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## Algebra Level 2 Test 7

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Question 1 |

Each member of the picnic party contributed twice as many rupees as the total number of the members and the total collection was Rs. 3402. How many members are there in that party?

20 | |

30 | |

38 | |

39 |

Question 1 Explanation:

It is a very simple question

Give that each member of the picnic party contributed

twice as many rupees

So let number of members of picnic party = p

Contributed money twice i.e. = 2p

Given that the collection = Rs. 3402

2p

P

p = 39

Therefore, the total number of members in the party is 39

Give that each member of the picnic party contributed

twice as many rupees

So let number of members of picnic party = p

Contributed money twice i.e. = 2p

Given that the collection = Rs. 3402

2p

^{2 }= 3402P

^{2}= 1521p = 39

Therefore, the total number of members in the party is 39

Question 2 |

If a + b + c = 0 then what will be the value of {a

^{2}/(a^{2}â€“ bc)} + {b^{2}/(b^{2}â€“ ac)} + {c^{2}/(c^{2}â€“ ba)}2 | |

4 | |

1 | |

0 |

Question 2 Explanation:

a + b + c = 0

so if we have three values suppose -1 ,-2, 3 respectively for a, b, c

then by putting all values in the given expression we will get the answer as option number (a)

but note that the sum of a + b+ c should be equal to 0

In general we have the expression

{a

If a + b + c = 0

Then a

So from these equations you can also get the answer as option number (a) i.e. 2

so if we have three values suppose -1 ,-2, 3 respectively for a, b, c

then by putting all values in the given expression we will get the answer as option number (a)

but note that the sum of a + b+ c should be equal to 0

In general we have the expression

{a

^{2}/(a^{2}â€“ bc)} + {b^{2}/(b^{2}â€“ ac)} + {c^{2}/(c^{2}â€“ ba)}If a + b + c = 0

Then a

^{2 }= (b +c )^{2}or a = (-b â€“ c)So from these equations you can also get the answer as option number (a) i.e. 2

Question 3 |

If (a â€“ 8) = b then determine the value ofÂ |a â€“b|- |b â€“a|

16 | |

0 | |

4 | |

2 |

Question 3 Explanation:

Simply put the value of b in the mode

We get |a â€“ (a-8)| - |(a â€“ 8) â€“ a|

So we get

8 - |-8|

0

Hence option (b) is the right answer

We get |a â€“ (a-8)| - |(a â€“ 8) â€“ a|

So we get

8 - |-8|

0

Hence option (b) is the right answer

Question 4 |

The least value of 3

^{x}+ 3^{-x}isGreater than equal to Â 2 | |

Less than 1 | |

0 | |

2/3 |

Question 4 Explanation:

Let us check with the lowest value i.e 0

IfÂ x = 0

Then the expression will become

3

= 1 +1 = 2

IfÂ x = 0

Then the expression will become

3

^{0}+ 3^{-0}= 1 +1 = 2

Question 5 |

If (a+1/a)

^{2}= 3 , then what will be the value of a^{3}+1/a^{3}?27 | |

0 | |

343 | |

81 |

Question 5 Explanation:

(a+1/a)

a

= (a+1/a)

=Â (a +1/a) [(a +1/a)

On solving we have answer option (b)

^{2}= 3a

^{3}+1/a^{3 }= (a+1/a)

^{3}â€“ 3(a +1/a)=Â (a +1/a) [(a +1/a)

^{2}â€“ 3]On solving we have answer option (b)

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