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Maths M.C.Q

Linear Equations in Two Variables · Jharkhand Board (JAC) STD 9 (Jharkhand - English Medium). 189 questions.

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M.C.Q

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189 questions · auto-graded multiple-choice test.

MCQ 11 Mark
$x = 2, y = -1$ is a solution of the linear equation:
  • ✓
    $x + 2y = 0$
  • B
    $x + 2y = 4$
  • C
    $2x + y = 0$
  • D
    $2x + y = 5$
Answer
Correct option: A.
$x + 2y = 0$
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 21 Mark
The equation of the $y-$axis is:
  • ✓
    $x = 0$
  • B
    $y = 0$
  • C
    $x + y = 0$
  • D
    $x = y$
Answer
Correct option: A.
$x = 0$
Since the $x-$coordinate of any point on $y-$axis is always $0.$
So, the equation of the $y-$axis is $x = 0.$
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MCQ 31 Mark
The equation $2x + 5y = 7$ has a unique solution, if $x$ and $y$ are:
  • ✓
    Natural numbers.
  • B
    Rational numbers.
  • C
    Positive real numbers.
  • D
    Real numbers.
Answer
Correct option: A.
Natural numbers.
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 41 Mark
The graph of the linear equation $2x + 5y = 10$ meets the $x-$axis at the point.
  • A
    $(0, 5)$
  • ✓
    $(5, 0)$
  • C
    $(0, 2)$
  • D
    $(2, 0)$
Answer
Correct option: B.
$(5, 0)$
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
$2x + 5(0) = 10$
$\Rightarrow 2x = 10$
$\Rightarrow\text{x}=\frac{10}{2}$
$\Rightarrow x = 5$
So, the point of meeting is $(5, 0).$
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MCQ 51 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
    $(0, 3)$
  • ✓
    $(3, 0)$
  • D
    $(2, 0)$
Answer
Correct option: C.
$(3, 0)$
$2x + 3y = 6$ 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 61 Mark
All linear equations in two variables have __________.
  • A
    One solution
  • ✓
    Infinitely many solutions
  • C
    Three solutions
  • D
    Two solution
Answer
Correct option: B.
Infinitely many solutions
Infinitely many solutions
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MCQ 71 Mark
The graph of the equation$ x + y = 4.$
  • ✓
    Intersects both the axis.
  • B
    Parallel to the $x-$axis.
  • C
    Intersects $x-$axis only.
  • D
    Intersects $y-$axis only.
Answer
Correct option: A.
Intersects both the axis.
The graph of the equation $x + y = 4,$
Put $x = 0$ cut $y$ axis at $y = 4,$
Put $y = 0$ cut $x$ axis at $x = 4.$
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MCQ 81 Mark
A linear equation in two variables $x$ and $y$ is of the form $ax = by + c = 0$, where:
  • ✓
    $\text{a}\neq0,\ \text{b}\neq0$
  • B
    $\text{a}\neq0,\ \text{b}=0$
  • C
    $\text{a}=0,\ \text{b}\neq0$
  • D
    $\text{a}=0,\ \text{c}=0$
Answer
Correct option: A.
$\text{a}\neq0,\ \text{b}\neq0$
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 91 Mark
How many lines pass through two points?
  • A
    Two.
  • ✓
    Only one.
  • C
    Many.
  • D
    Three.
Answer
Correct option: B.
Only one.
Only one because if a line is passing through two points then that two points are solution of a single linear equation so only one line passes over two given points.
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MCQ 101 Mark
Write the correct answer in the following:
Any point on the $X-$axis is of the form,
  • A
    $(x, y)$
  • B
    $(0, y)$
  • ✓
    $(x, 0)$
  • D
    $(x, x)$
Answer
Correct option: C.
$(x, 0)$
Every point on the $X-$axis has its $y-$coordinate equal to zero. i.e., $y = 0.$
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MCQ 111 Mark
Any point on the $x-$axis is of the form:
  • A
    $(x, y)$
  • B
    $(0, y)$
  • ✓
    $(x, 0)$
  • D
    $(x, x)$
Answer
Correct option: C.
$(x, 0)$
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 121 Mark
The cost of a notebook is twice the cost of a pen. The equation to represent this statement is:
  • A
    $x = 3y$
  • ✓
    $x - 2y = 0$
  • C
    $2x = 3y$
  • D
    None of these
Answer
Correct option: B.
$x - 2y = 0$
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 131 Mark
If $(a, 4)$ lies on the graph of $3x + y = 10$, then the value of a is:
  • A
    $3$
  • B
    $1$
  • ✓
    $2$
  • D
    $4$
Answer
Correct option: C.
$2$
$3x + y = 10$
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 141 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.
  • ✓
    Making an intercept of $-2$ on the $y-$axis.
Answer
Correct option: D.
Making an intercept of $-2$ on the $y-$axis.
As, the graph of $y+2=0$ or $y=-2$ is a line parallel to $x$-axis i.e. $y=0$.
$\Rightarrow$ 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 151 Mark
The linear equation $3x - 5y = 15$ has:
  • A
    A unique solution.
  • B
    Two solutions.
  • ✓
    Infinitely many solutions.
  • D
    No solution.
Answer
Correct option: C.
Infinitely many solutions.
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.
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MCQ 161 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
  • A
    $6x + y = 5$
  • ✓
    $x = 6y + 5$
  • C
    $x + 6y = 5$
  • D
    $x - 6 = 5$
Answer
Correct option: B.
$x = 6y + 5$
$x = 6y + 5$
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MCQ 171 Mark
The value of $y$ at $x = -1$ in the equation $5y = 2$ is:
  • A
    $\frac{5}{2}$
  • ✓
    $\frac{2}{5}$
  • C
    $10$
  • D
    $0$
Answer
Correct option: B.
$\frac{2}{5}$
$\frac{2}{5}$
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MCQ 181 Mark
$x = 0$ is the equation of:
  • A
    A line parallel to $x-$axis.
  • B
    $x-$axis.
  • C
    A line parallel to $y-$axis.
  • ✓
    $y-$axis.
Answer
Correct option: D.
$y-$axis.
$x = 0$ is a line of $y-$axis because $x-$coordinates of all points lie on $y-$axis are zero.
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MCQ 191 Mark
Equation of a line which is $5$ units distance above the $x -$ axis is:
  • A
    $x = 5$
  • B
    $x + 5 = y$
  • ✓
    $y - 5$
  • D
    $x - y = 0$
Answer
Correct option: C.
$y - 5$
$y - 5$
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MCQ 201 Mark
The equation of a line parallel to $y-$axis and $4$ units to the right of origin is:
  • ✓
    $x = 4$
  • B
    $x = -4$
  • C
    $y = -4$
  • D
    $y = 4$
Answer
Correct option: A.
$x = 4$
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 211 Mark
The point which lies on $y-$axis at a distance of $6$ units in the positive direction of $y-$axis is:
  • ✓
    $(0, 6)$
  • B
    $(-6, 0)$
  • C
    $(6, 0)$
  • D
    $(0, -6)$
Answer
Correct option: A.
$(0, 6)$
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 221 Mark
If the line represented by the equation $3x + ky = 9$ passes through the points $(2, 3)$, then the value of $'k'$ is:
  • A
    $2$
  • ✓
    $1$
  • C
    $3$
  • D
    $4$
Answer
Correct option: B.
$1$
If the line represented by the equation $3x + ky = 9$ passes through the points $(2, 3)$ then $(2, 3)$ will satisy the equation
$3x + ky = 93(2) + 3k = 9$
$\Rightarrow 6 + 3k = 9$
$\Rightarrow 3k - 9 - 6$
$\Rightarrow 3k = 3$
$\Rightarrow k = 1$
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MCQ 231 Mark
For what value of $‘k’, x = 2$ and $y = -1$ is a solution of $x + 3y - k = 0?$
  • A
    $2$
  • B
    $-2$
  • ✓
    $-1$
  • D
    $1$
Answer
Correct option: C.
$-1$
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 241 Mark
The graph of the line $y = -3$ does not pass through the point:
  • A
    $(2, -3)$
  • B
    $(3, -3)$
  • C
    $(0, -3)$
  • ✓
    $(-3, 2)$
Answer
Correct option: D.
$(-3, 2)$
The line $y = -3$ does not pass through the point $(-3, 2)$ since $\text{y}\neq2.$
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MCQ 251 Mark
The point of the form $(a, a)$, where a lies on:
  • ✓
    The line $y = x.$
  • B
    The line $x + y = 0.$
  • C
    The $x-$axis.
  • D
    The $y-$axis.
Answer
Correct option: A.
The line $y = x.$
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 261 Mark
Express $y$ in terms of $x$ in the equation$ 5x - 2y = 7.$
  • A
    $\text{y}=\frac{5\text{x}+7}{2}$
  • B
    $\text{y}=\frac{7\text{x}+5}{2}$
  • ✓
    $\text{y}=\frac{5\text{x}-7}{2}$
  • D
    $\text{y}=\frac{7-5\text{x}}{2}$
Answer
Correct option: C.
$\text{y}=\frac{5\text{x}-7}{2}$
$5x - 2y = 7$
$-2y = 7 - 5x$
$2y = 5x - $7
$\text{y}=\frac{5\text{x}-7}{2}.$
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MCQ 271 Mark
Write the correct answer in the following: The graph of $y = 6$ is a Line,
  • ✓
    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
Correct option: A.
Parallel to $X-$axis at a distance $6$ units from the origin.
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 281 Mark
The graph of the linear equation $x - y = 0$ passes through the point:
  • A
    $(-1,1)$
  • ✓
    $\Big(\frac{1}{1},\frac{1}{2}\Big)$
  • C
    $\Big(\frac{1}{1},-\frac{1}{2}\Big)$
  • D
    $(0,1)$
Answer
Correct option: B.
$\Big(\frac{1}{1},\frac{1}{2}\Big)$
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.
 
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MCQ 291 Mark
If $(2, 0)$ is a solution of the linear equation $2x + 3y = k$, then the value of $k$ is:
  • A
    $2$
  • ✓
    $4$
  • C
    $5$
  • D
    $6$
Answer
Correct option: B.
$4$
Substitute $x = 2$ and $y = 0$ in the given equation, we get2 $(2) + 3 (0) = k$
$k = 4 + 0$
$k = 4$.
Hence, the value of $k$ is $4$.
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MCQ 301 Mark
The equation $2x + 5y = 7$ has a unique solution, if $x, y$ are:
  • A
    Positive real numbers.
  • B
    Rational numbers.
  • ✓
    Natural numbers.
  • D
    Real numbers.
Answer
Correct option: C.
Natural numbers.
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.
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MCQ 311 Mark
Which of the following is a linear equation in two variables?
  • A
    $x + 5 = 8$
  • ✓
    $2x - 5y = 0$
  • C
    $x ^2 = 5x + 3$
  • D
    $5x = y ^2 + 3$
Answer
Correct option: B.
$2x - 5y = 0$
In linear equation power of variable $x$ and $y$ should be $1$ and here, the given linear equation has two variable $x$ and $y.$
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MCQ 321 Mark
Write the correct answer in the following: The equation of $X-$axis is of the form,
  • A
    $x = 0$
  • ✓
    $y = 0$
  • C
    $x + y = 0$
  • D
    $x = y$
Answer
Correct option: B.
$y = 0$
$y = 0$ is the equation of $x-$axis.
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MCQ 331 Mark
If a linear equation has solutions $(1, 2), (-1, -16)$ and $(0, -7)$, then it is of the form:
  • ✓
    $y = 9x - 7$
  • B
    $9x - y + 7 = 0$
  • C
    $x - 9y = 7$
  • D
    $x = 9y - 7$
Answer
Correct option: A.
$y = 9x - 7$
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.
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MCQ 341 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
  • ✓
    Infinitely many
Answer
Correct option: D.
Infinitely many
Infinitely many
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MCQ 351 Mark
The equation $x = 7$ in two variables can be written as:
  • A
    $1.x + 1.y = 7$
  • ✓
    $1.x + 0.y = 7$
  • C
    $0.x + 1.y = 7$
  • D
    $0.x + 0.y = 7$
Answer
Correct option: B.
$1.x + 0.y = 7$
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 $x=7$
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MCQ 361 Mark
$x - 4$ is the equation of:
  • A
    $x-$axis.
  • B
    A line parallel to $x-$axis.
  • C
    $y-$axis.
  • ✓
    A line parallel to $y-$axis.
Answer
Correct option: D.
A line parallel to $y-$axis.
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 371 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
    $(3, 0)$
  • ✓
    $(0, 2)$
Answer
Correct option: D.
$(0, 2)$
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 $
$\Rightarrow 3y = 6 $
$\Rightarrow y = 6 ÷ 3 = 2$
 
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MCQ 381 Mark
If a linear equation has solutions $(-2, 2), (0, 0)$ and $(2, -2)$, then it is of the form:
  • A
    $-x + 2y = 0$
  • ✓
    $x + y = 0$
  • C
    $x - y = 0$
  • D
    $-2x + y = 0$
Answer
Correct option: B.
$x + y = 0$
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 391 Mark
Express $‘x’$ in terms of $‘y’$ in the equation $2x - 3y - 5 = 0.$
  • A
    $\text{x}=\frac{5-3\text{y}}{2}$
  • B
    $\text{x}=\frac{5+3\text{y}}{2}$
  • ✓
    $\text{x}=\frac{3\text{y}+5}{2}$
  • D
    $\text{x}=\frac{3\text{y}-5}{2}$
Answer
Correct option: C.
$\text{x}=\frac{3\text{y}+5}{2}$
$2x - 3y -5 = 0$
$2x = 3y + 5$
$\text{x}=\frac{3\text{y}+5}{2}.$
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MCQ 401 Mark
If the point $(3, 4)$ lies on the graph of $3y = ax + 6$, then the value of ‘a’ is:
  • ✓
    $2$
  • B
    $0$
  • C
    $3$
  • D
    $1$
Answer
Correct option: A.
$2$
The point $(3, 4)$ lies on the graph of $3y = ax + 6$
So it will satisfy the equation
$3y = ax + 6$
$3(y) = ax + 6$
$12 = 3a + 6$
$12 - 6 = 3a$
$3a = 6$
$\text{a}=\frac{6}{3}$
$a = 2$
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MCQ 411 Mark
The distance between the graph of the equations $x = -3$ and $x = 2$ is:
  • ✓
    $5$
  • B
    $2$
  • C
    $1$
  • D
    $3$
Answer
Correct option: A.
$5$
Distance between the graph of the equations $x = -3$ and $x = 2$ is $= 2 - (-3) = 5$ units.
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MCQ 421 Mark
Write the correct answer in the following: The graph of the linear equation $2x + 3y = 6 $ is a line which meets the $X-$axis at the point.
  • A
    $(0, 2)$
  • B
    $(2, 0)$
  • ✓
    $(3, 0)$
  • D
    $(0, 3)$
Answer
Correct option: C.
$(3, 0)$
Since, the graph of linear equation $2x + 3y = 6$ meets the $X-$axis.
So, we put $y = 0$ in $2\text{x} + 3\text{y} = 6 \Rightarrow 2\text{x} + 3(0) = 6$
$\Rightarrow2\text{x}+0=6$
$\Rightarrow\text{x}=\frac{6}{2}\Rightarrow\text{x}=3$
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MCQ 431 Mark
The point of the form $(a, a)$, where a lies on:
  • A
    The $x-$axis
  • ✓
    The line $y = x$
  • C
    The $y-$axis
  • D
    The line $x + y = 0$
Answer
Correct option: B.
The line $y = x$
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 441 Mark
Any point on line $x = y$ is of the form:
  • A
    $(k, -k)$
  • B
    $(0, k)$
  • C
    $(k, 0)$
  • ✓
    $(k, k)$
Answer
Correct option: D.
$(k, k)$
$(k, k)$
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MCQ 451 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 $y = x$
  • ✓
    The line $x + y = 0$
Answer
Correct option: D.
The line $x + y = 0$
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 461 Mark
The graph of the equation $2x + 3y = 6$ cuts the $x -$ axis at the point.
  • A
    $(0, 3)$
  • ✓
    $(3, 0)$
  • C
    $(2, 0)$
  • D
    $(0, 2)$
Answer
Correct option: B.
$(3, 0)$
$(3, 0)$
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MCQ 471 Mark
If $(4, 19)$ is a solution of the equation $y = ax + 3$, then $a =$
  • A
    $3$
  • ✓
    $4$
  • C
    $5$
  • D
    $6$
Answer
Correct option: B.
$4$
$y = ax + 3$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 481 Mark
Any point on the line $y = 3x$ is of the form.
  • ✓
    $(\text{a}, 3\text{a})$
  • B
    $(3\text{a}, \text{a})$
  • C
    $(\text{a}, \frac{\text{a}}{3})$
  • D
    $(\frac{\text{a}}{3}, \text{-a})$
Answer
Correct option: A.
$(\text{a}, 3\text{a})$
$(\text{a}, 3\text{a})$
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MCQ 491 Mark
The line represented by the equation $x + y = 16$ passes through $(2, 14)$. How many more lines pass through the point $(2, 14).$
  • A
    $10$
  • B
    $2$
  • C
    $100$
  • ✓
    Many
Answer
Correct option: D.
Many
There are many lines pass through the point $(2, 14)$
$x - y = -12$
$2x + y = 18$
and many more
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MCQ 501 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.
  • ✓
    Parallel to the $y-$axis at a distance of $4$ units from the origin.
Answer
Correct option: D.
Parallel to the $y-$axis at a distance of $4$ units from the origin.
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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MCQ 511 Mark
Find the value of k, if $x = 1, y = 2$ is a solution of the equation $2x + 3y = k.$
  • A
    $5$
  • B
    $6$
  • C
    $7$
  • ✓
    $8$
Answer
Correct option: D.
$8$
$8$
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MCQ 521 Mark
The equation $y = 2x - 7$ has:
  • ✓
    Many solutions.
  • B
    No solution.
  • C
    Two solutions.
  • D
    One solution.
Answer
Correct option: A.
Many solutions.
$y = 2x - 7$Has many solutions because for different value of $x$ we have different value of $y$ for example.
At $x = 1$
$y = 2 (1) - 7$
$y = 2 - 7$
$y = -5$
At $x = 2$
$y = 2(2) - 7$
$y = 4 - 7$
$y = -3$
So we can say for many value of $x$ there is many value of $y.$
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MCQ 531 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.
  • ✓
    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
Correct option: C.
Making an intercept $-3$ on the $x-$axis.
As, the graph of $x+3=0$ or $x=-3$ is a line parallel to $y$-axis i.e. $x=0$.
$\Rightarrow$ 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 541 Mark
The equation of a line parallel to $x-$axis and $3$ units above the origin is:
  • A
    $x = 3$
  • ✓
    $y = 3$
  • C
    $x = -3$
  • D
    $y = -3$
Answer
Correct option: B.
$y = 3$
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 551 Mark
The equation of a line parallel to $y-$axis and $7$ units to the left of origin is:
  • ✓
    $x = -7$
  • B
    $y = 7$
  • C
    $y = -7$
  • D
    $x = 7$
Answer
Correct option: A.
$x = -7$
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 $x=-7$.
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MCQ 561 Mark
Any solution of the linear equation $2x + 0y + 9 = 0$ in two variables is of the form:
  • A
    $\Big(0,-\frac{9}{2}\Big)$
  • B
    $(-9,0)$
  • C
    $\Big(\text{n},-\frac{9}{2}\Big)$
  • ✓
    $\Big(-\frac{9}{2},\text{m}\Big)$
Answer
Correct option: D.
$\Big(-\frac{9}{2},\text{m}\Big)$
$2x + 9 = 0 \Rightarrow\text{x}=\frac{-9}{2}$ And $y = m$, where m is any real number,
Hence, $\Big(-\frac{9}{2},\text{m}\Big)$ is the solution of the given equation.
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MCQ 571 Mark
The linear equation $2x - 5y = 7$ has:
  • A
    Two solutions.
  • ✓
    Infinitely many solutions.
  • C
    No solution.
  • D
    A unique solution.
Answer
Correct option: B.
Infinitely many solutions.
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.
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MCQ 581 Mark
Write the correct answer in the following: The positive solutions of the equation $ax + by + c = 0$ always lie in the,
  • ✓
    I$^{st}$ quadrant.
  • B
    II$^{nd}$ quadrant.
  • C
    III$^{rd}$ quadrant.
  • D
    IV$^{th}$ quadrant.
Answer
Correct option: A.
I$^{st}$ quadrant.
We know that, if a line passes through the Ist quadrant, then all solution lying on the line in first quadrant must be positive because the coordinate of all points in the Ist quadrant are positive.
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MCQ 591 Mark
The point on the graph of the linear equation $2x + 5y = 19$, whose ordinate is $1^{\frac{1}{2}}$ times its abscissa is:
  • A
    $(-2, -3)$
  • ✓
    $(2, 3)$
  • C
    $(4, 6)$
  • D
    None of these.
Answer
Correct option: B.
$(2, 3)$
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 $(2, 3)$
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MCQ 601 Mark
How many lines pass through one point?
  • A
    Two.
  • B
    Three.
  • ✓
    Many.
  • D
    One.
Answer
Correct option: C.
Many.
Because one point can be solution of many equations. So many equations can be pass from one point.
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MCQ 611 Mark
For the equation $5x + 8y = 50$, if $y = 10$, then the value of $x$ is:
  • ✓
    $-6$
  • B
    $-12$
  • C
    $6$
  • D
    $12$
Answer
Correct option: A.
$-6$
For the equation $5x + 8y = 50$, if $y = 10$
Put $y = 10$ in given equation
$5x + 8 × 10 = 50$
$5x + 80 = 50$
$5x = 50 - 80$
$5x = -30$
$\text{x} = -\frac{30}{5}$
$x = -6$
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MCQ 621 Mark
The graph of the linear equation $y = 3x$ passes through the point.
  • A
    $(0,-\frac{2}{3})$
  • ✓
    $(\frac{2}{3},2)$
  • C
    $(,-\frac{2}{3},0)$
  • D
    $(0,\frac{2}{3})$
Answer
Correct option: B.
$(\frac{2}{3},2)$
$\text{y}=3\text{x}$
$\frac{\text{y}}{3}=\text{x}$
For $\text{x}=\frac{2}{3},$ the value of $\text{y}=3\times\frac{2}{3}=2$
So $(\frac{2}{3},2).$
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MCQ 631 Mark
Any point on the $y -$ axis is of the form.
  • A
    $(y, y)$
  • ✓
    $(0, y)$
  • C
    $(x, y)$
  • D
    $(x, 0)$
Answer
Correct option: B.
$(0, y)$
Any point on the $y -$ axis is of the form $(0, y).$
On the $y$ - axis, $y$ can take any values and $x$ should be equal to $0.$
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MCQ 641 Mark
Which of the following is the equation of a line parallel to $y -$ axis?
  • A
    $y = 0$
  • B
    $x + y = z$
  • C
    $y = x$
  • ✓
    $x = a$
Answer
Correct option: D.
$x = a$
$x = a$
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MCQ 651 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.
  • A
    $3$ units.
  • B
    $4$ units.
  • ✓
    $5$ units.
  • D
    None of these.
Answer
Correct option: C.
$5$ units.
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.
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MCQ 661 Mark
If $(2k - 1, k)$ is a solution of the equation $10x - 9y = 12$, then $k =$
  • A
    $1$
  • ✓
    $2$
  • C
    $3$
  • D
    $4$
Answer
Correct option: B.
$2$
If $(2k - 1, k)$ is solution of equation $10x - 9y = 12$, then it must satisfy this equation.
Thus, we have
$10(2k - 1) - 9k = 12$
$20k - 10 - 9k = 12$
$11k = 22$
$k = 2$ 
Hence, correct option is $(b).$
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MCQ 671 Mark
$x = 5$ and $y = -2$ is the solution of the linear equation.
  • A
    $x + 3y = 1$
  • B
    $2x + y = 9$
  • C
    $3x + y = 0$
  • ✓
    $2x - y = 12$
Answer
Correct option: D.
$2x - y = 12$
$x = 5$ 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 $2x - y = 12.$
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MCQ 681 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.
  • ✓
    $5$ sq. units.
Answer
Correct option: D.
$5$ sq. units.
To find the area of the triangle formed by the line $2 x+5 y=10$ 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 $\times$ heigh,
$=\frac{1}{2}\times2\times5$
$= 5 sq$. units.
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MCQ 691 Mark
The graph of a linear equation $\text{y}=\frac{9}{5}\text{x}+32$ cuts the $y-$axis at the point:
  • ✓
    $(0, 32)$
  • B
    $(-32, 0)$
  • C
    $(0, -32)$
  • D
    $(32, 0)$
Answer
Correct option: A.
$(0, 32)$
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 $(32, 0)$
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MCQ 701 Mark
Write the correct answer in the following: The graph of the linear equation $y = x$ passes through the point.
  • A
    $\Big(\frac{3}{2},\frac{-3}{2}\Big)$
  • B
    $\Big(0,\frac{3}{2}\Big)$
  • ✓
    $(1,1)$
  • D
    $\Big(\frac{-1}{2},\frac{1}{2}\Big)$
Answer
Correct option: C.
$(1,1)$
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).$
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MCQ 711 Mark
The graph of the linear equation $2x + 3y = 6$ meets the $y-$axis at the point.
  • A
    $(0, 3)$
  • B
    $(2, 0)$
  • C
    $(3, 0)$
  • ✓
    $(0, 2)$
Answer
Correct option: D.
$(0, 2)$
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
$2(0) + 3y = 6$
$\Rightarrow 3y = 6$
$\Rightarrow\text{y}=\frac{6}{3}$
$\Rightarrow y = 2$
So, the point of meeting is $(0, 2).$
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MCQ 721 Mark
If $(4, 19)$ is a solution of the equation $y = ax + 3$, then $a =$
  • A
    $3$
  • B
    $6$
  • ✓
    $4$
  • D
    $5$
Answer
Correct option: C.
$4$
Given, $(4, 19)$ is a solution of the equation $y = ax + 3= 19 = 4a + 3$
$= a = 4.$
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MCQ 731 Mark
The graph of the linear equation $y = 3x$ passes through the point.
  • A
    $\Big(0,-\frac{2}{3}\Big)$
  • B
    $\Big(-\frac{2}{3},0\Big)$
  • C
    $\Big(0,\frac{2}{3}\Big)$
  • ✓
    $\Big(\frac{2}{3},2\Big)$
Answer
Correct option: D.
$\Big(\frac{2}{3},2\Big)$
$\text{y}=3\text{x}$
$\frac{\text{y}}{3}=\text{x}$
For, $y = 2$, the value of x will be $\frac{2}{3}$
So, $\Big(\frac{2}{3},2\Big)$
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MCQ 741 Mark
The graph of the line $x - y = 0$ passes through the point:
  • A
    $\Big(\frac{-1}{2},\frac{1}{2}\Big)$
  • B
    $\Big(\frac{3}{2},\frac{-3}{2}\Big)$
  • C
    $(0,-1)$
  • ✓
    $(1, 1)$
Answer
Correct option: D.
$(1, 1)$
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.
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MCQ 751 Mark
The graph of $y = 5$ is a line.
  • A
    Parallel to the $x-$axis at a distance of $6$ units from the origin.
  • B
    Making an intercept $5$ on the $x-$axis.
  • C
    Parallel to the $y-$axis at a distance of $5$ units from the origin.
  • ✓
    Making an intercept $5$ on the $y-$axis.
Answer
Correct option: D.
Making an intercept $5$ on the $y-$axis.
As, the graph of $y=5$ is a line parallel to $x$-axis i.e. $y=0$.
$\Rightarrow$ 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.
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MCQ 761 Mark
The graph of $x = 3$ is a line:
  • A
    Parallel to $x -$ axis at a distance of $3$ units from the origin.
  • ✓
    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
Correct option: B.
Parallel to $y -$ axis at a distance of $3$ units from the origin.
Parallel to $y -$ axis at a distance of $3$ units from the origin.
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MCQ 771 Mark
The point which lies on $x-$axis at a distance of $4$ units in the negative direction of $x-$axis is:
  • A
    $(0, -4)$
  • B
    $(0, 4)$
  • ✓
    $(-4, 0)$
  • D
    $(4, 0)$
Answer
Correct option: C.
$(-4, 0)$
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 $(-4,0)$.
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MCQ 781 Mark
The line represented by the equation $x + y = 16$ passes through $(2, 14).$ How many more lines pass through the point $(2, 14).$
  • A
    $2$
  • B
    $100$
  • ✓
    Many
  • D
    $10$
Answer
Correct option: C.
Many
There are many lines pass through the point $(2, 14).$
For example
$x - y = -12$
$2x + y = 18$
And many more.
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MCQ 791 Mark
Which of the following is not a solution of $2x - 3y = 12?$
  • A
    $(6, 0)$
  • B
    $(3, -2)$
  • C
    $(0, -4)$
  • ✓
    $(2, 3)$
Answer
Correct option: D.
$(2, 3)$
We have to check $(2,3)$ is a solution of $2 x-3 y=12$ if $(2,3)$ satisfy the equation then $(2,3)$ solution of $2 x-3 y=12$.
$LHS = 2x - 3y$
$2 × 2 - 3 × 3$
$4 - 9 = -5$
$RHS = -5$
$LHS ≠ RHS$
So $(2,3)$ is not a solution of $2 x-3 y=12$.
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MCQ 801 Mark
The linear equation $3x - y = x - 1$ has:
  • A
    No solution
  • B
    Unique solution
  • C
    Two solutions
  • ✓
    Infinitely many solutions
Answer
Correct option: D.
Infinitely many solutions
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.
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MCQ 811 Mark
The equation of a line parallel to $y-$axis and $4$ units to the right of origin is:
  • A
    $x = -4$
  • B
    $y = -4$
  • C
    $y = 4$
  • ✓
    $x = 4$
Answer
Correct option: D.
$x = 4$
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 $x=4$.
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MCQ 821 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,
  • ✓
    $\Big(-\frac{9}{2},\text{m}\Big)$
  • B
    $\Big(\text{n},-\frac{9}{2}\Big)$
  • C
    $\Big(0,-\frac{9}{2}\Big)$
  • D
    $(-9,0)$
Answer
Correct option: A.
$\Big(-\frac{9}{2},\text{m}\Big)$
The given linear equation is
$2x + 0y + 9 = 0$
$\Rightarrow 2x + 9 = 0$
$\Rightarrow 2x = -9$
$\Rightarrow x = -\frac{9}{2}$ and $y$ can be any real number.
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MCQ 831 Mark
Which of the following is a linear equation in two variables?
  • ✓
    $2x - 5y = 0$
  • B
    $x + y = 8$
  • C
    $x ^2  = 5x + 3$
  • D
    $5x = y^2 + 3$
Answer
Correct option: A.
$2x - 5y = 0$
In linear equation power of variable $x$ and $y$ should be $1$ and here, the given linear equation has two variable $x$ and $y.$
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MCQ 841 Mark
If we divide both sides of a linear equation with a non-zero number, then the solution of the linear equation.
  • A
    Changes.
  • ✓
    Remains the same.
  • C
    None of these.
  • D
    Gets divided by the number.
Answer
Correct option: B.
Remains the same.
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.
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MCQ 851 Mark
The linear equation $3x - 11y = 10$ has:
  • A
    Unique solution
  • B
    Two solutions
  • ✓
    Infinitely many solutions
  • D
    No solutions
Answer
Correct option: C.
Infinitely many solutions
$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.
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MCQ 861 Mark
$x = 3$ and $y = -2$ is a solution of the equation $4px - 3y = 12$, then the value of $p$ is:
  • A
    $0$
  • ✓
    $\frac{1}{2}$
  • C
    $2$
  • D
    $3$
Answer
Correct option: B.
$\frac{1}{2}$
$\frac{1}{2}$
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MCQ 871 Mark
Express $'y'$ in terms of $'x'$ in the equation $5y - 3x - 10 = 0.$
  • A
    $\text{y}=\frac{3-10\text{x}}{5}$
  • B
    $\text{y}=\frac{3+10\text{x}}{5}$
  • C
    $\text{y}=\frac{3\text{x}-10\text{}}{5}$
  • ✓
    $\text{y}=\frac{3\text{x}+10}{5}$
Answer
Correct option: D.
$\text{y}=\frac{3\text{x}+10}{5}$
$(D) \text{y}=\frac{3\text{x}+10}{5}$
$5y - 3, x - 10 = 0$
$5y - 3, x = 10$
$5y = 10 + 3x$
$\text{y}=\frac{3\text{x}+10}{5}$
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MCQ 881 Mark
The graph of the linear equation $3x - 5y = 15,$ cuts the $y-$axis at the point:
  • A
    $(2, 0)$
  • B
    $(-2, 0)$
  • C
    $(0, 3)$
  • ✓
    $(0, -3)$
Answer
Correct option: D.
$(0, -3)$
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 $(0, -3).$
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MCQ 891 Mark
The graph of $x = 3 $is a line:
  • A
    Parallel to the $x -$ axis at a distance of $3$ units from the origin.
  • ✓
    Parallel to the $y -$ axis at a distance of $3$ units from the origin.
  • C
    Makes an intercept $3$ on the $x -$ axis.
  • D
    Makes an intercept $3$ on the $y -$ axis.
Answer
Correct option: B.
Parallel to the $y -$ axis at a distance of $3$ units from the origin.
Parallel to the $y -$ axis at a distance of $3$ units from the origin.
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MCQ 901 Mark
If we multiply both sides of a linear equation with a non-zero number, then the solution of the linear equation:
  • A
    Gets multiplied by the number.
  • ✓
    Remains the same.
  • C
    Changes.
  • D
    None of these.
Answer
Correct option: B.
Remains the same.
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
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MCQ 911 Mark
The linear equation $3x - 5y = 15$ has:
  • A
    Two solutions.
  • B
    A unique solution.
  • C
    No solution.
  • ✓
    Infinitely many solutions.
Answer
Correct option: D.
Infinitely many solutions.
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 921 Mark
$x = 2, y = 5$ is a solution of the linear equation.
  • A
    $x + 2y = 7$
  • ✓
    $x + y = 7$
  • C
    $5x + y = 7$
  • D
    $5x + 2y = 7$
Answer
Correct option: B.
$x + y = 7$
$x = 2$ and $y = 5$ satisfy the given equation.
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MCQ 931 Mark
Write the correct answer in the following: Any point on the line $y = x$ is of the form,
  • ✓
    $(a, a)$
  • B
    $(0, a)$
  • C
    $(a, 0)$
  • D
    $(a, -a)$
Answer
Correct option: A.
$(a, a)$
Every point on the line $y = x$ has same value of $x-$and $y-$coordinates i.e., $x = a$ and $y = a.$
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MCQ 941 Mark
The equation $x - 2 = 0$ on number line is represented by:
  • A
    Infinitely many lines.
  • B
    A line.
  • C
    Two lines.
  • ✓
    A point.
Answer
Correct option: D.
A point.
$x - 2 = 0$
$x = 2$ is a point on the number line.
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MCQ 951 Mark
If the point $(3, 4)$ lies on the graph of $3y = ax + 6$, then the value of $'a'$ is:
  • A
    $0$
  • ✓
    $2$
  • C
    $1$
  • D
    $3$
Answer
Correct option: B.
$2$
The point $(3, 4)$ lies on the graph of $3y = ax + 6$So, it will satisfy the equation
$3y = ax + 6$
$3(y) = ax + 6$
$12 = 3a + b$
$12 - 6 = 3a$
$3a = 6$
$\text{a}=\frac{6}{3}$
$\text{a}=2$
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MCQ 961 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.
  • ✓
    Making an intercept $4$ on the $x-$axis.
  • D
    Parallel to the $x-$axis at a distance of $4$ units from the origin.
Answer
Correct option: C.
Making an intercept $4$ on the $x-$axis.
As, the graph of $x=4$ is a line parallel to $y$-axis i.e. $x=0$.
$\Rightarrow$ 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 971 Mark
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:
  • A
    Changes.
  • ✓
    Remains the same.
  • C
    Only changes in case of multiplication.
  • D
    Only changes in case of division.
Answer
Correct option: B.
Remains the same.
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.
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MCQ 981 Mark
The point of the form $(-a, a)$, where a lies on
  • ✓
    The line$ x + y = 02$
  • B
    The $y-$axis
  • C
    The $x-$axis
  • D
    The line $y = x$
Answer
Correct option: A.
The line$ x + y = 02$
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 $x+y=0$
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MCQ 991 Mark
If $x$ and $y$ are both positive solutions of equation $ax + by + c = 0$, always lie in the:
  • ✓
    First quadrant
  • B
    Second quadrant
  • C
    Third quadrant
  • D
    Fourth quadrant
Answer
Correct option: A.
First quadrant
First quadrant
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MCQ 1001 Mark
The linear equation $3x - 11y = 10$ has:
  • A
    Unique solution
  • B
    Two solution
  • ✓
    Infinitely many solutions
  • D
    No solution
Answer
Correct option: C.
Infinitely many solutions
Infinitely many solutions
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MCQ 1011 Mark
The distance between the graphs of the equations $y = -1$ and $y = 3$ is:
  • A
    $3$
  • B
    $1$
  • ✓
    $4$
  • D
    $2$
Answer
Correct option: C.
$4$
Distance between the graphs of the equations $y = -1$ and $y = 3$ is $= 3 - (-1) = 4$ units.
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MCQ 1021 Mark
The area of the triangle formed by the line $3x + 4y = 12$ and the co-ordinate axis is:
  • ✓
    $6$ sq. units.
  • B
    $12$ sq. units.
  • C
    $4$ sq. units.
  • D
    $3$ sq. units.
Answer
Correct option: A.
$6$ sq. units.

To find the area of the triangle $A O B$ formed by the line $3 x+4 y=12$ and co-ordinate axis we put $x=0$ in given equation to find the point on $y$ axies.
So, at $x=0$
$3(0) + 4y = 12$
$4y = 12$
We get $y = 3$
$At y = 0$
$3x + 4(0) = 12$
$3x = 12$
We get $x=4$
So the line cut $y$ axis at 3 and $x$ axis at $4$
So the hight of triangle $A O B$ is $O B=3$ unit and base $O A=4$ unit
Area ot triangle $A O B=12$ (base $\times$ height)
$= 12 \times 4 \times 3$
$= 6$ unit square.
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MCQ 1031 Mark
If $(2, 0)$ is a solution of the linear equation $2x + 3y = k$ then the value of $k$ is:
  • A
    $6$
  • B
    $5$
  • C
    $2$
  • ✓
    $4$
Answer
Correct option: D.
$4$
Since, $(2, 0)$ is a solution of the linear equation $2x + 3y = k$, substituting $x = 2$ and $y = 0$ in the given equation,We have:
$2(2) + 3(0) = k$
$\Rightarrow 4 + 0 = k$
$\Rightarrow k = 4$
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MCQ 1041 Mark
The distance between the graph of the equations $x = -3$ and $x = 2$ is:
  • A
    $1$
  • B
    $2$
  • C
    $3$
  • ✓
    $5$
Answer
Correct option: D.
$5$
The distance between the graph of the equations $x = -3$ and $x = 2= 2 - (-3)$
$= 2 + 3$
$= 5$
Hence, correct option is $(d).$
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MCQ 1051 Mark
Cost of book $(x)$ exceeds twice the cost of pen $(y)$ by Rs $10$. This statement can be expressed as linear equation.
  • ✓
    $x - 2y - 10 = 0$
  • B
    $2x - y - 10 = 0$
  • C
    $2x + y - 10 = 0$
  • D
    $x - 2y + 10 = 0$
Answer
Correct option: A.
$x - 2y - 10 = 0$
$x - 2y - 10 = 0$
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MCQ 1061 Mark
The graph of the line $y = 3$ passes through the point:
  • A
    $(3, 0)$
  • B
    $(3, 2)$
  • ✓
    $(2, 3)$
  • D
    None of these.
Answer
Correct option: C.
$(2, 3)$
Since, the $y$ coordinate is $3$, the graph of the line $y = 3$ passes through the point $(2, 3).$
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MCQ 1071 Mark
Point $(3, 4)$ lies on the graph of the equation $3y = kx + 7$. The value of $k$ is:
  • A
    $\frac{4}{3}$
  • ✓
    $\frac{5}{3}$
  • C
    $3$
  • D
    $\frac{6}{3}$
Answer
Correct option: B.
$\frac{5}{3}$
$\frac{5}{3}$
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MCQ 1081 Mark
The graph of the linear equation $x + y = 0$ passes through the point.
  • ✓
    $(1, -1)$
  • B
    $(1, 1)$
  • C
    $(1, 0)$
  • D
    $(0, 1)$
Answer
Correct option: A.
$(1, -1)$
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
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MCQ 1091 Mark
The graph of every linear equation in two variables is a:
  • A
    Circle.
  • ✓
    Straight line.
  • C
    Square.
  • D
    Curve.
Answer
Correct option: B.
Straight line.
Because for one value of one variable their is only one and unique value of other variables.
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MCQ 1101 Mark
The equation of the $y-$axis is:
  • A
    $x = 0$
  • ✓
    $y = 0$
  • C
    $x = y$
  • D
    $x + y = 0$
Answer
Correct option: B.
$y = 0$
The equation of the $y-$axis is $x = 0.$
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MCQ 1111 Mark
How many linear equation in x and $y$ can be satisfied by $x = 1$ and $y = 2?$
  • A
    Only one
  • B
    Two
  • ✓
    Infinitely many
  • D
    Three
Answer
Correct option: C.
Infinitely many
Infinitely many
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MCQ 1121 Mark
The equation $x = 7$ in two variables can be written as:
  • A
    $0.x + 0.y = 7$
  • ✓
    $1.x + 0.y = 7$
  • C
    $1.x + 1.y = 7$
  • D
    $0.x + 1.y = 7$
Answer
Correct option: B.
$1.x + 0.y = 7$
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 $x =7$.
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MCQ 1131 Mark
$x = 5, y = 2$ is a solution of the linear equation:
  • A
    $x + 2y = 7$
  • B
    $5x + 2y = 7$
  • ✓
    $x + y = 7$
  • D
    $5x + y = 7$
Answer
Correct option: C.
$x + y = 7$
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 $x + y = 7.$
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MCQ 1141 Mark
$3x + 10 = 0$ will have:
  • ✓
    Unique solution
  • B
    Two solutions
  • C
    Infinitely many solutions
  • D
    No solutions
Answer
Correct option: A.
Unique solution
$3\text{x}+10 = 0$
$\text{x}=\frac{-10}{3}.$
Hence, only one solution is possible.
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MCQ 1151 Mark
In equation, $y = mx + c, m$ is:
  • A
    Intercept
  • ✓
    Slope
  • C
    Solution of the equation
  • D
    None of the above
Answer
Correct option: B.
Slope
Slope
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MCQ 1161 Mark
How many linear equations can be satisfied by $x = 2$ and $y = 3?$
  • ✓
    Many.
  • B
    None of these.
  • C
    Two.
  • D
    Only one.
Answer
Correct option: A.
Many.
There are infinite many eqution which satisfy the given value $x = 2, y = 3$For example
$x + y = 5$
$x - y = -1$
$3x - 2y = 0$
Etc..
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MCQ 1171 Mark
The graph of a linear equation $x - 5y + 3 = 0$ cuts the $x-$axis at the point.
  • A
    $(-5, 0)$
  • B
    $(5, 0)$
  • ✓
    $(-3, 0)$
  • D
    $(3, 0)$
Answer
Correct option: C.
$(-3, 0)$
When a line cuts $x-$axis in that case $y$ co-ordinate is $0.$
So to find the co-ordinate of $x$ we put $y = 0$ in given equation,
$x - 5y + 3 = 0$
at $y = 0$
$x - 5.0 + 3 = 0$
$x + 3 = 0$
$x = -3$
So the co-ordinate are $(-3, 0)$
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MCQ 1181 Mark
lf 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:
  • A
    $4$ units.
  • B
    $3$ units.
  • ✓
    $5$ units.
  • D
    None of these.
Answer
Correct option: C.
$5$ units.

$4x + 3y = 12$
At $x = 0, 3y = 12 $
$\Rightarrow y = 4$ units
At $y = 0, 4x = 12$
$ \Rightarrow x = 3$ units
The triangle formed is $\triangle\text{AOB},$ where
$OB = 4$ units
$OA = 3$ units
Hypotenuse $=\text{AB}=\sqrt{\text{OB}^2+\text{OA}^2}=\sqrt{16+9}=5\text{ units}$
Hence, correct option is $(c).$
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MCQ 1191 Mark
The taxi fare in a city is as follows: For the first kilometer, the fare is $₹ 8$ and for the subsequent distance it is $₹ 5$ per kilometer. Taking the distance covered as $x \ km$ and total fare as $₹ y$, write a linear equation for this information.
  • A
    $x = 5y - 3$
  • ✓
    $y = 5x + 3$
  • C
    $x = 5y + 3$
  • D
    $y = 5x - 3$
Answer
Correct option: B.
$y = 5x + 3$
Taxi fare for first kilometer $= ₹ 8$
Taxi fare for subsequent distance $= ₹ 5$
Total distance covered $= x$
Total fare $= y$
Since the fare for first kilometer $= ₹ 8$
According to problem, Fare for $(x - 1)$ kilometer $= 5(x - 1)$
So, the total fare $y = 5(x - 1) + 8$
$\Rightarrow y = 5(x - 1) + 8$
$\Rightarrow y = 5x - 5 + 8$
$\Rightarrow y = 5x + 3$
Hence, $y = 5x + 3$ is the required linear equation.
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MCQ 1201 Mark
The graph of $y = 6$ is a line.
  • A
    Parallel to $y-$axis at a distance $6$ units from the origin.
  • B
    Making an intercept $6$ on both the axes.
  • C
    Making an intercept $6$ on the $x-$ axis.
  • ✓
    Parallel to $x-$axis at a distance $6$ units from the origin.
Answer
Correct option: D.
Parallel to $x-$axis at a distance $6$ units from the origin.
As $y = a$ is an equation of a line parallel to $x-$axis at a distance of a unit from the origin.
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MCQ 1211 Mark
For the equation $5x - 7y = 35$, if $y = 5$, then the value of $‘x’$ is:
  • A
    $-14$
  • B
    $12$
  • C
    $-12$
  • ✓
    $14$
Answer
Correct option: D.
$14$
For the equation $5x - 7y = 35$, if $y = 5,$
$5x - 7y = 35$
$y = 55$
$x - 7.5 = 35$
$5x - 35 = 35$
$5x = 35 + 35$
$5x = 70$
$\text{x}=\frac{70}{5}=14$
$x = 14.$
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MCQ 1221 Mark
If $(a, 4)$ lies on the graph of $3x + y = 10$, then the value of a is:
  • A
    $4$
  • B
    $1$
  • C
    $3$
  • ✓
    $2$
Answer
Correct option: D.
$2$
Given, $(a, 4)$ lies on the graph of $3x + y = 10$
Thus it is a solution
$= 3a + 4 = 10$
$= a = 2.$
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MCQ 1231 Mark
The solution of equation $x - 2y = 4$ is:
  • A
    $(0, 2)$
  • B
    $(2, 0)$
  • ✓
    $(4, 0)$
  • D
    $(1, 1)$
Answer
Correct option: C.
$(4, 0)$
Explanation: Putting $x = 4$ and $y = 0$, on the
$L.H.S$. of the given equation, we get;
$4 - 2 (0) = 4 - 0 = 4$
Which is equal to $R.H.S.$
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MCQ 1241 Mark
The equation of a line parallel to $x -$ axis and $3$ units above the origin is:
  • A
    $x = -3$
  • B
    $x = 3$
  • C
    $y = -3$
  • ✓
    $y = 3$
Answer
Correct option: D.
$y = 3$
$y = 3$
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MCQ 1251 Mark
Which of the following pair is a solution of the equation $3x - 2y = 7?$
  • A
    $(-2, 1)$
  • B
    $(5, 1)$
  • ✓
    $(1, -2)$
  • D
    $(1, 5)$
Answer
Correct option: C.
$(1, -2)$
Solution of the equation $3x - 2y = 7$ is $(1, -2)$ as it satisfy the given equation,
$3x - 2y = 7$
$\Rightarrow 3(1) - 2(-2) = 7$
$\Rightarrow 3 + 4 = 7$
$LHS = RHS.$
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MCQ 1261 Mark
If $(k, -3)$ lies on the line $3x - y = 6,$ then the value of $‘k’$ is:
  • A
    $0$
  • B
    $3$
  • ✓
    $1$
  • D
    $2$
Answer
Correct option: C.
$1$
$(k, -3)$ lies on the line $3x - y = 6$, it means that $(k, -3)$ is a solutio of a line $3x - y = 6,$
So,
$3k -(-3) = 6$
$3k + 3 = 6$
$3k = 6 - 3$
$3k = 3$
$\text{k}=\frac{3}{3}=1$
$k = 1.$
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MCQ 1271 Mark
Write the correct answer in the following: The linear equation $2x – 5y = 7$ has,
  • A
    A unique solution.
  • B
    Two solutions.
  • ✓
    Infinitely many solutions.
  • D
    No solution.
Answer
Correct option: C.
Infinitely many solutions.
$2x – 5y = 7$ is a linear equation in two variables. A linear equation in two variables has infinitely many solutions.
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MCQ 1281 Mark
A linear equation in two variables has maximum:
  • A
    Only one solution
  • B
    Two solution
  • ✓
    Infinite solution
  • D
    None of these
Answer
Correct option: C.
Infinite solution
Infinite solution
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MCQ 1291 Mark
If $(2, 0)$ is a solution of the linear equation $2x + 3y = k$, then the value of $k$ is:
  • A
    $5$
  • B
    $2$
  • ✓
    $4$
  • D
    $6$
Answer
Correct option: C.
$4$
$(2, 0)$ is a solution of the linear equation $2x + 3y = k,$
$\Rightarrow 4 = k.$
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MCQ 1301 Mark
Write the correct answer in the following: The equation $2x + 5y = 7$ has a unique solution, if $x$ and $y$ are,
  • ✓
    Natural numbers.
  • B
    Positive real numbers.
  • C
    Real numbers.
  • D
    Rational numbers.
Answer
Correct option: A.
Natural numbers.
The equation $2x + 5y = 7$ has a unique solution if $x, y$ are natural numbers.
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MCQ 1311 Mark
Equation of a line passing through origin is:
  • A
    $x + y = 1$
  • B
    $x = 2y - 4$
  • ✓
    $x + y = 0$
  • D
    $y = x - 1$
Answer
Correct option: C.
$x + y = 0$
$x + y = 0$
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MCQ 1321 Mark
If $(2, 0)$ is a solution of the linear equation $2x +3y = k$, then the value of $k$ is:
  • ✓
    $4$
  • B
    $6$
  • C
    $5$
  • D
    $2$
Answer
Correct option: A.
$4$
$4$
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MCQ 1331 Mark
The graph of the linear equation $3x - 2y = 6$, cuts the $x-$axis at the point:
  • ✓
    $(2, 0)$
  • B
    $(0, 2)$
  • C
    $(0, -2)$
  • D
    $(-2, 0)$
Answer
Correct option: A.
$(2, 0)$
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 $(2, 0).$
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MCQ 1341 Mark
The linear equation $2x + 3y = 6$ has:
  • ✓
    Infinitely many solutions.
  • B
    Two solutions.
  • C
    A unique solution.
  • D
    Three solutions.
Answer
Correct option: A.
Infinitely many solutions.
$2x + 3y = 62x = 6 - 3y$
$\text{x}=\frac{6-3\text{y}}{2}$
$x$
$0$
$3232$
$3$
$y$
$2$
$1$
$0$
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 1351 Mark
The graph of the linear equation $2x - 3y = 6$, cuts the $y-$axis at the point:
  • A
    $(2, 0)$
  • B
    $(0, 2)$
  • ✓
    $(0, -2)$
  • D
    $(-2, 0)$
Answer
Correct option: C.
$(0, -2)$
The linear equation $2x - 3y = 6$, cuts the $y-$axis when $x$ co-ordinate is $0.$
So we put $x = 0$ in given equation $2x - 3y = 6$
$2 × 0 - 3y = 6$
$0 - 3y = 6$
$-y = 63$
$-y = 2$
$y = -2$
So the co-ordinates are $(0, -2).$
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MCQ 1361 Mark
The graph of the line $x = -2$ passes through:
  • A
    $(0, 4)$
  • ✓
    $(-2, 3)$
  • C
    $(-1, 4)$
  • D
    $(3, -2)$
Answer
Correct option: B.
$(-2, 3)$
Because value of $x$ co-ordinate is $-2.$
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MCQ 1371 Mark
The equation $3x + 4y = 7$ has a unique solution, if $x$ and $y$ are:
  • A
    Real numbers.
  • ✓
    Natural numbers.
  • C
    Rational numbers.
  • D
    Positive real numbers.
Answer
Correct option: B.
Natural numbers.
$3x + 4y = 7$
$3x = 7 - 4y$
$\text{x} = 7−\frac{4\text{y}}{3}$
The equation will have a unique solution only if $x$ and $y$ are natural numbers with only one value which is,
For $y = 1.$
$\text{x} = 7−\frac{4.1}{3}$
$\text{x} = 7−\frac{4}{3}$
$\text{x} = \frac{3}{3} = 1$
$x = 1$
I.e., $x = 1, y = 1$ will be unique value for this equation.
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MCQ 1381 Mark
Which of the following is not a solution of $3x + 4y = 12?$
  • A
    $(0, 3)$
  • ✓
    $(2, 3)$
  • C
    $(4, 0)$
  • D
    $(8, -3)$
Answer
Correct option: B.
$(2, 3)$
The given co-ordinate is solution of a eqution if on puting the co-ordiates $L.H.S = R.H.S$
$3x + 4y = 12$
Put co-ordinate $(2, 3)$ in given equation,
$L.H.S$
$3.2 + 4.3$
$6 + 12 = 18$
$L.H.S ≠ R.H.S$
So we can say $(2, 3)$ is a not a solution of $3x + 4y = 12.$
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MCQ 1391 Mark
Write the linear equation such that each point on its graph has an ordinate $5$ times it's abscissa.
  • A
    $5x + y = 2$
  • B
    None of these
  • ✓
    $y = 5x$
  • D
    $x = 5y$
Answer
Correct option: C.
$y = 5x$
$y = 5x$
$At x = 1$
$y = 5.1 = 5$
$y = 5$
$(1, 5)$
$At x = 2$
$y = 5.2 = 10$
$y = 10$
$(2, 10)$
$At x = 3$
$y = 5.3 = 15$
$y = 15$
$(3, 15).$
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MCQ 1401 Mark
The point of the form $(a, -a)$, where a lies on:
  • A
    The line $x = y.$
  • B
    The $x-$axis.
  • ✓
    The line $y + x = 0.$
  • D
    The $y-$axis.
Answer
Correct option: C.
The line $y + x = 0.$
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 $x + y = 0.$
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MCQ 1411 Mark
The value of k if $x = 2, y = 1$ is a solution of equation $2x - k = -3y$ is:
  • A
    $6$
  • B
    $5$
  • ✓
    $7$
  • D
    $-7$
Answer
Correct option: C.
$7$
$7$
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MCQ 1421 Mark
The graph of the linear equation $2x - y = 4$ cuts $x-$axis at:
  • ✓
    $(2, 0)$
  • B
    $(-2, 0)$
  • C
    $(0, -4)$
  • D
    $(0, 4)$
Answer
Correct option: A.
$(2, 0)$
On $x-$axis, the $y-$co-ordinate is always $0.$
So, $2x - y = 4$ will cut the x-axis where $y = 0$
i.e. $2x = 4$
i.e. $x = 2$
Thus, $2x - y = 4$ will cut the $x-$axis at $(2, 0).$
Hence, correct option is $(a).$
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MCQ 1431 Mark
The positive solutions of the equation $ax + by + c = 0$ always lie in the:
  • A
    $2$nd quadrant.
  • ✓
    $1$st quadrant.
  • C
    $3$rd quadrant.
  • D
    $4$th quadrant.
Answer
Correct option: B.
$1$st quadrant.
The positive solutions of the equation $a x+b y+c=0$ always lie in the $1$ st quadrant. Because in $1$st quadrant both $x$ and $y$ have positive value.
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MCQ 1441 Mark
The distance between the graphs of the equations $y = -1$ and $y = 3$ is:
  • A
    $2$
  • ✓
    $4$
  • C
    $3$
  • D
    $1$
Answer
Correct option: B.
$4$
The distance between given two graphs
$= 3 - (-1)$
$= 3 + 1$
$= 4$
Hence, correct option is $(b).$
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MCQ 1451 Mark
The graph of $y = 4x$ will:
  • A
    Intersect $x-$axis.
  • ✓
    Pass through the origin.
  • C
    None of these.
  • D
    Intersect $y-$axis.
Answer
Correct option: B.
Pass through the origin.
The graph of $y = 4x$ will pass through the origin $(0, 0)$
$y = 4x$
At $x = 0$
$y = 4.0$
$y = 0$
So the graph $y = 4x$ will pass from point $(0, 0).$
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MCQ 1461 Mark
Write the linear equation such that each point on its graph has an ordinates times its abscissa.
  • ✓
    $y = 5x$
  • B
    $x = 5y$
  • C
    $5x + y = 2$
  • D
    None of these.
Answer
Correct option: A.
$y = 5x$
At $x = 1$
$y = 5.1 = 5$
$y = 5$
$(1, 5)$
At $x = 2$
$y = 5.2 = 10$
$y = 10$
$(2, 10)$
At $x = 3$
$y = 5.3 = 15$
$y = 15$
$(3, 15)$
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MCQ 1471 Mark
Which of the following ordered pairs is a solution of the equation $x - 2y - 6?$
  • A
    $(2, 4)$
  • B
    $(0, 3)$
  • C
    $(-4, 1)$
  • ✓
    $(4, -1)$
Answer
Correct option: D.
$(4, -1)$
$(4, -1)$
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MCQ 1481 Mark
The equation $x - 2 = 0$ on number line is represented by:
  • A
    A line.
  • ✓
    A point.
  • C
    Infinitely many lines.
  • D
    Two lines.
Answer
Correct option: B.
A point.
The equation $x - 2 = 0$ is represented by a point on the number line.
Therefore, the correct answer is $(b).$
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MCQ 1491 Mark
Write the correct answer in the following: The equation $x = 7$, in two variables can be written as,
  • A
    $1 - x + 1.y = 7$
  • B
    $1 - x + 0.y = 7$
  • C
    $0 - x + 1.y = 7$
  • ✓
    $0 - x + 0.y = 7$
Answer
Correct option: D.
$0 - x + 0.y = 7$
The equation $x = 7$ in two variables can be expressed as $1.x + 0.y = 7.$
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MCQ 1501 Mark
Point $(3, 4)$ lies on the graph of the equation $3y = kx + 7$. The value of $k$ is:
  • A
    $\frac{4}{3}$
  • ✓
    $\frac{5}{3}$
  • C
    $3$
  • D
    $\frac{7}{3}$
Answer
Correct option: B.
$\frac{5}{3}$
$3y = kx + 7$
Here, $x = 3$ and $y = 4$
Hence,
$(3 × 4) = (kx3) + 7$
$12 = 3k + 7$
$3k = 12 - 7$
$3k = 5$
$\text{k}=\frac{5}{3}$
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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
    None of these
  • D
    $y = x$
Answer
Correct 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.
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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
    $a = 0, b \neq 0$
  • ✓
    $a \neq 0, b \neq 0$
Answer
Correct 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 $0.$
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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
    $x - 2y = 160$
  • ✓
    $2x + y = 160$
Answer
Correct 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 $2 x + y =160$.
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MCQ 1541 Mark
The linear equation $3x - y = x - 1$ has:
  • A
    Two solutions.
  • B
    No solution.
  • ✓
    Infinitely many solutions.
  • D
    A unique solution.
Answer
Correct 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.
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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
    $\frac{3}{5}$
Answer
Correct 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
$3 \times 4 = 3a + 7$
$\Rightarrow 12 = 3a + 7$
$\Rightarrow 3a = 12 - 7 = 5$
$\Rightarrow\text{a}=\frac{5}{3}.$
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MCQ 1561 Mark
Find the value of k, if $x = 1, y = 2$ is a solution of the equation $2x + 3y = k.$
  • A
    $5$
  • B
    $6$
  • C
    $7$
  • ✓
    $8$
Answer
Correct option: D.
$8$
$2x + 3y = k$
$k = 2 (1) + 3 (2)$
$= 2 + 6 = 8$
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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:
  • A
    $2$
  • B
    $4$
  • C
    $3$
  • ✓
    $1$
Answer
Correct option: D.
$1$
If the line represented by the equation $3x + ky = 9$ passes through the points $(2, 3)$ then $(2, 3)$ will satisy the equation
$3x + ky = 9$
$3(2) + 3k = 9$
$\Rightarrow 6 + 3k = 9$
$\Rightarrow 3k = 9 - 6$
$\Rightarrow 3k = 3$
$\Rightarrow k = 1$
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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
    $a = 0, b = 0$
  • ✓
    $a \neq 0, b \neq 0$
Answer
Correct option: D.
$a \neq 0, b \neq 0$
$a \neq 0, b \neq 0$
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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
    $-x + 2y = 0$
Answer
Correct 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.
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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
    $x - 2y = 0$
Answer
Correct 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
$x + y = 0.$
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MCQ 1611 Mark
If $x = 3$ and $y = -2$ satisfies $5x - y = k$, then the value of $k$ is:
  • A
    $3$
  • B
    $-2$
  • ✓
    $17$
  • D
    $12$
Answer
Correct option: C.
$17$
If $x = 3$ and $y = -2$ satisfies $5x - y = k$
Then
$5x - y = k$
$5 \times 3 - (-2) = k$
$15 + 2 = k$
$k = 17.$
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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
    $(0, 3)$
Answer
Correct 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 $(0, 2).$
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MCQ 1631 Mark
The graph of $x = - 4$ is a straight line.
  • A
    Parallel to $x-$axis.
  • ✓
    Parallel to $y-$axis.
  • C
    Passing through origin.
  • D
    Intersecting the axes.
Answer
Correct 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.
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MCQ 1641 Mark
Any point on the $x -$ axis is of the form.
  • A
    $(x, y)$
  • B
    $(0, y)$
  • ✓
    $(x, 0)$
  • D
    $(x, x)$
Answer
Correct 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 $0.$
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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
    $(0, 3)$
Answer
Correct 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 $(3,0)$.
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MCQ 1661 Mark
The point of the form $(a, –a)$ always lies on the line:
  • A
    $x = a$
  • B
    $y = –a$
  • C
    $y = x$
  • ✓
    $x + y = 0$
Answer
Correct 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 $x + y = 0.$
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MCQ 1671 Mark
The value of k if $x = 3$ and $y = -2$ is a solution of the equation $2x - 13y = k$ is:
  • ✓
    $32$
  • B
    $30$
  • C
    $31$
  • D
    $23$
Answer
Correct option: A.
$32$
We have to find the value of ‘k’ if $x = 3$ and $y = -2$ is a solution of the equation $2x - 13y = k$
$2x - 13y = k$
$2(3) - 13(-2) = k$
$6 + 26 = k$
$k = 32.$
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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
    $\Big(0,\frac{3}{2}\Big)$
  • ✓
    $(1,1)$
Answer
Correct option: D.
$(1,1)$
$y = x, \Rightarrow$ Both the coordinates are the same. Hence $(1, 1)$ is correct option.
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MCQ 1691 Mark
If $(-2, 5)$ is a solution of $2x + my = 11$, then the value of $‘m’$ is:
  • A
    $-3$
  • B
    $2$
  • ✓
    $3$
  • D
    $-2$
Answer
Correct option: C.
$3$
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 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:
  • ✓
    $4$
  • B
    $6$
  • C
    $5$
  • D
    $2$
Answer
Correct option: A.
$4$
Since, $(2, 0)$ is a solution of the given linear equation $2x + 3y = k$, then put $x = 2$ and $y = 0$ in the equation.
$\Rightarrow 2(2) + 3(0) = k$
$\Rightarrow k = 4$
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MCQ 1711 Mark
A linear equation in two variables is of the form $ax + by + c = 0$, where?
  • ✓
    $a \neq 0$ and $b \neq 0$
  • B
    $a = 0$ and $b = 0$
  • C
    $a \neq 0$ and $b = 0$
  • D
    $a = 0$ and $b \neq 0$
Answer
Correct 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.
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MCQ 1721 Mark
Solutions of the equation $2x + 5y = 0$ is:
  • A
    $3, 0$
  • B
    $-3, 2$
  • ✓
    $0, 0$
  • D
    $0, 4$
Answer
Correct option: C.
$0, 0$
$0, 0$
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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
    $5x + y = 7$
Answer
Correct option: C.
$x + y = 7$
$x = 5, y = 2$ is a solution of the linear equation $x + y = 7$, as $5 + 2 = 7.$
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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:
  • ✓
    Remains the same
  • B
    Changes
  • C
    Changes in case of multiplication only
  • D
    Changes in case of division only
Answer
Correct option: A.
Remains the same
If 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.
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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
    $2 + 3y = 7x$
Answer
Correct option: B.
$x + y = 0$
$x + y = 0$
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MCQ 1761 Mark
If $x = 3$ and $y = -2$ satisfies $2x - 3y = k$, then the value of $k$ is:
  • A
    $-2$
  • B
    $10$
  • ✓
    $12$
  • D
    $3$
Answer
Correct option: C.
$12$
If $x = 3$ and $y = -2$ satisfies $2x - 3y = k.$
It means $x = 3$ and $y = -2$ is a solution of equation $2x - 3y = k$
$2 × 3 - 3(-2) = k$
$6 + 6 = k$
$k = 12$
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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
    $y = x$
  • ✓
    $x + y = 0$
Answer
Correct option: D.
$x + y = 0$
$x + y = 0$
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MCQ 1781 Mark
How many linear equation can be satisfied by $x = 2$ and $y = 3?$
  • A
    Only one.
  • B
    Only two.
  • C
    Only three.
  • ✓
    Infinitely many.
Answer
Correct option: D.
Infinitely many.
Infinitely many linear equations can be satisfied by $x = 2$ and $y = 3.$
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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
    $(1, 1)$
Answer
Correct 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 $(0, 1).$
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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
Answer
Correct 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.
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MCQ 1811 Mark
The linear equation $2x - 5y = 7$ has:
  • A
    No solution
  • B
    Unique solution
  • C
    Two solutions
  • ✓
    Infinitely many solutions
Answer
Correct 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.
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MCQ 1821 Mark
Any point on line $x = y$ is of the form:
  • A
    $(k, -k)$
  • B
    $(0, k)$
  • C
    $(k, 0)$
  • ✓
    $(k, k)$
Answer
Correct option: D.
$(k, k)$
$(k, k)$
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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
    $x = -5$
Answer
Correct 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 $y$ $=-5$.
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MCQ 1841 Mark
$x = 2, y = - 1$ is a solution of the linear equation:
  • A
    $x + 2y = 4$
  • B
    $2x + y = 5$
  • C
    $2x + y = 0$
  • ✓
    $x + 2y = 0$
Answer
Correct option: D.
$x + 2y = 0$
$2 + 2(-1) = 2 - 2 = 0.$
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MCQ 1851 Mark
If $(3, 2)$ is the solution $3x - ky = 5$, then $k$ equals of the equation.
  • ✓
    $2$
  • B
    $4$
  • C
    $3$
  • D
    $\frac{1}{2}$
Answer
Correct option: A.
$2$
$2$
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MCQ 1861 Mark
If $(-2, 5)$ is a solution of $2x + my = 11$, then the value of $'m'$ is:
  • A
    $-2$
  • B
    $2$
  • ✓
    $3$
  • D
    $-3$
Answer
Correct option: C.
$3$
If $(-2, 5)$ is a solution of $2x + my = 11$
then it will satisfy the given equation
$2.(-2) + 5 m = 11$
$-4 + 5m = 11$
$5m = 11 + 4$
$5m = 15$
$\text{m}=\frac{15}{5}=3$
$\text{m}=3$
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MCQ 1871 Mark
$y = 0$ is the equation of:
  • A
    A line parallel to $x -$ axis
  • ✓
    A line parallel to $y -$ axis
  • C
    $x -$ axis
  • D
    $y -$ axis
Answer
Correct option: B.
A line parallel to $y -$ axis
A line parallel to $y -$ axis
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MCQ 1881 Mark
The equation $2x + 5y = 7$ has a unique solution, if $x, y$ are:
  • A
    Rational numbers
  • B
    Real numbers
  • ✓
    Natural numbers
  • D
    Positive real numbers
Answer
Correct option: C.
Natural numbers
The 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.
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MCQ 1891 Mark
How many linear equations are satisfied by $x = 2$ and $y = -3?$
  • A
    Only one.
  • B
    Two.
  • C
    Three.
  • ✓
    Infinitely many.
Answer
Correct option: D.
Infinitely many.
From 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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