intercept 3 on y - axis.

Answer

Parallel to y - axis at a distance of 3 units from the origin.

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MCQ 841 Mark

The linear equation 3x - 5y = 15 has:

A
Two solutions.
B
A unique solution.
C
No solution.
D
Infinitely many solutions.

Answer

Infinitely many solutions.
Solution:
Given linear equation: 3x - 5y = 15
Or, $\text{x}=5\text{y}+\frac{15}{3}$
When y = 0, x = 153 = 5
When y = 3, x = 303 = 10
When y = - 3, x = 03 = 0

xx	5	10	0
yy	0	3	-3

Plot the points A(5, 0), B(10, 3) and C(0, -3). Join the points and extend them in both the directions.
We get infinite points that satisfy the given equation.
Hence, the linear equation has infinitely many solutions.

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MCQ 851 Mark

The equation 2x + 5y = 7 has a unique solution, if x, y are:

A
Rational numbers
B
Real numbers
C
Natural numbers
D
Positive real numbers

Answer

Natural numbers
Solution:
The equation 2x + 5y = 7 has a unique solution, if x, y are natural numbers.
In natural numbers, there exists only one pair (1, 1) which satisfies the given equation.
But for rational numbers, real numbers, positive real numbers, there exist many solution pairs to satisfy the equation.

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MCQ 861 Mark

The graph of linear equation x + 2y = 2, cuts the y - axis at:

A
(2, 0)
B
(0, 2)
C
(0, 1)
D
(1, 1)

Answer

(0, 1)
Solution:
x + 2y = 2
$\text{y}=\frac{(2-\text{x})}{2}$
If x = 0, then;
$\text{y}=\frac{(2-0)}{2}=\frac{2}{2}=1$
Hence, x + 2y = 2 cuts the y - axis at (0, 1).

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MCQ 871 Mark

The graph of y + 2 = 0 is a line.

A
Parallel to the y-axis at a distance of 2 units to the left of y-axis.
B
Parallel to the x-axis at a distance of 2 units below the x-axis.
C
Making an intercept of -2 on the x-axis.
D
Making an intercept of -2 on the y-axis.

Answer

Making an intercept of -2 on the y-axis.
Solution:
As, the graph of y + 2 = 0 or y = -2 is a line parallel to x-axis i.e. y = 0.
⇒ The line represented by the equation y = -2 is parallel to x-axis and intersects y-axis at y = -2.
So, the graph of y + 2 = 0 is a line parallel to the x-axis at a distance of 2 units below the x-axis making an intercept -2 on the y-axis.

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MCQ 881 Mark

The cost of a notebook is twice the cost of a pen. The equation to represent this statement is:

A
x = 3y
B
x - 2y = 0
C
2x = 3y
D
None of these

Answer

x - 2y = 0
Solution:
Let the cost of the notebook is ₹ x and pen is ₹ y and we have given that the cost of a notebook is twice the cost of a pen.
So we have
x = 2y
Or x - 2y = 0.

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MCQ 891 Mark

The graph of the linear equation 2x + 5y = 10 meets the x-axis at the point.

A
(0, 5)
B
(5, 0)
C
(0, 2)
D
(2, 0)

Answer

(5, 0)
Solution:
If the graph of the linear equation 2x + 5y = 10 meets the x-axis, then y = 0.
Substituting the value of y = 0 in equation 2x + 5y = 10, we get
2x + 5(0) = 10
⇒ 2x = 10
$\Rightarrow\text{x}=\frac{10}{2}$
⇒ x = 5
So, the point of meeting is (5, 0).

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MCQ 901 Mark

The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point.

A
(0, 2)
B
(0, 3)
C
(3, 0)
D
(2, 0)

Answer

(3, 0)
Solution:
2x + 3y = 6 meets the x-axis.
Put y = 0,
2x + 3(0) = 6
x = 3
Therefore, graph of the given line meets x-axis at (3, 0).

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MCQ 911 Mark

The equation 2x + 5y = 7 has a unique solution, if x and y are:

A
Natural numbers.
B
Rational numbers.
C
Positive real numbers.
D
Real numbers.

Answer

Natural numbers.
Solution:
The equation 2x + 5y = 7 has a unique solution, if x and y are natural numbers.
If we take x = 1 and y = 1, the given equation is satisfied.

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MCQ 921 Mark

Any point on the x-axis is of the form:

A
(x, y)
B
(0, y)
C
(x, 0)
D
(x, x)

Answer

(x, 0)
Solution:
Any point on x-axis is of the form (x, 0), where $\text{x}\neq0,$
Since its y-coordinate will be 0 always.

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MCQ 931 Mark

The point which lies on y-axis at a distance of 6 units in the positive direction of y-axis is:

A
(0, 6)
B
(-6, 0)
C
(6, 0)
D
(0, -6)

Answer

(0, 6)
Solution:
At y-axis the value of x co-ordinate is 0 and y-axis at a distance of 6 units in the positive direction so the co-ordinate of the y-axis is 6. So the co-ordinate of point is (0, 6).

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MCQ 941 Mark

Write the correct answer in the following:
The graph of y = 6 is a Line,

A
Parallel to X-axis at a distance 6 units from the origin.
B
Parallel to Y-axis at a distance 6 units from the origin.
C
Making an intercept 6 on the X-axis.
D
Making an intercept 6 on both axes.

Answer

Parallel to X-axis at a distance 6 units from the origin.
Solution:
The given equation y = 6 does not contain x. Its graph is a line parallel to x-axis.
So, the graph of y = 6 is a line parallel to x-axis at a distance 6 units from the origin.

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MCQ 951 Mark

Write the correct answer in the following: The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point,

A
(2, 0)
B
(0, 3)
C
(3, 0)
D
(0, 2)

Answer

(0, 2)
Solution:
The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point where x coordinate is zero.
Putting x = 0 in 2x + 3y = 6, we get
2(0) + 3y = 6 ⇒ 3y = 6 ⇒ y = 6 ÷ 3 = 2

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MCQ 961 Mark

x - 4 is the equation of:

A
x-axis.
B
A line parallel to x-axis.
C
y-axis.
D
A line parallel to y-axis.

Answer

A line parallel to y-axis.
Solution:
We know that the line parallel to y-axis is given by x = a
x - 4 = 0
x = 4
So it is a line parallel to y-axis, at a distance of 4 units from it, to the right.

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MCQ 971 Mark

Express ‘x’ in terms of ‘y’ in the equation 2x - 3y - 5 = 0.

A
$\text{x}=\frac{5-3\text{y}}{2}$
B
$\text{x}=\frac{5+3\text{y}}{2}$
C
$\text{x}=\frac{3\text{y}+5}{2}$
D
$\text{x}=\frac{3\text{y}-5}{2}$

Answer

$\text{x}=\frac{3\text{y}+5}{2}$
Solution:
2x - 3y -5 = 0
2x = 3y + 5
$\text{x}=\frac{3\text{y}+5}{2}.$

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MCQ 981 Mark

The point of the form $(\text{a},-\text{a}),\ \text{a}\neq0$ lies on:

A
The x-axis
B
The y-axis
C
The line y = x
D
The line x + y = 0

Answer

The line x + y = 0
Solution:
A point which lies on the x-axis has its y-coordinate = 0
While a point which lies on the y-axis has its x-coordinate = 0.
So, the points of the form (a, -a) will not lie on either axes.
Also, it does not satisfy the equation on of the line y = x.
The point of the form (a, -a) lies on the line x + y = 0 since it satisifes the equation of the given line.

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MCQ 991 Mark

The graph of x + 3 = 0 is a line.

A
Making an intercept -3 on the y-axis.
B
Parallel to the x-axis at a distance of 3 units below the x-axis.
C
Making an intercept -3 on the x-axis.
D
Parallel to the y-axis at a distance of 3 units to the left of y-axis.

Answer

Making an intercept -3 on the x-axis.
Solution:
As, the graph of x + 3 = 0 or x = -3 is a line parallel to y-axis i.e. x = 0.
⇒ The line represented by the equation x = -3 is parallel to y-axis and intersects x-axis at x = -3.
So, the graph of x + 3 = 0 is a line parallel to the y-axis at a distance of 3 units to the left of y-axis making an intercept -3 on the x-axis.

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MCQ 1001 Mark

The graph of x = 4 is a line:

A
Making an intercept 4 on the x-axis.
B
Making an intercept 4 on the y-axis.
C
Parallel to the x-axis at a distance of 4 units from the origin.
D
Parallel to the y-axis at a distance of 4 units from the origin.

Answer

Parallel to the y-axis at a distance of 4 units from the origin.
Solution:
The graph of x = 4 is a line parallel to the y-axis at a distance of 4 units from the origin.

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Maths M.C.Q