MCQ 1511 Mark
The force applied on a body is directly proportional to the acceleration produced on it. The equation to represent the above statement is:
- ✓
$y = kx$
- B
$y + x = 0$
- C
- D
$y = x$
AnswerCorrect option: A. $y = kx$
Let force applied be $y$ and acceleration produced be $x$. The force applied on a body is directly proportional to the acceleration produced on it.Yαx
$y = kx$
Where $k$ is proportionality constant.
View full question & answer→MCQ 1521 Mark
A linear equation in two variables is of the form $ax + by + c = 0$, where:
- A
$a = 0, c = 0$
- B
$a \neq 0, b = 0$
- C
$a = 0, b \neq 0$
- ✓
$a \neq 0, b \neq 0$
AnswerCorrect option: D. $a \neq 0, b \neq 0$
A linear equation in two variables is of the form $ax + by + c = 0$, where $a \neq 0, b \neq 0.$
If the values of $“a”$ and $“b”$ are equal to $0$, the equation becomes $c = 0.$
Hence, the values of a and b should not be equal to $0.$
View full question & answer→MCQ 1531 Mark
The cost of $2\ kg$ of apples and $1\ kg$ of grapes on a day was found to be $₹ 160$. A linear equation in two variables to represent the above data is:
- A
$x + y = 160$
- B
$2x - y = 160$
- C
$x - 2y = 160$
- ✓
$2x + y = 160$
AnswerCorrect option: D. $2x + y = 160$
Let the cost of apples be ₹ $x$ per $Kg$ and cost of grapes be $₹ y$ per $Kg$ . The cost of $2 \ kg$ of apples and $1 \ kg$ of grapes on a day was found to be $₹ 160 .$
So the equation will be $2 x + y =160$.
View full question & answer→MCQ 1541 Mark
The linear equation $3x - y = x - 1$ has:
- A
- B
- ✓
Infinitely many solutions.
- D
AnswerCorrect option: C. Infinitely many solutions.
$3x - y = x - 1$
$y = 3x - x + 1$
$y = 2x + 1$
This is linear equation of two variable. If we take any random value of $x$ and solve $y$ corresponding value of $x$. We will get infinite many solutions.
View full question & answer→MCQ 1551 Mark
If the point $(3, 4)$ lies on the graph of $3y = ax + 7$ then the value of a is:
- A
$\frac{2}{7}$
- B
$\frac{2}{5}$
- ✓
$\frac{5}{3}$
- D
$\frac{3}{5}$
AnswerCorrect option: C. $\frac{5}{3}$
Given equation:$ 3y = ax + 7$
Also, $(3, 4)$ lies on the graph of the equation.
Putting $x = 3, y = 4$ in the equation, we get
$3 \times 4 = 3a + 7$
$\Rightarrow 12 = 3a + 7$
$\Rightarrow 3a = 12 - 7 = 5$
$\Rightarrow\text{a}=\frac{5}{3}.$
View full question & answer→MCQ 1561 Mark
Find the value of k, if $x = 1, y = 2$ is a solution of the equation $2x + 3y = k.$
Answer$2x + 3y = k$
$k = 2 (1) + 3 (2)$
$= 2 + 6 = 8$
View full question & answer→MCQ 1571 Mark
If the line represented by the equation $3x + ky = 9$ passes through the points $(2, 3)$, then the value of $k$ is:
AnswerIf the line represented by the equation $3x + ky = 9$ passes through the points $(2, 3)$ then $(2, 3)$ will satisy the equation
$3x + ky = 9$
$3(2) + 3k = 9$
$\Rightarrow 6 + 3k = 9$
$\Rightarrow 3k = 9 - 6$
$\Rightarrow 3k = 3$
$\Rightarrow k = 1$
View full question & answer→MCQ 1581 Mark
The condition that the equation $ax + by + c = 0$ represents a linear equation in two variables is:
- A
$a \neq 0, b = 0$
- B
$b \neq 0, a = 0$
- C
$a = 0, b = 0$
- ✓
$a \neq 0, b \neq 0$
AnswerCorrect option: D. $a \neq 0, b \neq 0$
$a \neq 0, b \neq 0$
View full question & answer→MCQ 1591 Mark
Write the correct answer in the following:
If a linear equation has solutions $(-2, 2), (0, 0)$ and $(2, -2)$, then it is of the form,
- A
$y – x = 0$
- ✓
$x + y = 0$
- C
$-2x + y = 0$
- D
$-x + 2y = 0$
AnswerCorrect option: B. $x + y = 0$
Thinking Process,
$i.$Firstly, consider a linear equation $ax + by + c = 0.$
$ii.$Secondly, substitute all points one by one and get three different equations.
$iii.$Further, simplify the three equations and then substitute the values of $a, b$ and $c$ in the considered equation.
View full question & answer→MCQ 1601 Mark
Each of the points $(-2, 2), (0, 0), (2, 2)$ satisfies the linear equation:
- A
$x - y = 0$
- ✓
$x + y = 0$
- C
$-x + 2y = 0$
- D
$x - 2y = 0$
AnswerCorrect option: B. $x + y = 0$
Since given that each of the three points is a solution of the linear equation, all three points have to satisfy the linear equation.
We need to check for each of the four given equations.
Substituting $x = -2$ and $y = 2$ in option $(b),$
We get:
$LHS$
$= x + y$
$= -2 + 2$
$0 = RHS$
$\therefore\ x = -2$ and $y = 2$
Satisfy the given linear equation.
Substituting $x = 0$ and $y = 0$ in option $(b),$
We get:
$LHS$
$= x + y$
$= 0 + 0$
$0 = RHS$
$\therefore\ x = 0$ and $y = 0$
Satisfy the given linear equation.
Substituting $x = -2$ and $y = 2$ in option $(b),$
We get:
$LHS$
$= x + y$
$= 2 - 2$
$0 = RHS$
$\therefore\ x = 2$ and $y = -2$
Satisfy the given linear equation.
So, clearly all the three points satisfy the equation
$x + y = 0.$
View full question & answer→MCQ 1611 Mark
If $x = 3$ and $y = -2$ satisfies $5x - y = k$, then the value of $k$ is:
AnswerIf $x = 3$ and $y = -2$ satisfies $5x - y = k$
Then
$5x - y = k$
$5 \times 3 - (-2) = k$
$15 + 2 = k$
$k = 17.$
View full question & answer→MCQ 1621 Mark
The graph of the linear equation $2x + 3y = 6$ cuts the $y -$ axis at the point.
- A
$(2, 0)$
- ✓
$(0, 2)$
- C
$(3, 0)$
- D
$(0, 3)$
AnswerCorrect option: B. $(0, 2)$
Given that the graph of the linear equation $2x + 3y = 6$ cuts the $y -$ axis at the point.
Let the point be $“P”.$
Hence, the x - coordinate of point $P$ is $0.$
Now, substitute $x = 0$ in the given equation,
$2 (0) + 3y = 6$
$3y = 6$
$y = 2$
Hence, the cooridnate point is $(0, 2).$
View full question & answer→MCQ 1631 Mark
The graph of $x = - 4$ is a straight line.
- A
Parallel to $x-$axis.
- ✓
Parallel to $y-$axis.
- C
- D
AnswerCorrect option: B. Parallel to $y-$axis.
We know that the general equation of a line parallel to $y-$axis is $x = a.$
So $x = -4$ is a line parallel to $y-$axis.
View full question & answer→MCQ 1641 Mark
Any point on the $x -$ axis is of the form.
- A
$(x, y)$
- B
$(0, y)$
- ✓
$(x, 0)$
- D
$(x, x)$
AnswerCorrect option: C. $(x, 0)$
Any point on the $x -$ axis is of the form $(x, 0).$
On the $x -$ axis, $x$ can take any values, whereas $y$ should be equal to $0.$
View full question & answer→MCQ 1651 Mark
The graph of the linear equation $4x + 2y = 12$, cuts the $x-$axis at the point:
- ✓
$(3, 0)$
- B
$(0, -2)$
- C
$(-2, 0)$
- D
$(0, 3)$
AnswerCorrect option: A. $(3, 0)$
The graph of the linear equation $4 x+2 y=12$, 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 $(3,0)$.
View full question & answer→MCQ 1661 Mark
The point of the form $(a, –a)$ always lies on the line:
- A
$x = a$
- B
$y = –a$
- C
$y = x$
- ✓
$x + y = 0$
AnswerCorrect option: D. $x + y = 0$
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 $x + y = 0.$
View full question & answer→MCQ 1671 Mark
The value of k if $x = 3$ and $y = -2$ is a solution of the equation $2x - 13y = k$ is:
AnswerWe have to find the value of ‘k’ if $x = 3$ and $y = -2$ is a solution of the equation $2x - 13y = k$
$2x - 13y = k$
$2(3) - 13(-2) = k$
$6 + 26 = k$
$k = 32.$
View full question & answer→MCQ 1681 Mark
The graph of the linear equation $y = x$ passes through the point.
- A
$\Big(\frac{3}{2},\frac{-3}{2}\Big)$
- B
$\Big(\frac{-1}{2},\frac{1}{2}\Big)$
- C
$\Big(0,\frac{3}{2}\Big)$
- ✓
$(1,1)$
AnswerCorrect option: D. $(1,1)$
$y = x, \Rightarrow$ Both the coordinates are the same. Hence $(1, 1)$ is correct option.
View full question & answer→MCQ 1691 Mark
If $(-2, 5)$ is a solution of $2x + my = 11$, then the value of $‘m’$ is:
AnswerIf $(-2, 5)$ is a solution of $2x + my = 11$ then it will satisfy the given equation,
$2.(-2) + 5m = 11$
$-4 + 5m = 11$
$5m = 11 + 4$
$5m = 15$
$\text{m}=\frac{15}{5}=3$
$m = 3.$
View full question & answer→MCQ 1701 Mark
Write the correct answer in the following: If $(2, 0)$ is a solution of the linear equation $2x + 3y = k$, then the value of $k$ is:
AnswerSince, $(2, 0)$ is a solution of the given linear equation $2x + 3y = k$, then put $x = 2$ and $y = 0$ in the equation.
$\Rightarrow 2(2) + 3(0) = k$
$\Rightarrow k = 4$
View full question & answer→MCQ 1711 Mark
A linear equation in two variables is of the form $ax + by + c = 0$, where?
AnswerCorrect option: A. $a \neq 0$ and $b \neq 0$
A linear equation in two variables is of the form $a x+b y+c=0$ as $a$ and $b$ are coefficient of $x$ and $y$ so if $a=0$ and $b$ $=0$ or either of one is zero in that case the equation will be one variable or their will be no equation respectively. Therefore when $a \neq 0$ and $b \neq 0$ then only the equation will be in two variable.
View full question & answer→MCQ 1721 Mark
Solutions of the equation $2x + 5y = 0$ is:
- A
$3, 0$
- B
$-3, 2$
- ✓
$0, 0$
- D
$0, 4$
AnswerCorrect option: C. $0, 0$
$0, 0$
View full question & answer→MCQ 1731 Mark
Write the correct answer in the following: $x = 5$ and $y = 2$ is a solution of the linear equation,
- A
$x + 2y = 7$
- B
$5x + 2y = 7$
- ✓
$x + y = 7$
- D
$5x + y = 7$
AnswerCorrect option: C. $x + y = 7$
$x = 5, y = 2$ is a solution of the linear equation $x + y = 7$, as $5 + 2 = 7.$
View full question & answer→MCQ 1741 Mark
If we multiply or divide both sides of a linear equation with the same non - zero number, then the solution of the linear equation:
- ✓
- B
- C
Changes in case of multiplication only
- D
Changes in case of division only
AnswerIf we multiply or divide both sides of a linear equation with the same non - zero number, then the solution of the linear equation remains the same.
View full question & answer→MCQ 1751 Mark
Straight line passing through the points $(-1, 1), (0, 0)$ and $(1, -1)$ has equation.
- A
$y - x$
- ✓
$x + y = 0$
- C
$y = 2x$
- D
$2 + 3y = 7x$
AnswerCorrect option: B. $x + y = 0$
$x + y = 0$
View full question & answer→MCQ 1761 Mark
If $x = 3$ and $y = -2$ satisfies $2x - 3y = k$, then the value of $k$ is:
AnswerIf $x = 3$ and $y = -2$ satisfies $2x - 3y = k.$
It means $x = 3$ and $y = -2$ is a solution of equation $2x - 3y = k$
$2 × 3 - 3(-2) = k$
$6 + 6 = k$
$k = 12$
View full question & answer→MCQ 1771 Mark
Any point of the form $(a, -a)$ always lie on the graph of the equation.
- A
$x = -a$
- B
$y = a$
- C
$y = x$
- ✓
$x + y = 0$
AnswerCorrect option: D. $x + y = 0$
$x + y = 0$
View full question & answer→MCQ 1781 Mark
How many linear equation can be satisfied by $x = 2$ and $y = 3?$
AnswerInfinitely many linear equations can be satisfied by $x = 2$ and $y = 3.$
View full question & answer→MCQ 1791 Mark
The graph of linear equation $x + 2y = 2$, cuts the $y -$ axis at:
- A
$(2, 0)$
- B
$(0, 2)$
- ✓
$(0, 1)$
- D
$(1, 1)$
AnswerCorrect option: C. $(0, 1)$
$x + 2y = 2$
$\text{y}=\frac{(2-\text{x})}{2}$
If $x = 0$, then;
$\text{y}=\frac{(2-0)}{2}=\frac{2}{2}=1$
Hence, $x + 2y = 2$ cuts the $y -$ axis at $(0, 1).$
View full question & answer→MCQ 1801 Mark
The point of the form $(a, a)$ always lies on:
- A
On the line $x + y = 0$
- ✓
On the line $y = x$
- C
$x -$ axis
- D
$y -$ axis
AnswerCorrect option: B. On the line $y = x$
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.
View full question & answer→MCQ 1811 Mark
The linear equation $2x - 5y = 7$ has:
- A
- B
- C
- ✓
Infinitely many solutions
AnswerCorrect option: D. Infinitely many solutions
The linear equation $2x - 5y$ has infinitely many solutions.
Because, the equation $2x - 5y = 7$ is a single equation, that involves two variables.
Hence, for different values of $x$, we will get different values of y and vice - versa.
View full question & answer→MCQ 1821 Mark
Any point on line $x = y$ is of the form:
- A
$(k, -k)$
- B
$(0, k)$
- C
$(k, 0)$
- ✓
$(k, k)$
AnswerCorrect option: D. $(k, k)$
$(k, k)$
View full question & answer→MCQ 1831 Mark
The equation of a line parallel to $x-$axis and $5$ units below the origin is:
- ✓
$y = -5$
- B
$x = 5$
- C
$y = 5$
- D
$x = -5$
AnswerCorrect option: A. $y = -5$
The equation of a line parallel to $x$-axis and $5$ units below the origin is $y=-5$ because when a line parallel to $x$ axis in that case equation of line is $y=a$.
Where $a$ is the co-ordinate of $y$-axes and $5$ units below the origin value $x$-coordinate is $-5$ . So required equation is $y$ $=-5$.
View full question & answer→MCQ 1841 Mark
$x = 2, y = - 1$ is a solution of the linear equation:
- A
$x + 2y = 4$
- B
$2x + y = 5$
- C
$2x + y = 0$
- ✓
$x + 2y = 0$
AnswerCorrect option: D. $x + 2y = 0$
$2 + 2(-1) = 2 - 2 = 0.$
View full question & answer→MCQ 1851 Mark
If $(3, 2)$ is the solution $3x - ky = 5$, then $k$ equals of the equation.
- ✓
$2$
- B
$4$
- C
$3$
- D
$\frac{1}{2}$
View full question & answer→MCQ 1861 Mark
If $(-2, 5)$ is a solution of $2x + my = 11$, then the value of $'m'$ is:
AnswerIf $(-2, 5)$ is a solution of $2x + my = 11$
then it will satisfy the given equation
$2.(-2) + 5 m = 11$
$-4 + 5m = 11$
$5m = 11 + 4$
$5m = 15$
$\text{m}=\frac{15}{5}=3$
$\text{m}=3$
View full question & answer→MCQ 1871 Mark
$y = 0$ is the equation of:
AnswerCorrect option: B. A line parallel to $y -$ axis
A line parallel to $y -$ axis
View full question & answer→MCQ 1881 Mark
The equation $2x + 5y = 7$ has a unique solution, if $x, y$ are:
AnswerThe equation $2 x+5 y=7$ 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.
View full question & answer→MCQ 1891 Mark
How many linear equations are satisfied by $x = 2$ and $y = -3?$
AnswerFrom Point $(2, -3)$ there are infinitely many lines passing in every-direction.
So $(2, -3)$ is satisfied with infinite linear equations.
Hence, correct option is $(d).$
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