- 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: Functions Test-4

Start

Congratulations - you have completed

*Algebra: Functions 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 |

The following functions have been defined:
$ \displaystyle \begin{array}{l}la\,\,\left( x,y,z \right)\,=\min \,\left( x+y,y+z \right)\\le\,\,\left( x,y,z \right)\,=\max \,\left( x-y,y-z \right)\\ma\,\,\left( x,y,z \right)\,=\left( 1/2 \right)\,\left[ le\,\left( x,y,z \right)+la\,\left( x,y,z \right) \right]\end{array}$

For x = 15, y = 10 and z = 9, find the value of : le (x, min (y,x - z), le (9, 8, ma (x, y, z)))

For x = 15, y = 10 and z = 9, find the value of : le (x, min (y,x - z), le (9, 8, ma (x, y, z)))

A | 5 |

B | 12 |

C | 9 |

D | 4 |

Question 1 Explanation:

Segregating and simplifying,

ma (15, 10, 9)= 1/2 [{le (15,10,9)}+(la (15,10,9)}]

=1/2 [{max (5,1)}+(min (25,19)}]

=1/2 [5+19]

=12

le (x, min (y,x - z), le (9, 8, 12))

= le (15, min (10,6), le (9, 8, 12))

= le (15, 6, max(1,-4))

= le (15, 6,1)

= max (9,5)

= 9

ma (15, 10, 9)= 1/2 [{le (15,10,9)}+(la (15,10,9)}]

=1/2 [{max (5,1)}+(min (25,19)}]

=1/2 [5+19]

=12

le (x, min (y,x - z), le (9, 8, 12))

= le (15, min (10,6), le (9, 8, 12))

= le (15, 6, max(1,-4))

= le (15, 6,1)

= max (9,5)

= 9

Question 2 |

The following operations are defined for real numbers a # b = a + b if a and b both are positive else a # b = 1 .aâˆ‡b = (ab)

^{a+ b}if ab is positive else aâˆ‡b = 1. (2 # 1)/(1âˆ‡2) =A | 1/8 |

B | 1 |

C | 3/8 |

D | 3 |

Question 2 Explanation:

Segregating and simplifying,

(1âˆ‡2)

= (1 x 2)

= (2)

=8 .

2#1= 2+1, since both are positive.

=3

Therefore the value of the given expression is 3/8.

(1âˆ‡2)

= (1 x 2)

^{1+ 2}, since both are positive.= (2)

^{3}=8 .

2#1= 2+1, since both are positive.

=3

Therefore the value of the given expression is 3/8.

Question 3 |

The following operations are defined for real numbers a # b = a + b if a and b both are positive else a # b = 1 .aâˆ‡b = (ab)<sup>a+ b</sup> if ab is positive else aâˆ‡b = 1.
{((I # 1) # 2) - (10<sup>1.3</sup>Â âˆ‡log<sub>10</sub> 0Â·1)}/(1âˆ‡2) =

A | 3/8 |

B | 4log _{10}0Â·1/8 |

C | (4+10 ^{1.3})/8 |

D | None of these |

Question 3 Explanation:

Segregating and simplifying,

{((I # 1) # 2) - (10

={((I # 1) # 2) - (10

={((I # 1) # 2) - (10

={((I # 1) # 2) - 1}/(8)

={(2 # 2) - 1}/(8)

={4 - 1}/(8)

=3/8

{((I # 1) # 2) - (10

^{1.3}Â âˆ‡log_{10}0Â·1)}/(1âˆ‡2)={((I # 1) # 2) - (10

^{1.3}Â âˆ‡log_{10}0Â·1)}/(8)={((I # 1) # 2) - (10

^{1.3}Â âˆ‡-1)}/(8)={((I # 1) # 2) - 1}/(8)

={(2 # 2) - 1}/(8)

={4 - 1}/(8)

=3/8

Question 4 |

The following operations are defined for real numbers a # b = a + b if a and b both are positive else a # b = 1 .aâˆ‡b = (ab)<sup>a+ b</sup> if ab is positive else aâˆ‡b = 1.
. ((X # - Y)/(- Xâˆ‡Y)) =3/8, then which of the following must be true ?

A | X = 2, Y= 1 |

B | X> 0, Y< 0 |

C | X, Y both positive |

D | X, Y both negative |

Question 4 Explanation:

Checking by options:

a) doesn't satisfy. Incorrect option

b) Absolutely possible since for no real value of x denominator would be able to take 8/3 as

it is expressed as (ab)

positive which can happen only when y <0.Â Correct option. Checking other.

c) X, Y both positive, doesnâ€™t satisfy. Incorrect option

d) X, Y both negative. Then both numerator and denominator is 1.

a) doesn't satisfy. Incorrect option

b) Absolutely possible since for no real value of x denominator would be able to take 8/3 as

it is expressed as (ab)

^{a+b}but x+y can take a positive value 3/8 if both arepositive which can happen only when y <0.Â Correct option. Checking other.

c) X, Y both positive, doesnâ€™t satisfy. Incorrect option

d) X, Y both negative. Then both numerator and denominator is 1.

Question 5 |

If x and yare real numbers, the functions are defined as f(x, y) = I x + Y I, F (x, y) = - f (x, y) and G (x, y) = - F (x, y). Now with the help of this information answer the following questions:
Which of the following will be necessarily true

A | G( f(x, y), F (x, y))> F (f(x, y), G (x, y)) |

B | F (F (x, y), F (x, y)) = F (G (x, y), G (x, y)) |

C | F (G (x, y), (x + y) â‰ G (F (x, y), (x - y))) |

D | f (f(x, y), F (x - y)) = G (F (x, y),f (x - y)) |

Question 5 Explanation:

Take some values of x and y and put in the given expression find which satisfies the answer choices.
Going by option elimination.
(a) will be invalid when$ \displaystyle x+y=0$
(b) is the correct option as both sides $ \displaystyle -2\,\left| \,\,x+y\,\,\, \right|$as the result.
(c) will be equal when$ \displaystyle \left( x+y \right)=0$
(d) is not necessarily equal (plug values and check)

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!