Algebra Test

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Algebra Test - 12

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Question 1
1 / -0

In a playground, kids are playing in the groups of $$5$$.

If there is one group of kids, then, total number of kids = $$5$$
If there is two group of kids, then, total number of kids = $$5+5 = 5\times 2$$
and so on.

So the total number of kids playing in the playground are
$$5 + 5+5+....= 5\times n$$
Here, the variable $$n$$ is

A
The number of groups

B
The number of kids

C
The number of toys

D
The number of games

Solution

We observe that $$Total \quad no. \quad of\quad kids \quad= \quad5 \quad\times\quad no.\quad of\quad groups$$

$$\therefore$$, $$n =$$ No. of groups
Question 2
1 / -0

The non variable part in the expression $$x-18$$ is

A
$$1$$

B
$$18$$

C
$$x$$

D
$$-x$$

Solution

The non-variable/constant part of the expression $$x-18$$ is $$18$$.
Question 3
1 / -0

$$x = -1$$ is a solution of the equation

A
$$x - 5 =6$$

B
$$2x + 5 = 7$$

C
$$2(x - 2) + 6 =0$$

D
$$3x + 5 =4$$

Solution

$${\textbf{Step -1: Considering option A.}}$$

$${\text{We have given,}}$$ $$x - 5 = 1$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$ - 1 - 5 = 6$$

$$ \Rightarrow - 6 = 1$$ $${\text{Which is not possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S}} \ne {\text{R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is not a solution of }}x - 5 = 6.$$

$${\textbf{Step -2: Considering option B.}}$$

$${\text{We have given,}}$$ $$2x + 5 = 7$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$2\left( { - 1} \right) + 5 = 7$$

$$ \Rightarrow - 2 + 5 = 7$$

$$ \Rightarrow 3 = 7$$ $${\text{Which is not possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S }} \ne {\text{ R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is not a solution of 2}}x + 5 = 7.$$

$${\textbf{Step -3: Considering option C.}}$$

$${\text{We have given,}}$$ $$2\left( {x - 2} \right) + 6 = 0$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$2\left( { - 1 - 2} \right) + 6 = 0$$

$$ \Rightarrow 2\left( { - 3} \right) + 6 = 0$$

$$ \Rightarrow - 6 + 6 = 0$$

$$ \Rightarrow 0 = 0$$ $${\text{Which is possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S = R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is a solution of 2}}\left( {x - 2} \right) + 6 = 0.$$

$${\textbf{Step -4: Considering option D.}}$$

$${\text{We have given,}}$$ $$3x + 5 = 4$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$3\left( { - 1} \right) + 5 = 4$$

$$ \Rightarrow - 3 + 5 = 4$$

$$ \Rightarrow 2= 4$$ $${\text{Which is not possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S}} \ne {\text{R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is not a solution of }}3x + 5 = 4.$$

$${\textbf{ Hence, option C}}{\textbf{. 2}}\left(\mathbf {x - 2} \right)\mathbf{ + 6 = 0}{\textbf{ is correct answer.}}$$
Question 4
1 / -0

Which equation among the following don't have $$(-1)$$ as a solution?

A
$$x + 1=0$$

B
$$3x + 4 =1$$

C
$$5x + 7= 2$$

D
$$x -1 =2$$

Solution

$${\textbf{Step -1: Considering option A.}}$$
$${\text{We have given,}}$$ $$x +1 = 0$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$ - 1 +1 = 0$$
$$ \Rightarrow 0 = 0$$ $${\text{Which is possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S}} = {\text{R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is a solution of }}x +1 = 0.$$
$${\textbf{Step -2: Considering option B.}}$$
$${\text{We have given,}}$$ $$3x + 4 = 1$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$3\left( { - 1} \right) + 4 = 1$$
$$ \Rightarrow - 3 + 4 = 1$$
$$ \Rightarrow 1 = 1$$ $${\text{Which is possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S }} = {\text{ R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is a solution of 3}}x + 4 = 1.$$
$${\textbf{Step -3: Considering option C.}}$$
$${\text{We have given,}}$$ $$5x + 7 = 2$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$5\left( { - 1 } \right) + 7 = 2$$
$$ \Rightarrow -5+ 7 = 2$$
$$ \Rightarrow 2 = 2$$ $${\text{Which is possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S = R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is a solution of }}5x+7 =2.$$
$${\textbf{Step -4: Considering option D.}}$$
$${\text{We have given,}}$$ $$x -1 = 2$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$-1-1= 2$$
$$ \Rightarrow - 2 = 2$$ $${\text{Which is not possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S}} \ne {\text{R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is not a solution of }}x -1 = 2.$$
$${\textbf{ Hence, option D. }}\mathbf{ x-1 =2}{\textbf{ is correct answer.}}$$
Question 5
1 / -0

In the expression $$-24x$$, the variable is

A
$$24$$

B
$$-24$$

C
$$x$$

D
$$-x$$

Solution

In the expression $$-24x$$, the variable is $$x$$ and the constant / non-variable is $$-24$$.
Question 6
1 / -0

Let Arjun bought $$2$$ apple on $$Day \ 1$$.
Then he bought $$4$$ apple on $$Day \ 2$$.
He bought $$6$$ apple on $$Day \ 3$$. And so on.

So we can say, Arjun bought $$2\times N$$ apple on $$Day \ N$$.
Here $$"N"$$ in $$2\times N$$ represents

A
The number of apples

B
The number of days

C
$$N$$ is a constant

D
Can't say.

Solution
Question 7
1 / -0

If $$\dfrac{x+6}{3} = 7$$, what is the value of $$x$$? ( using trail and error method)

A
$$x= 21$$

B
$$x= 20$$

C
$$x= 15$$

D
$$x= 14$$

Solution

We need to find $$x$$ such that $$\dfrac{x+6}{3}$$ is $$7$$.

We know that $$\dfrac{21}{3}$$ is $$7$$.

We thus get $$7$$ if $$x+6=21$$ $$\Longrightarrow$$ $$x=15$$
Question 8
1 / -0

What value of $$x$$ that makes the following equation true ( using trail and error method) ?
$$\dfrac{x+5}{2} = 3$$

A
$$x = 0$$

B
$$x = 1$$

C
$$x = 2$$

D
$$x = 3$$
Question 9
1 / -0

Find the suitable value of $$x$$ for the following equation by trial and method:
$$2x-21 = 21$$

A
$$x = 20$$

B
$$x = 21$$

C
$$x = 22$$

D
$$x = 23$$
Question 10
1 / -0

The non variable part in the expression $$2n$$ is

A
$$2$$

B
$$n$$

C
$$2n$$

D
None of the above.

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Algebra Test - 12

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Algebra Test - 12

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SHARING IS CARING

Question 1

The number of groups

The number of kids

The number of toys

The number of games

Solution

Question 2

$$1$$

$$18$$

$$x$$

$$-x$$

Solution

Question 3

$$x - 5 =6$$

$$2x + 5 = 7$$

$$2(x - 2) + 6 =0$$

$$3x + 5 =4$$

Solution

Question 4

$$x + 1=0$$

$$3x + 4 =1$$

$$5x + 7= 2$$

$$x -1 =2$$

Solution

Question 5

$$24$$

$$-24$$

$$x$$

$$-x$$

Solution

Question 6

The number of apples

The number of days

$$N$$ is a constant

Can't say.

Solution

Question 7

$$x= 21$$

$$x= 20$$

$$x= 15$$

$$x= 14$$

Solution

Question 8

$$x = 0$$

$$x = 1$$

$$x = 2$$

$$x = 3$$

Question 9

$$x = 20$$

$$x = 21$$

$$x = 22$$

$$x = 23$$

Question 10

$$2$$

$$n$$

$$2n$$

None of the above.

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