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    Mathematics Entrance Exam

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    husnainkashif375

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    Mathematics Entrance Exam

    Uploaded by

    husnainkashif375
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    3 views3 pages

    Mathematics Entrance Exam

    Uploaded by

    husnainkashif375

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    Mathematics Entrance Exam

    1. Please, classify the following numbers to the right group of numbers. Which ones of the following
    numbers are integer, rational, irrational real numbers?
    
     
    a) . , b) −, c)  , d) , e) , f) , g) 
     h) −
     
    
    Taking into account your solution, what is the correct answer from the followings:

    A.) integers: b), c), h); rationals: b), d) irrational real numbers: a), e), f)
    B.) integers: b), c); rationals: a), b), c), d), g) irrational real numbers: e), f)
    C.) integers: b), c), g); rationals: a), b), c), d), g) irrational real numbers: e), f)
    D.) integers: b), c), g); rationals: a), b), c), d), g) irrational real numbers: e), f), h)

    2. Please, simplify the following mathematical algebraic sentence, and give the final result!

    (∙ ∙ ) ∙ ∙


    ÷ ,  ≠ ,  ≠ .
    (∙ ∙ ) (∙ ∙ )

    What is the result? Choose the correct answer from the following possibilities!

    2
    A.) Result is:
    7
    ∙∙
    2
    B.) Result is:
    7
    C.) Result is: 
    D.) Result is:  ∙ 

    3. Solve the following algebraic equation if  is an integer number!

      
    − =
       

                         ,                       ?

    A.) Result is:  = 


    1
    B.) Results are:  =  and  = −
    2
    1
    C.) Result is:  = −
    2
    D.) Result is: there is no solution for this problem

    1/3 2023. 02. 22. 13:17


    4. Solve the following algebraic system of equation if ,  are both positive real numbers!

     −  = 
     ∙  = 

    Checking your solution, which is the correct answer from the followings:

    A.) there is no solution for this problem


    B.) Results are:  =  and  = 
    5 5
    C.) Results are:  = 2 and  = 2
    D.) Results are:  =  and  = 

    5. If the universal set  = { ǀ       ≤  ≤ } and , ,  are subsets of  such
    that  = { ǀ      } ,  = { ǀ     },  =
    { ǀ       −  +  < 0 }. Please, list the elements of the following
    sets:

     ∩ ,  ∪ ,  ∩ ( ∪ ), \ (difference of sets of  and )

    Choose the correct answer from the followings:

    A.)  ∩  = {; ; 9; 0; ; 3; ; ; 9; 0; },  ∪  = {0},
     ∩ ( ∪ ) = {; ; 9; 0; ; 3; ; ; 9; }, \ = {6; 8; 0; ; 4; 6; 8; 0}

    B.)  ∩  = {; },  ∪  = {; ; 8; 9; 0; ; ; 3; 4; ; 0},
     ∩ ( ∪ ) = {; ; 9; ; 3; }, \ = ∅ ,where ∅ means the empty set.

    C.)  ∩  = {; ; 9; 0; ; 3; ; ; 9; 0; },  ∪  = {0},
     ∩ ( ∪ ) = {; ; 9; 0; ; 3; ; ; 9; }, \ = ∅ , where ∅ means the empty set.

    D.)  ∩  = {; },  ∪  = {; ; 8; 9; 0; ; ; 3; 4; ; 0},
     ∩ ( ∪ ) = {; ; 9; ; 3; }, \ = {6; 8; 0; ; 4; 6; 8; 0}

    6. Give the possible widest domain of the real numbers for the following mathematical sentence:

    √  

    Using your solution, choose the correct answer from the following possibilities:

    A.) Only  is real number and  <  gives solution for the problem mentioned above.
    B.) Only  is real number and 0 <  gives solution for the problem mentioned above.
    C.) Only  is real number and  ≤  gives solution for the problem mentioned above.
    D.) Any  real number gives solution for the problem mentioned above.

    2/3 2023. 02. 22. 13:17



    7. Let  = given. Which are/is correct sentence(s) from the followings regarding
    ( )∙( )
    to .

    A.) In the case of  ∙  if  is any integer real number, the domain of  is an empty set.
    B.) There is  real number, which case  = 0.
    C.) There is  integer number, which case  = 00.
    D.) There is no any  real number, which case the domain of  is an empty set.

    3/3 2023. 02. 22. 13:17

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