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Arithmetic Aptitude :: Algebra Problems

  1.  The absorption law is defined as

  2. A.

    a * ( a ⊕ b ) = a

    B.

    a  * ( a * b ) = b

    C.

    a * ( a ⊕ b ) = b

    D.

    a * ( a * b ) = a ⊕ b

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  3.  A partial order is deined on the set S = {x, a1, a2, a3,...... an, y} as x ≤ a i for all i and ai ≤ y for all i, where n ≥ 1. Number of total orders on the set S which contain partial order ≤

  4. A.

    n !

    B.

    1

    C.

    n

    D.

    n + 2

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  5.  Let L be a set with a relation R which is transitive, antisymmetric and reflexive and for any two elements a, b ∈ L. Let least upper bound lub (a, b) and the greatest lower bound glb (a, b) exist.

  6. A.

    L is a Poset

    B.

    L is a lattice

    C.

    L is a boolean algebra

    D.

    none of these

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  7.  On solving 2p - 3q - 4r + 6r - 2q + p, answer will be

  8. A.

    8q -5r

    B.

    7p + 5r

    C.

    3p - 5q + 2r

    D.

    10p + 3q - 5r

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  9.  Is the equation 3(2 x−4) =−18 equivalent to 6x−12 =−18?

  10. A.

    Yes, the equations are equivalent by the Distributive Property of Multiplication over Addition.  

    B.

    Yes, the equations are equivalent by the Commutative Property of Multiplication

    C.

    Yes, the equations are equivalent by the Associative Property of Multiplication. 

    D.

    No, the equations are not equivalent. 

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  11.  √16 + 3√ 8 =

  12. A.

    2

    B.

    4

    C.

    6

    D.

    8

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  13.  Which number does not have a reciprocal?

  14. A.

    -1

    B.

    0

    C.

    1

    D.

    1/1000 

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  15.  What is the multiplicative inverse of 1/2 ?

  16. A.

    -2

    B.

    2

    C.

    -1/2

    D.

    1/2

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  17.  What is the solution for this equation? 2x −3 = 5

  18. A.

    x =−1 or x = 4 

    B.

    x =−1 or x = 3 

    C.

    x =−4 or x = 4 

    D.

    x =−4 or x = 3 

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  19.  What is the solution set of the inequality 5 − x + 4 ≤−3?

  20. A.

    − ≤2 x ≤6

    B.

    − ≤ 12 x ≤ 4

    C.

    x ≤−2 or x ≥6

    D.

    x ≤−12 or x ≥ 4

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