- This is an assessment test.
- To draw maximum benefit, study the concepts for the topic concerned.
- Kindly take the tests in this series with a pre-defined schedule.

## Algebra: Linear Equation Test-4

Start

Congratulations - you have completed

*Algebra: Linear Equation Test-4*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

1 yr ago, a mother was 4 times older to her son. After 6 yr. her age becomes more than double her son's age by 5 yr. The present ratio of their age will be

A | 13 : 12 |

B | 3 : 1 |

C | 11 : 3 |

D | 25 : 7 |

Question 1 Explanation:

Let present age of the mother is m & age of her son is s year.

According to question:

(m -1)=4(s-1)

m = 4s-3……………………………………a

& (m+6)=2(s+6)+5

m = 2s + 11………………………………..b

From equation a and b

4s – 3 = 2s +11

s = 7

and m = 25 years

According to question:

(m -1)=4(s-1)

m = 4s-3……………………………………a

& (m+6)=2(s+6)+5

m = 2s + 11………………………………..b

From equation a and b

4s – 3 = 2s +11

s = 7

and m = 25 years

Question 2 |

Students of a class are made to stand in rows. If 4 students are extra in each row, there would be 2rows less. If 4 students are less in each row, there would be 4 more rows. The number of students in the class is

A | 90 |

B | 94 |

C | 92 |

D | 96 |

Question 2 Explanation:

Suppose there are x rows & y students in each row

Then according to question

(x-2)(y+4)=xy &

(x+4)(y-4)=xy ,

Solving these equations

We get x=8 & y=12 then total students=96

Then according to question

(x-2)(y+4)=xy &

(x+4)(y-4)=xy ,

Solving these equations

We get x=8 & y=12 then total students=96

Question 3 |

$ \displaystyle If\,\,\frac{x}{\left( 2x+y+z \right)}=\frac{y}{\left( x+2y+z \right)}=\frac{z}{\left( x+y+2z \right)}=a,\,\,\,then\,\,\,find\,\,\,a,\,\,if\,\,\,x+y+z\ne 0$

A | $ \displaystyle \frac{1}{3}$ |

B | $ \displaystyle \frac{1}{4}$ |

C | $ \displaystyle \frac{1}{8}$ |

D | $l \displaystyle \frac{1}{2}$ |

Question 3 Explanation:

Put x=y=z=1 then a=1/4

Question 4 |

One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and the remaining 15 are on the banks of a river. The total number of cows is

A | 6 |

B | 100 |

C | 63 |

D | 36 |

Question 4 Explanation:

Let total no of cows is x,

then according to question

x-(x/4+2 √x)=15

then 3x-8√x+60=0

Now if we look at the options then we see that there are two answer

options which are perfect square and for the value of √x we need

a perfect square so if the value of x is 100 then the equation will become

3 x 100 – 8 x 10 + 60 = 300 – 80 + 60

which is not equal to zero then the value of x is 36.

then according to question

x-(x/4+2 √x)=15

then 3x-8√x+60=0

Now if we look at the options then we see that there are two answer

options which are perfect square and for the value of √x we need

a perfect square so if the value of x is 100 then the equation will become

3 x 100 – 8 x 10 + 60 = 300 – 80 + 60

which is not equal to zero then the value of x is 36.

Question 5 |

$ \displaystyle The\,\,\,\,value\,\,\,of\,\,\,\left( \frac{1}{{{x}^{2}}} \right)+\left( \frac{1}{{{y}^{2}}} \right),\,\,\,where\,\,x=2+\sqrt{3}\,\,\,\,and\,\,\,y=2-\sqrt{3},\,\,\,is$

A | 14 |

B | 12 |

C | 10 |

D | 16 |

Question 5 Explanation:

$ \displaystyle \begin{array}{l}\frac{1}{{{x}^{2}}}+\frac{1}{{{x}^{2}}}=\frac{1}{{{\left( 2x+\sqrt{3} \right)}^{2}}}+\frac{1}{{{\left( 2-\sqrt{3} \right)}^{2}}}\\=\frac{1}{\left( 7+4\sqrt{3} \right)}+\frac{1}{\left( 7-4\sqrt{3} \right)}\\=\frac{14}{49-16\times 3}=14\end{array}$

Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results

There are 5 questions to complete.

← | List | → |

Return

Shaded items are complete.

1 | 2 | 3 | 4 | 5 |

End |

Return

You have completed

questions

question

Your score is

Correct

Wrong

Partial-Credit

You have not finished your quiz. If you leave this page, your progress will be lost.

Correct Answer

You Selected

Not Attempted

Final Score on Quiz

Attempted Questions Correct

Attempted Questions Wrong

Questions Not Attempted

Total Questions on Quiz

Question Details

Results

Date

Score

Hint

Time allowed

minutes

seconds

Time used

Answer Choice(s) Selected

Question Text

All done

Need more practice!

Keep trying!

Not bad!

Good work!

Perfect!