Algebra Test

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Algebra Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following equations has $$x = 2$$ as a solution?

A
$$x + 2 = 5$$

B
$$x - 2 = 0$$

C
$$2x + 1= 0$$

D
$$x + 3 = 6$$

Solution

(A) Putting $$x = 2$$ in $$x + 2$$, we get $$2 + 2 = 4\neq 5$$
(B) Putting $$x = 2$$ in $$x - 2$$, we get $$2 - 2 = 0$$
(C) Putting $$x = 2$$ in $$2x + 1$$, we get $$2\times 2 + 1 = 5\neq 0$$
(D) Putting $$x = 2$$ in $$x + 3$$, we get $$2 + 3 = 5\neq 6$$
Thus, the above conditions shows that $$x = 2$$ is the solution of $$x - 2 = 0$$ only.
Question 2
1 / -0

Which of these could be solved by using the sentence $$'A-5'$$?

A
Ishan is $$5$$ times as old as Sanjit. If $$A$$ is Sanjit's age in years, how old is Ishan?

B
Tarun is $$5$$ years younger than Anny. If $$A$$ is Anny's age in years, how old is Tarun?

C
Naman is one-fifth as old as Aman, If $$A$$ is Naman's age, how old is Aman?

D
Geet is $$5$$ years older than Suhana. If $$A$$ is Suhana's age in years, how old is Geet?

Solution

(a) Age of Ishan$$=5A$$
(b) Age of Rarun$$=A-5$$
(c) Age of Aman$$=5A$$
(d) Age of Geet $$=A+5$$
Hence the correct answer is option B.
Question 3
1 / -0

Is this an equation $$21=z+11$$

A
$$Yes$$

B
$$NA$$

C
$$No$$

D
$$15$$

Solution

$$21=z+11$$ is a equation
Question 4
1 / -0

The substraction of 3 from 2x is represent as

A
2x-3

B
3-2x

C
2x+3

D
$$\frac{2x}{3}$$

Solution

Subtraction $$3$$ from $$2x=2x-3$$
Question 5
1 / -0

The subtraction of $$5$$ times of $$y$$ from $$x$$ is

A
$$5x-y$$

B
$$y-5x$$

C
$$x-5y$$

D
$$5y-x$$

Solution

According to question, $$5$$ times of $$y=5y$$
Now, subtraction of $$5$$ times of $$y$$ from $$x$$ is written as $$x-5y$$
Question 6
1 / -0

In algebra, letters may stand for

A
Known quantities

B
Unknown quantities

C
Fixed numbers

D
None of these

Solution

In algebra, letters may stand for 'variables' or unknown quantities.
Question 7
1 / -0

$$x = 5, y = 2$$ is a solution of the linear equation

A
$$x + 2 y = 7$$

B
$$5x + 2y = 7$$

C
$$x + y = 7$$

D
$$5 x + y = 7$$

Solution

$$\textbf{Step 1: Check which of the equation passes through (5,2).}$$

$$\text{The solution should satisfy the appropriate equation.}$$
$$\text{So, let us investigate each option by substituting }x=5$$ & $$y=2$$

$$(A)$$ $$x+2y=7$$.
$$\text{L.H.S. }=5+2\times 2=9\neq$$ $$\text{R.H.S.}$$
$$ \therefore$$ $$\text{It is not the appropriate equation.}$$

$$(B)$$ $$5x+2y=7$$
$$\text{L.H.S. }=5\times 5+2\times 2=29\neq$$ $$\text{R.H.S.}$$
$$\therefore $$ $$\text{It is not the appropriate equation.}$$

$$(C)$$ $$x+y=7$$
$$\text{L.H.S. }=5+2=7=$$ $$\text{R.H.S}$$
$$\therefore$$ $$\text{It is the appropriate equation.}$$

$$(D)$$ $$ 5x+y=7$$
$$\text{L.H.S. }=5\times 5+2=27\neq$$ $$\text{R.H.S.}$$
$$\therefore $$ $$\text{It is not the appropriate equation.}$$

$$\textbf{Hence, option C is correct.}$$
Question 8
1 / -0

The algebraic expression for the statement "Product of $$x$$ and $$a $$ subtracted from the product of $$b$$ and $$y$$'' is

A
$$ax-by$$

B
$$x+a-by$$

C
$$by-ax$$

D
$$xa-b-y$$

Solution

Product of $$ b$$ and $$y$$ = $$by$$ ..... $$(1)$$
Product of $$a$$ and $$x$$ = $$ax$$ .....$$(2)$$

We need $$(1)$$ - $$(2)$$; wiz. $$by-ax$$
Question 9
1 / -0

Convert this statement in mathematical form.
The number is $$8$$ greater than $$80.$$

A
$$x+8=80$$

B
$$x-8=80$$

C
$$8x=80$$

D
$$x=80\times8$$

Solution

Let the number be $$x$$. Here, the given statement is the number is $$8$$ greater than $$80$$.

The word 'greater than' suggests addition. So, the verbal expression the number is $$8$$ greater than $$80$$ can be represented by the algebraic expression:

$$x=80+8\\ \Rightarrow x-8=80$$

Hence, the statement the number is $$8$$ greater than $$80$$ can be rewritten as $$x-8=80$$.
Question 10
1 / -0

$$6$$ more than twice the number is $$ 22$$. Express the statement in mathematical form.

A
$$2x+6=22$$

B
$$2x-6=22$$

C
$$2x+22=6$$

D
$$2x-22=6$$

Solution

Let the number be $$x.$$

Twice the number $$=2x$$
Six more than $$2x$$ will be $$6+2x.$$
This is equal to $$22.$$

Hence, the answer is $$6+2x=22.$$

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Algebra Test - 10

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Algebra Test - 10

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Question 1

$$x + 2 = 5$$

$$x - 2 = 0$$

$$2x + 1= 0$$

$$x + 3 = 6$$

Solution

Question 2

Ishan is $$5$$ times as old as Sanjit. If $$A$$ is Sanjit's age in years, how old is Ishan?

Tarun is $$5$$ years younger than Anny. If $$A$$ is Anny's age in years, how old is Tarun?

Naman is one-fifth as old as Aman, If $$A$$ is Naman's age, how old is Aman?

Geet is $$5$$ years older than Suhana. If $$A$$ is Suhana's age in years, how old is Geet?

Solution

Question 3

$$Yes$$

$$NA$$

$$No$$

$$15$$

Solution

Question 4

2x-3

3-2x

2x+3

$$\frac{2x}{3}$$

Solution

Question 5

$$5x-y$$

$$y-5x$$

$$x-5y$$

$$5y-x$$

Solution

Question 6

Known quantities

Unknown quantities

Fixed numbers

None of these

Solution

Question 7

$$x + 2 y = 7$$

$$5x + 2y = 7$$

$$x + y = 7$$

$$5 x + y = 7$$

Solution

Question 8

$$ax-by$$

$$x+a-by$$

$$by-ax$$

$$xa-b-y$$

Solution

Question 9

$$x+8=80$$

$$x-8=80$$

$$8x=80$$

$$x=80\times8$$

Solution

Question 10

$$2x+6=22$$

$$2x-6=22$$

$$2x+22=6$$

$$2x-22=6$$

Solution

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