M.C.Q. [1 Marks Each]

MCQ 11 Mark

If $43m = 0.086$, then the value of m is:

✓
$0.002$
B
$0.02$
C
$0.2$
D
$2$

Answer

Correct option: A.

$0.002$

Given equation is $43m = 0.086$
On dividing the given equation by $43$, we get
$\text{m}=\frac{0.086}{43}$
If we remove the decimal, we get $1000$ in denominator
$\text{m}=\frac{86}{43}\times\frac{1}{1000}=\frac{1}{1000}=0.002$

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MCQ 21 Mark

$x$ Exceeds $3$ by $7$, can be represented as:

A
$x + 3 = 2$
B
$x + 7 = 3$
C
$x - 3 = 7$
✓
$x - 7 = 3$

Answer

Correct option: D.

$x - 7 = 3$

The given statement means $x$ is $7$ more than $3.$
So, the equation is $x - 7 = 3$
We can also write it as $x - 3 = 7.$

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MCQ 31 Mark

The equation which cannot be solved in integers is:

A
$5y - 3 = - 18$
B
$3x - 9 = 0$
✓
$3z + 8 = 3 + z$
D
$9y + 8 = 4y - 7$

Answer

Correct option: C.

$3z + 8 = 3 + z$

Let us solve the equation:
$a.$ Given equation is $5y - 3 = -18$
$\Rightarrow5\text{y}=-18+3 [$transposing $3$ to $\text{RHS}]$
$\Rightarrow5\text{y}=-15$
$\Rightarrow\text{y}=-3 ($integer$) [$dividing both sides by $5]$
$b.$ Given equation is $3z - 9 = 0$
$\Rightarrow3\text{x}=9 [$transposing $9$ to $\text{RHS}]$
$\Rightarrow\text{x}=3 ($integer$) [$dividing both sides by $3]$
$c.$ Given equation is $3z + 8 = 3 + z$
On transposing $z$ and $8$ to $\text{LHS}$ and $\text{RHS}$ respectively, we get
$\Rightarrow3\text{z}-\text{z}=3-8$
$\Rightarrow2\text{z}=-5$
$\Rightarrow\text{z}=-\frac{5}{2} [$dividing both sides by $2]$
Which is neither a positive fraction nor an integer.
$d.$ Given equation is $9y + 8 = 4y - 7$
On transposing $4y$ and $8$ to $\text{LHS}$ and $\text{RHS}$ respectively, we get
$\Rightarrow9\text{y}-4\text{y}=-7-8$
$5\text{y}=-15$
$\Rightarrow\frac{5\text{y}}{5}=-\frac{15}{5} [$dividing both sides by $5]$
$\Rightarrow\text{y}=-3 ($integer$)$

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MCQ 41 Mark

Which of the following equations can be formed starting with $x = 0$?

A
$2x + 1 = -1$
B
$\frac{\text{x}}{2}+5=7$
✓
$3x - 1 = -1$
D
$3x - 1 = 1$

Answer

Correct option: C.

$3x - 1 = -1$

We have, $x = 0$
On multiplying both the sides by $3$, we get
$3 \times x = 3 \times 0$
$\Rightarrow 3x = 0$
On adding $(-1)$ both the sides, we get
$3x + (-1) = 0 + (-1)$
$\Rightarrow 3x - 1 = -1$

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MCQ 51 Mark

Which of the following numbers satisfy the equation $-6 + x = -12$?

A
$2$
B
$6$
✓
$-6$
D
$-2$

Answer

Correct option: C.

$-6$

Let us put the values given in the options in equation $-6 + x = -12$
$a.$ Put $x = 2$
$\Rightarrow -6 + 2 = -2$
$\Rightarrow -4 = -12$
$\therefore$ $\text{LHS} \neq \text{RHS}$
$b.$ Put $x = 6$
$\Rightarrow -6 + (6) = -12$
$\Rightarrow 0 = -12$
$\therefore$ $\text{LHS} \neq \text{RHS}$
$c.$ Put $x = -6$
$\Rightarrow -6 + (-6) = -12$
$\Rightarrow -6 - 6 = -12$
$\Rightarrow -12 = -12$
$\therefore$ $\text{LHS} = \text{RHS} ($satisfied$)$
Now, there is no need to check the next option.
Hence, $x = -6$ satisfied the given equation.

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MCQ 61 Mark

The solution of which of the following equations is neither a positive fraction nor an integer?

A
$2x + 6 = 0$
B
$3x - 5=0$
C
$5x - 8 = x + 4$
✓
$4x + 7 = x +$

Answer

Correct option: D.

$4x + 7 = x +$

Let us solve the equation:
$a.$ Given equation is $2x + 6 = 0$
$\Rightarrow2\text{x}=-6 [$transposing $6$ to $\text{RHS}]$
$\Rightarrow\text{x}=-\frac{6}{2} [$dividing both sides by $2]$
$\Rightarrow\text{x}=-3 ($integer$)$
$b.$ Given equation is $3x - 5 = 0$
$\Rightarrow3\text{x}=5 [$transposing $5 $to $\text{RHS}]$
$\Rightarrow\text{k}=\frac{5}{3} ($fraction$) [$dividing both sides by $3]$
$c.$ Given equation is $5x - 8 = x + 4$
$\Rightarrow5\text{x}=\text{x}+4+8 [$transposing $8$ to $\text{RHS}]$
$\Rightarrow5\text{x}=\text{x}+12$
$\Rightarrow5\text{x}-\text{x}=12 [$transposing $x$ to $\text{LHS}]$
$\Rightarrow4\text{x}=12$
$\Rightarrow\text{x}=3 ($integer$) [$dividing both sides by $4]$
$d.$ Given equation is $4x + 7 = x + 2$
$\Rightarrow4\text{x}+7-\text{x}=2 [$transposing $x$ to $\text{LHS}]$
$\Rightarrow3\text{x}=2-7 [$transposing $7$ to $\text{RHS}]$
$\Rightarrow3\text{x}=-5$
$\Rightarrow\text{x}=-\frac{5}{3} [$dividing both sides by $3]$
Which is neither a positive fraction nor an integer.

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MCQ 71 Mark

The equation having $-3$ as a solution is:

A
$x + 3 = 1$
B
$8 + 2x = 3$
✓
$10 + 3x = 1$
D
$2x + 1 = 3$

Answer

Correct option: C.

$10 + 3x = 1$

Let us solve the equation:
$a.$ Given equation is $x + 3 = 1$
$\Rightarrow x = 1 - 3$
$\Rightarrow x = -2$
$b.$ Given equation is $8 + 2x = 3$
$\Rightarrow 2x = 3 - 8$
$\Rightarrow 2x = -5$
$\Rightarrow\text{x}=-\frac{5}{2}$
$c.$ Given equation is $10 + 3x = 1$
$\Rightarrow 3x = 1 - 10$
$\Rightarrow 3x = -9$
$\Rightarrow x = -3$
Now, we don't have to solve next equation as we get the answer.

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MCQ 81 Mark

If a and b are positive integers, then the solution of the equation $ax = b$ will always be a.

✓
Positive number.
B
Negative number.
C
$1$
D
$0$

Answer

Correct option: A.

Positive number.

Given equation is $ax = b$
On dividing the equation by a, we get
$\text{x}=\frac{\text{b}}{\text{a}}$
Now, if $a$ and $b$ are positive integers, then the solution of the equation is also positive number as division of two positive integers is also a positive number.

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MCQ 91 Mark

If $7x + 4 = 25$, then $x$ is equal to:

A
$\frac{29}{7}$
B
$\frac{100}{7}$
C
$2$
✓
$3$

Answer

Correct option: D.

$3$

Given equation is $7x + 4 = 25$
$\Rightarrow 7x = 25 - 4$ $[$transposing $4$ to $RHS]$
$\Rightarrow 7x = 21$
On dividing the above equation by $7$, we get
$x = 3$
Hence, the solution of the given equation is $3.$

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MCQ 101 Mark

If $\frac{\text{x}}{2}=3,$ then the value of $3x + 2$ is:

✓
$20$
B
$11$
C
$\frac{13}{2}$
D
$8$

Answer

Correct option: A.

$20$

Given, $\frac{\text{x}}{2}=3$
On muliplying both sides by $2$, we get $\frac{\text{x}}{2}\times2=3\times2$
$\Rightarrow\text{x}=3\times2=6$
Put $x = 6$ in the equation $3x + 2$, we get
$3(6) + 2 = 18 + 2 = 20$

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MCQ 111 Mark

The value of $y$ for which the expressions $(y - 15)$ and $(2y + 1)$ become equal is:

A
$0$
B
$16$
C
$8$
✓
$-16$

Answer

Correct option: D.

$-16$

It is given that both the expressions are equal. So the equation is:
$\Rightarrow y - 15 = 2y + 1$
$\Rightarrow y - 2y = 1 + 15$ [transposing $2y$ to $LHS$ and $(-15)$ to $RHS$]
$-y = 16$
Multiplying both sides by $(-1)$, we get
$y = -16$

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MCQ 121 Mark

If $k + 7 = 16$, then the value of $8k - 72$ is:

✓
$0$
B
$1$
C
$112$
D
$56$

Answer

Correct option: A.

$0$

Given equation is $k + 7 = 6$
On transposing $7$ to $RHS$, we get
$k = 16 - 7 = 9$
Put the value of k in the equation $(8k - 72)$, we get
$8(9) - 72 = 72 - 72 = 0$

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MCQ 131 Mark

Which of the following is not allowed in a given equation?

A
Adding the same number to both sides of the equation.
B
Subtracting the same number from both sides of the equation.
C
Multiplying both sides of the equation by the same non-zero number.
✓
Dividing both sides of the equation by the same number.

Answer

Correct option: D.

Dividing both sides of the equation by the same number.

Dividing both sides of the equation by the same non-zero number is allowed in a given equation, division of any number by zero is not allowed as set division of number by zero is not defined.
Note: If we add same number to both sides of the equation while adding subtracting, then there will be no change in the given equation.

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MCQ 141 Mark

The solution of the equation $ax + b = 0$ is:

A
$\frac{\text{a}}{\text{b}}$
B
$-\text{b}$
✓
$-\frac{\text{b}}{\text{a}}$
D
$\frac{\text{b}}{\text{a}}$

Answer

Correct option: C.

$-\frac{\text{b}}{\text{a}}$

Given equation is $ax + b = 0$
$\Rightarrow\text{ax}=-\text{b}$ [transposing b to $RHS$]
$\Rightarrow\text{x}=-\frac{\text{b}}{\text{a}}$ [on dividing both sides by $a$]

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MCQ 151 Mark

The solution of the equation $3x + 7 = -20$ is:

A
$\frac{17}{7}$
✓
$-9$
C
$9$
D
$\frac{13}{3}$

Answer

Correct option: B.

$-9$

Given equation is $3x + 7 = -20$
$\Rightarrow 3x = -20 - 7$ [transposing $7$ to $RHS$]
$\Rightarrow 3x = -27$
On dividing the above equation by $3$, we get
$x = -9$
Hence, the solution of the given equation is $-9.$

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MCQ 161 Mark

The equation having $5$ as a solution is:

A
$4x + 1 = 2$
B
$3 - x = 8$
C
$x - 5 = 3$
✓
$3 + x = 8$

Answer

Correct option: D.

$3 + x = 8$

Let us solve the equations:
$a.$ Given equation is $4x + 1 = 2$
$\Rightarrow4\text{x}=2-1$
$\Rightarrow4\text{x}=1$
$\Rightarrow\text{x}=\frac{1}{4}$
$b.$ Given equation is $3 - x = 8$
$\Rightarrow -x = 8 - 3 $
$\Rightarrow -x = 5 $
$\Rightarrow x = -5$
$c.$ Given equation is $x - 5 = 3$
$\Rightarrow x = 3 + 5 $
$\Rightarrow x = 8$
$d.$ Given equation is $3 + x = 8$
$\Rightarrow x = 8 - 3 $
$\Rightarrow x = 5$

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MCQ 171 Mark

Shifting one term from one side of an equation to another side with a change of sign is known as:

✓
Commutativity.
B
Transposition.
C
Distributivity.
D
Associativity.

Answer

Correct option: A.

Commutativity.

Transposition means shifting one term from one side of an equation to another side with a change of sign.

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MCQ 181 Mark

Which of the following equations cannot be formed using the equation $x = 7$?

A
$2x + 1 = 15$
✓
$7x - 1 = 50$
C
$x - 3 = 4$
D
$\frac{\text{x}}{7}-1=0$

Answer

Correct option: B.

$7x - 1 = 50$

We have, $x = 7$
On multiplying both the sides by $7$, we get
$7 \times x = 7 \times 7 \Rightarrow 7x = 49$
On adding $(-1)$ both the sides, we get
$7x + (-1) = 49 + (-1)$
$\Rightarrow 7x - 1 = 49 - 1$
$\Rightarrow 7x - 1 = 48$

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Maths M.C.Q. [1 Marks Each]

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