Question 1011 Mark
Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.
Answer
View full question & answer→- 8
Questions · Page 3 of 4
M.C.Q
Question 1021 Mark
The cost of a notebook is twice the cost of a pen. The equation to represent this statement is:
Answer
View full question & 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.
Question 1031 Mark
The linear equation 3x - 11y = 10 has:
Answer
View full question & answer→- Infinitely many solutions
Question 1041 Mark
Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:
Answer
View full question & answer→- $\frac{5}{3}$
Question 1051 Mark
If x represents the age of father and y represents the present age of the son, then the statement for ‘present age of father is 5 more than 6 times the age of the son’ in terms of mathematical equation is
Answer
View full question & answer→- x = 6y + 5
Question 1061 Mark
A linear equation in two variables has maximum:
Answer
View full question & answer→- Infinite solution
Question 1071 Mark
x = 3 and y = -2 is a solution of the equation 4px - 3y = 12, then the value of p is:
Answer
View full question & answer→- $\frac{1}{2}$
Question 1081 Mark
The equation x = 7 in two variables can be written as:
Answer
View full question & answer→- 1.x + 0.y = 7
Solution:
The equation x = 7 in two variables can be written as exactly 1.x + 0.y = 7
because it contain two variable x and y and coefficient of y is zero as there is no term containing yin equation x = 7
Question 1091 Mark
The equation x = 7 in two variables can be written as:
Answer
View full question & answer→- 1.x + 0.y = 7
Solution:
The equation x = 7 in two variables can be written as exactly 1.x + 0.y = 7 because it contain two variable x and y and coefficient of y is zero as there is no term containing y in equation x = 7.
Question 1101 Mark
The graph of the linear equation x + y = 0 passes through the point.
Answer
View full question & answer→- (1, -1)
Solution:
The graph of the linear equation x + y = 0 passes through the point (1, -1) because the co-ordinate of x and y axis satisfy the given equation.
x + y = 0
1 - 1 = 0
So we can say (1, -1) is a solution of above equation
Question 1111 Mark
The linear equation 3x - 5y = 15 has:
Answer
View full question & answer→- Infinitely many solutions.
Solution:
The linear equation 3x - 5y = 15 has infinitely many solutions since any every point on this line will be a solution of this equation.
For different values of x, we will get get the corresponding different values of y.
Since x can take infinitely many values, y will also have infinite values.
Hence, the line will have infinitely many solutions.
Question 1121 Mark
x = 2, y = - 1 is a solution of the linear equation:
Answer
View full question & answer→- x + 2y = 0
Solution:
2 + 2(-1) = 2 - 2 = 0.
Question 1131 Mark
If the point (3, 4) lies on the graph of 3y = ax + 6, then the value of ‘a’ is:
Answer
View full question & answer→- 2
Solution:
The point (3, 4) lies on the graph of 3y = ax + 6
So it will satisfy the equation
3y = ax + 6
3(y) = ax + 6
12 = 3a + 6
12 - 6 = 3a
3a = 6
$\text{a}=\frac{6}{3}$
a = 2
Question 1141 Mark
The equation of a line parallel to y-axis and 4 units to the right of origin is:
Answer
View full question & 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 to y-axis in that case equation of line is x = 4. So required equation is x = 4.
Question 1151 Mark
The graph of the linear equation 2x + 3y = 6 meets the y-axis at the point.
Answer
View full question & answer→- (0, 2)
Solution:
If the graph of the linear equation 2x + 3y = 6 meets the y-axis, then x = 0.
Substituting the value of x = 0 in equation 2x + 3y = 6, we get
2(0) + 3y = 6
⇒ 3y = 6
$\Rightarrow\text{y}=\frac{6}{3}$
⇒ y = 2
So, the point of meeting is (0, 2).
Question 1161 Mark
If we multiply or 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 we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation remains the same.
Question 1171 Mark
If the point (3, 4) lies on the graph of 3y = ax + 6, then the value of 'a' is:
Answer
View full question & answer→- 2
Solution:
The point (3, 4) lies on the graph of 3y = ax + 6
So, it will satisfy the equation
3y = ax + 6
3(y) = ax + 6
12 = 3a + b
12 - 6 = 3a
3a = 6
$\text{a}=\frac{6}{3}$
$\text{a}=2$
Question 1181 Mark
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is:
Answer
View full question & answer→- 4
Solution:
(2, 0) is a solution of the linear equation 2x + 3y = k,
⇒ 4 = k.
Question 1191 Mark
The point of the form (a, –a) always lies on the line:
Answer
View full question & answer→- x + y = 0
Solution:
Taking option (d), x + y = a + (-a) = a – a = 0 [since, give point is of the form (a, -a)] Hence, the point (a, – a) always lies on the line x + y = 0.
Question 1201 Mark
The graph of the linear equation 4x + 2y = 12, cuts the x-axis at the point:
Answer
View full question & answer→- (3, 0)
Solution:
The graph of the linear equation 4x + 2y = 12, cuts the x-axis at the point when line cut x-axis the co-ordinate of y becomes zero.
So we put y = 0 in given equation to find the co-ordinate,
4x + 2y = 124x + 2(0) = 124x = 12
$\text{x}=\frac{12}{4}$
x = 3
So the required coordinate is (3, 0).
Question 1211 Mark
x = 5, y = 2 is a solution of the linear equation:
Answer
View full question & answer→- x + y = 7
Solution:
Substituting x = 5 and y = 2 in L.H.S. of equation x + y = 7,
We get:
LHS
= 5 + 2
7 = RHS
Hence, x = 5 and y = 2 is a solution of the linear equation x + y = 7.
Question 1221 Mark
If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form:
Answer
View full question & answer→- y = 9x - 7
Solution:
Since all the given co- ordinate (1, 2), (-1, -16) and (0, -7) satisfy the given line y = 9x - 7
For point (1, 2)
y = 9x - 7
2 = 9(1) - 7
2 = 9 - 7
2 = 2
Hence (2, 1) is a solution.
For point (-1, -16)
y = 9x - 7
-16 = 9(-1) - 7
-16 = -9 - 7
-16 = -16
Hence (-1, -16) is a solution.
For point (0, -7)
y = 9x - 7
-7 = 9(0) -7
-7 = -7
Hence (0, -7) is a solution.
Question 1231 Mark
If we multiply 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 for any c. where c is any natural number.
Like addition and subtraction, we can multiply and divide both sides of an equation by a number, c, without changing the equation, where c is any natural number
Question 1241 Mark
The equation 2x + 5y = 7 has a unique solution, if x, y are:
Answer
View full question & answer→- Natural numbers.
Solution:
There is only one pair i.e., (1, 1) which satisfies the given equation but in positive real numbers, real numbers and rational numbers there are many pairs to satisfy the given linear equation. Hence, unique solution is possible only in case of Natural numbers.
Question 1251 Mark
The graph of the linear equation x - y = 0 passes through the point:
Answer
View full question & answer→- $\Big(\frac{1}{1},\frac{1}{2}\Big)$
Solution:
The graph of the linear equation x - y = 0 passes through the point $\Big(\frac{1}{1},\frac{1}{2}\Big)$ because the co-ordinate of x and y axis satisfy the given equation x - y = 0.
$\frac{1}{1}-\frac{1}{2}=0$
0 = 0
So we can say $\Big(\frac{1}{1},\frac{1}{2}\Big)$ is a solution of above equation.
So we can say the value of x co-ordinate must be equal to y co-ordinate.
Question 1261 Mark
The point of the form (a, -a), where a lies on:
Answer
View full question & answer→- The line y + x = 0.
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.
Question 1271 Mark
The graph of the linear equation 3x - 2y = 6, cuts the x-axis at the point:
Answer
View full question & answer→- (2, 0)
Solution:
The linear equation 3x - 2y = 6, cuts the x-axis when y co-ordinate is 0.
So we put y = 0 in given equation 3x - 2y = 6
3x - 2.0 = 6
3x = 6
$\text{x}=\frac{6}{3}$
x = 2
So the co-ordinates are (2, 0).
Question 1281 Mark
All linear equations in two variables have __________.
Answer
View full question & answer→- Infinitely many solutions
Question 1291 Mark
x = 0 is the equation of:
Answer
View full question & answer→- y-axis.
Solution:
x = 0 is a line of y-axis because x-coordinates of all points lie on y-axis are zero.
Question 1301 Mark
The graph of the line y = -3 does not pass through the point:
Answer
View full question & answer→
Question 1311 Mark
The value of y at x = -1 in the equation 5y = 2 is:
Answer
View full question & answer→- $\frac{2}{5}$
Question 1321 Mark
If a linear equation has solutions (-2, 2), (0, 0) and (2, -2), then it is of the form:
Answer
View full question & 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.
Question 1331 Mark
The distance between the graph of the equations x = -3 and x = 2 is:
Answer
View full question & answer→- 5
Solution:
Distance between the graph of the equations x = -3 and x = 2 is = 2 - (-3) = 5 units.
Question 1341 Mark
The equation of a line parallel to x-axis and 3 units above the origin is:
Answer
View full question & 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.
Question 1351 Mark
The area of the triangle formed by the line 2x + 5y = 10 and the co-ordinate axis is:
Answer
View full question & 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.
Question 1361 Mark
3x + 10 = 0 will have:
Answer
View full question & answer→- Unique solution
Solution:
$3\text{x}+10 = 0$
$\text{x}=\frac{-10}{3}.$
Hence, only one solution is possible.
Question 1371 Mark
The equation of a line parallel to x - axis and 3 units above the origin is:
Answer
View full question & answer→- y = 3
Question 1381 Mark
Any point of the form (a, -a) always lie on the graph of the equation.
Answer
View full question & answer→- x + y = 0
Question 1391 Mark
If x and y are both positive solutions of equation ax + by + c = 0, always lie in the:
Answer
View full question & answer→- First quadrant
Question 1401 Mark
The maximum number of points that lie on the graph of a linear equation in two variables is:
Answer
View full question & answer→- Infinitely many
Question 1411 Mark
Express y in terms of x in the equation 5x - 2y = 7.
Answer
View full question & answer→- $\text{y}=\frac{5\text{x}-7}{2}$
Solution:
5x - 2y = 7
-2y = 7 - 5x
2y = 5x - 7
$\text{y}=\frac{5\text{x}-7}{2}.$
Question 1421 Mark
The graph of the linear equation 3x - 5y = 15, cuts the y-axis at the point:
Answer
View full question & answer→- (0, -3)
Solution:
The graph of the linear equation 3x - 5y = 15, cuts the y-axis at the point when line cut y-axis the co-ordinate of x becomes zero.
So we put x = 0 in given equation to find the co-ordinate.
3x - 5y = 15
3(0) - 5y = 15
-5y = 15
$\text{y} = −\frac{15}{5}$
y = -3
So the required cordinate is (0, -3).
Question 1431 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 1441 Mark
The graph of y = 5 is a line.
Answer
View full question & answer→- Making an intercept 5 on the y-axis.
Solution:
As, the graph of y = 5 is a line parallel to x-axis i.e. y = 0.
⇒ The line represented by the equation y = 5 is parallel to x-axis and intersects y-axis at y = 5.
So, the graph of y = 5 is a line parallel to the x-axis at a distance of 5 units from the origin making an intercept 5 on the y-axis.
Question 1451 Mark
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.
Answer
View full question & answer→- 5 units.
Solution:
According to the given question, triangle so formed has sides of units 3 and 4, using pythagoras theorem, the largest side is of 5 units.
Question 1461 Mark
How many lines pass through one point?
Answer
View full question & answer→- Many.
Solution:
Because one point can be solution of many equations. So many equations can be pass from one point.
Question 1471 Mark
The graph of a linear equation $\text{y}=\frac{9}{5}\text{x}+32$ cuts the y-axis at the point:
Answer
View full question & answer→- (0, 32)
Solution:
When the graph cut at y axis in that case the value of x- coordinate is 0.
$\text{y}=\frac{9}{5}\text{x}+32$
$\text{y}=\frac{9}{5}.0+\text{32}$
$\text{y}=32$
So, the co-ordinates are (32, 0)
Question 1481 Mark
The area of the triangle formed by the line 3x + 4y = 12 and the co-ordinate axis is:
Question 1491 Mark
The equation x - 2 = 0 on number line is represented by:
Answer
View full question & answer→- A point.
Solution:
x - 2 = 0
x = 2 is a point on the number line.
Question 1501 Mark
x = 2, y = 5 is a solution of the linear equation.
Answer
View full question & answer→- x + y = 7
Solution:
x = 2 and y = 5 satisfy the given equation.