Question 11 Mark
The graph of x = 3 is a line:
Answer
View full question & answer→- Parallel to y - axis at a distance of 3 units from the origin.
Questions · Page 1 of 4
M.C.Q
🎯
Test yourself on this topic
50 questions · timed · auto-graded
Question 21 Mark
The graph of the linear equation 2x + 5y = 10 meets the x-axis at the point.
Answer
View full question & 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).
Question 31 Mark
The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point.
Answer
View full question & 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).
Question 41 Mark
The equation 2x + 5y = 7 has a unique solution, if x and y are:
Answer
View full question & 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.
Question 51 Mark
Any point on the x-axis is of the form:
Answer
View full question & 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.
Question 61 Mark
The point which lies on y-axis at a distance of 6 units in the positive direction of y-axis is:
Answer
View full question & 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).
Question 71 Mark
Write the correct answer in the following:
The graph of y = 6 is a Line,
The graph of y = 6 is a Line,
Answer
View full question & 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.
Question 81 Mark
Which of the following is a linear equation in two variables?
Answer
View full question & answer→- 2x - 5y = 0
Solution:
In linear equation power of variable x and y should be 1 and here, the given linear equation has two variable x and y.
Question 91 Mark
Write the correct answer in the following: The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point,
Answer
View full question & 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
Question 101 Mark
x - 4 is the equation of:
Answer
View full question & 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.
Question 111 Mark
Express ‘x’ in terms of ‘y’ in the equation 2x - 3y - 5 = 0.
Answer
View full question & answer→- $\text{x}=\frac{3\text{y}+5}{2}$
Solution:
2x - 3y -5 = 0
2x = 3y + 5
$\text{x}=\frac{3\text{y}+5}{2}.$
Question 121 Mark
The point of the form (a, a), where a lies on:
Answer
View full question & 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
Question 131 Mark
The point of the form $(\text{a},-\text{a}),\ \text{a}\neq0$ lies on:
Answer
View full question & 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.
Question 141 Mark
The graph of x + 3 = 0 is a line.
Answer
View full question & 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.
Question 151 Mark
The graph of x = 4 is a line:
Answer
View full question & 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.
Question 161 Mark
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form:
Answer
View full question & answer→- $\Big(-\frac{9}{2},\text{m}\Big)$
Solution:
2x + 9 = 0
$\Rightarrow\text{x}=\frac{-9}{2}$ And y = m, where m is any real number,
Hence, $\Big(-\frac{9}{2},\text{m}\Big)$ is the solution of the given equation.
Question 171 Mark
If (-2, 5) is a solution of 2x + my = 11, then the value of ‘m’ is:
Answer
View full question & 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.
Question 181 Mark
Any point on line x = y is of the form:
Answer
View full question & answer→- (k, k)
Question 191 Mark
If (a, 4) lies on the graph of 3x + y = 10, then the value of a is:
Answer
View full question & answer→- 2
Solution:
Given, (a, 4) lies on the graph of 3x + y = 10
Thus it is a solution
= 3a + 4 = 10
= a = 2.
Question 201 Mark
The value of k if x = 2, y = 1 is a solution of equation 2x - k = -3y is:
Answer
View full question & answer→- 7
Question 211 Mark
The distance between the graphs of the equations y = -1 and y = 3 is:
Answer
View full question & answer→- 4
Solution:
The distance between given two graphs
= 3 - (-1)
= 3 + 1
= 4
Hence, correct option is (b).
Question 221 Mark
If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of k is:
Answer
View full question & 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
Question 231 Mark
Solutions of the equation 2x + 5y = 0 is:
Answer
View full question & answer→- 0, 0
Question 241 Mark
The point of the form (a, a) always lies on:
Answer
View full question & 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.
Question 251 Mark
y = 0 is the equation of:
Answer
View full question & answer→- A line parallel to y - axis
Question 261 Mark
If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of 'k' is:
Answer
View full question & 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
Question 271 Mark
The condition that the equation ax + by + c = 0 represents a linear equation in two variables is:
Answer
View full question & answer→- a ≠ 0, b ≠ 0
Question 281 Mark
The linear equation 3x - 5y = 15 has:
Answer
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.
View full question & 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 |
We get infinite points that satisfy the given equation.
Hence, the linear equation has infinitely many solutions.
Question 291 Mark
The equation 2x + 5y = 7 has a unique solution, if x, y are:
Answer
View full question & 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.
Question 301 Mark
The graph of linear equation x + 2y = 2, cuts the y - axis at:
Answer
View full question & 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).
Question 311 Mark
The line represented by the equation x + y = 16 passes through (2, 14). How many more lines pass through the point (2, 14).
Answer
View full question & answer→- Many
Solution:
There are many lines pass through the point (2, 14)
x - y = -12
2x + y = 18
and many more
Question 321 Mark
The linear equation 2x - 5y = 7 has:
Answer
View full question & answer→- Infinitely many solutions.
Solution:
Given equation is 2x - 5y = 7,
There is no given value of x and y so we can take any values. For every value of x, we get a corresponding value of y and vice-versa.
Therefore, it has infinitely many solutions.
Question 331 Mark
The graph of y + 2 = 0 is a line.
Answer
View full question & 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.
Question 341 Mark
The equation of a line parallel to y-axis and 7 units to the left of origin is:
Answer
View full question & answer→- x = -7
Solution:
The equation of a line parallel to y-axis and 7 units to the left of the origin is x = -7.
Because when a line parallel to y-axis in that case equation of line is x = a.
Where a is the co-ordinate of x-axis and 7 units to the left of the origin value x -co-ordinate is -7. So required equation is x = -7.
Question 351 Mark
The graph of the linear equation y = 3x passes through the point.
Answer
View full question & answer→- $(\frac{2}{3},2)$
Solution:
$\text{y}=3\text{x}$
$\frac{\text{y}}{3}=\text{x}$
For $\text{x}=\frac{2}{3},$ the value of $\text{y}=3\times\frac{2}{3}=2$
So $(\frac{2}{3},2).$
Question 361 Mark
For the equation 5x + 8y = 50, if y = 10, then the value of x is:
Answer
View full question & answer→- -6
Solution:
For the equation 5x + 8y = 50, if y = 10
Put y = 10 in given equation
5x + 8 × 10 = 50
5x + 80 = 50
5x = 50 - 80
5x = -30
$\text{x} = -\frac{30}{5}$
x = -6
Question 371 Mark
The point on the graph of the linear equation 2x + 5y = 19, whose ordinate is $1^{\frac{1}{2}}$ times its abscissa is:
Answer
View full question & answer→- (2, 3)
Solution:
Ordinate means y-coordinate. It means we need to find a point on the given line where y-coordinte $=\frac{3}{2}$ ex-coordinate).
Just put $\text{y}=\Big[\frac{3}{2}\Big].\text{x}$ in the given eqn.
$2\text{x}+5\times\frac{3}{2}\text{x}=19$
$2\text{x}+\frac{15}{2}\text{x}=19$
$\frac{19\text{x}}{2}=19$
$\text{x}=\frac{19\times2}{19}$
$\text{y}=\frac{3}{2}\text{x}$
$\text{y}=\frac{3}{2}\times2$
$\text{y}=3$
So the co-ordinate are (2, 3)
Question 381 Mark
x = 5 and y = -2 is the solution of the linear equation.
Answer
View full question & answer→- 2x - y = 12
Solution:
x = 5 and y = -2 is the solution of the linear equation 2x - y = 12
2x - y = 12
LHS = 2x - y
2.5 - (-2)
10 + 2
12
RHS = 12
LHS = RHS
It means that x = 5 and y = -2 is the solution of the linear equation 2x - y = 12.
Question 391 Mark
Which of the following is the equation of a line parallel to y - axis?
Answer
View full question & answer→- x = a
Question 401 Mark
Write the correct answer in the following:
The graph of the linear equation y = x passes through the point.
The graph of the linear equation y = x passes through the point.
Answer
View full question & answer→- $(1,1)$
Solution:
We know that any point on the line y = x will have x and y coordinates same.
So, the graph of the linear equation y = x passes through the point (1, 1).
Question 411 Mark
The graph of the line x - y = 0 passes through the point:
Answer
View full question & answer→- $(1, 1)$
Solution:
The given linear equation is x = y = 0.
We have to check which of the point satisfy the given equation.
consider option (a):
Substituting $\text{x}=-\frac{1}{2}$ and $\text{y}=\frac{1}{2}$ in the LHS if the given linear equation
$\therefore\ \text{x}-\text{y}=-\frac{1}{2}-\frac{1}{2}=-1\neq\text{RHS}$
$\therefore\ \text{x}=-\frac{1}{2}$ and $\text{y}=\frac{1}{2}$ does not satisfy the given linear equation.
Consider option (b):
Substituting $\text{a}=\frac{3}{2}$ and $\text{y}=-\frac{3}{2}$ in the LHS if the given linear equation on
$\therefore\ \text{x}-\text{y}=\frac{3}{2}+\frac{3}{2}=3\neq\text{RHS}$
$\therefore\ \text{x}=-\frac{3}{2}$ and $\text{y}=-\frac{3}{2}$ does not satisfy the given linear eqation on.
Consider option (d):
Substitution x = 1 and y = 1 in the LHS if the given linear equation
$\therefore\ $x - y = 1 - 1 = 0 = RHS
$\therefore\ $x = 1 and y = 1 satisfies the given linear equation.
Question 421 Mark
The line represented by the equation x + y = 16 passes through (2, 14). How many more lines pass through the point (2, 14).
Answer
View full question & answer→- Many
Solution:
There are many lines pass through the point (2, 14).
For example
x - y = -12
2x + y = 18
And many more.
Question 431 Mark
The point which lies on x-axis at a distance of 4 units in the negative direction of x-axis is:
Answer
View full question & answer→- (-4, 0)
Solution:
At x-axis the value of y co-ordinate is 0 x-axis at a distance of 4 units in the negative direction so the co-ordinate of x-axis is -4. So the co-ordinate of point is (-4, 0).
Question 441 Mark
The linear equation 3x - y = x - 1 has:
Answer
View full question & answer→- Infinitely many solutions
Solution:
The linear equation 3x - y = x - 1 has infinitely many solutions.
On simplification, the given equation becomes 2x - y = -1, which is a single equation with two variables.
Thus, 3x - y = x - 1 has infinitely many solutions.
Question 451 Mark
The linear equation 3x - 11y = 10 has:
Answer
View full question & answer→- Infinitely many solutions
Solution:
$3\text{x}-11\text{y}=10$
$\text{y}=\frac{(3\text{x}-10)}{11}$
Now for infinite values of x, y will also have infinite solutions.
Question 461 Mark
Write the correct answer in the following:
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form,
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form,
Answer
View full question & answer→- $\Big(-\frac{9}{2},\text{m}\Big)$
Solution:
The given linear equation is
2x + 0y + 9 = 0
⇒ 2x + 9 = 0
⇒ 2x = -9
$⇒ x = -\frac{9}{2}$ and y can be any real number.
Question 471 Mark
If we divide both sides of a linear equation with a non-zero number, then the solution of the linear equation.
Answer
View full question & answer→- Remains the same.
Solution:
If then for any non-zero c.
We can divide both sides of an equation by a non-zero number c, without changing the equation.
Question 481 Mark
Write the correct answer in the following:
Any point on the line y = x is of the form,
Any point on the line y = x is of the form,
Answer
View full question & answer→- (a, a)
Solution:
Every point on the line y = x has same value of x-and y-coordinates i.e., x = a and y = a.
Question 491 Mark
The distance between the graphs of the equations y = -1 and y = 3 is:
Answer
View full question & answer→- 4
Solution:
Distance between the graphs of the equations y = -1 and y = 3 is = 3 - (-1) = 4 units.
Question 501 Mark
The point of the form (-a, a), where a lies on
Answer
View full question & answer→- The line x + y = 02
Solution:
The point (a, -a) lies on line x + y = 0
Here is the verification
Put x = a in equation
x + y = 0
a + y = 0
y = -a
Hence it is prove that (a, -a) is a solution of x + y = 0