12 - Maths - Unit 9 - Discrete Mathematics

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  • 1/20 Questions
    In the set of integers with operation * defined by , the value of  is (1)  25  (2)  15  (3)  10  (4)  5 - ProProfs

    In the set of integers with operation * defined by , the value of  is (1)  25  (2)  15  (3)  10  (4)  5

    • (1)
    • (2)
    • (3)
    • (4)
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About This Quiz

Prepared by, R VISVANATHAN, PG ASST IN MATHS, GHSS, PERIYATHACHUR, TINDIVANAM TK-605651
  ; &nbs p; & www. Padasalai. Net

12 - Maths - Unit 9 - Discrete Mathematics - Quiz

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  • 2. 

    Which of the following are statements? (i)  May God bless you.    (ii)  Rose is a flower. (iii) Milk is white.     (iv)  1 is a prime number (1)  (i), (ii), (iii)    (2)  (i), (ii), (iv)   (3)  (i), (iii), (iv)  (4)  (ii), (iii), (iv)

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (4)
    Explanation
    The correct answer is (4) because statements are sentences that can be either true or false. In this case, options (i), (ii), and (iii) are all statements because they express facts that can be verified. However, option (iv) is not a statement because it is a classification or definition rather than a factual statement. Therefore, the correct answer is (4) because it includes all the statements.

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  • 3. 
    Which of the following is a tautology? (1)    (2)     (3)    (4)   - ProProfs

    Which of the following is a tautology? (1)    (2)     (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (3)
  • 4. 
    Which of the following is not a group? (1)    (2)    (3)    (4)   - ProProfs

    Which of the following is not a group? (1)    (2)    (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (3)
    Explanation
    The given options are (1), (2), (3), and (4). The question asks for the option that is not a group. While options (1), (2), and (4) can be considered as groups since they are enclosed in parentheses, option (3) is not a group as it is not enclosed in parentheses. Therefore, the correct answer is (3).

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  • 5. 
    In the multiplicative group of th roots of unity, the inverse of  is  (1)    (2)    (3)    (4)   - ProProfs

    In the multiplicative group of th roots of unity, the inverse of  is  (1)    (2)    (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (3)
    Explanation
    The multiplicative group of th roots of unity consists of all complex numbers that can be written as e^(2Ï€ik/n), where k is an integer and n is a positive integer. The inverse of a complex number z in this group is the complex number z^(-1), which is equal to e^(-2Ï€ik/n). Therefore, the correct answer is (3).

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  • 6. 

    If a compound statement is made up of three simple statements, then the number of rows in the truth table is (1)  8  (2)  6  (3)  4  (4)  2

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (1)
    Explanation
    A compound statement made up of three simple statements will have 2^3 = 8 possible combinations of truth values for the simple statements. Therefore, the number of rows in the truth table for this compound statement will be 8.

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  • 7. 
    Which of the following is a contradiction? (1)    (2)    (3)    (4)   - ProProfs

    Which of the following is a contradiction? (1)    (2)    (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (4)
  • 8. 
    The order of  in  is (1)  9  (2)  6  (3)  3   (4)  1 - ProProfs

    The order of  in  is (1)  9  (2)  6  (3)  3   (4)  1

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (1)
    Explanation
    The given answer (1) is the correct answer because it follows the order of the numbers given in the question. The numbers are listed in ascending order, starting from 1 and increasing by 3 each time. Therefore, the correct order is 1, 4, 7, 10, and so on. Among the given options, option (1) is the only one that matches this pattern.

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  • 9. 

    A monoid becomes a group if it also satisfies the  (1)  closure axiom  (2)  associative axiom  (3)  identity axiom  (4)  inverse axiom

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (4)
    Explanation
    A monoid becomes a group if it also satisfies the inverse axiom. The inverse axiom states that for every element in the set, there exists an inverse element such that the product of the element and its inverse is equal to the identity element. This means that every element in the group has an inverse element that cancels out its effect when multiplied together. Without the inverse axiom, the monoid would not have the necessary property to be considered a group.

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  • 10. 
    Which of the following is not a binary operation on R (1)    (2)     (3)    (4)   - ProProfs

    Which of the following is not a binary operation on R (1)    (2)     (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (3)
  • 11. 
    The number of rows in the truth table of  is (1)  2  (2)  4  (3)  6  (4)  8 - ProProfs

    The number of rows in the truth table of  is (1)  2  (2)  4  (3)  6  (4)  8

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (2)
  • 12. 
    The value of is (1)    (2)    (3)    (4)   - ProProfs

    The value of is (1)    (2)    (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (4)
    Explanation
    The given question does not provide any information or context about what "the value of " is referring to. Therefore, it is impossible to determine the correct answer without additional information.

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  • 13. 
    Which of the following is correct? (1)  An element of a group can have more than one inverse. (2)  If every element of a group is its own inverse, then the group is abelian. (3)  The set of all  real matrices forms a group under matrix multiplication. (4)  for all  - ProProfs

    Which of the following is correct? (1)  An element of a group can have more than one inverse. (2)  If every element of a group is its own inverse, then the group is abelian. (3)  The set of all  real matrices forms a group under matrix multiplication. (4)  for all 

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (2)
    Explanation
    If every element of a group is its own inverse, then the group is abelian. This statement is correct because if every element in a group is its own inverse, it means that for every element a in the group, a * a = e, where e is the identity element. This implies that a * b = b * a for any elements a and b in the group, which is the definition of an abelian group.

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  • 14. 
    In the set of real numbers R, an operation * is defined by . Then the value of  is (1)  5  (2)    (3)  25  (4)  50 - ProProfs

    In the set of real numbers R, an operation * is defined by . Then the value of  is (1)  5  (2)    (3)  25  (4)  50

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (2)
  • 15. 
    In the set of integers under the operation * defined by , then the identity element is (1)  0  (2)  1  (3)  a  (4)  b - ProProfs

    In the set of integers under the operation * defined by , then the identity element is (1)  0  (2)  1  (3)  a  (4)  b

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (2)
  • 16. 
    If p is T and q is F, then which of the following have the truth value T? (i)    (ii)    (iii)    (iv)   (1)  (i), (ii), (iii)   (2)  (i), (ii), (iv)   (3)  (i),(iii),(iv)   (4)  (ii), (iii),(iv) - ProProfs

    If p is T and q is F, then which of the following have the truth value T? (i)    (ii)    (iii)    (iv)   (1)  (i), (ii), (iii)   (2)  (i), (ii), (iv)   (3)  (i),(iii),(iv)   (4)  (ii), (iii),(iv)

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (3)
    Explanation
    If p is T and q is F, then the truth value of (i) is T because it does not depend on q. The truth value of (ii) is F because it depends on q, which is F. The truth value of (iii) is T because it does not depend on q. The truth value of (iv) is T because it depends on p, which is T. Therefore, options (i), (iii), and (iv) have the truth value T.

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  • 17. 
     is equivalent to (1)    (2)    (3)    (4)   - ProProfs

     is equivalent to (1)    (2)    (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (4)
  • 18. 
    The conditional statement  is equivalent to (1)    (2)    (3)    (4)   - ProProfs

    The conditional statement  is equivalent to (1)    (2)    (3)    (4)  

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (3)
  • 19. 
    The order of  in the multiplicative group of  roots of unity is (1)  4  (2)  3  (3)  2  (4)  1 - ProProfs

    The order of  in the multiplicative group of  roots of unity is (1)  4  (2)  3  (3)  2  (4)  1

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (1)
    Explanation
    The order of an element in the multiplicative group of nth roots of unity is equal to n divided by the greatest common divisor of n and the order of the element. In this case, the order of the element is 4, and the greatest common divisor of 4 and 4 is 4. Therefore, the order of the element is 4/4 = 1.

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  • 20. 
    In the multiplicative group of cube root of unity the order of  is (1)  4  (2)   3  (3)  2  (4)  1 - ProProfs

    In the multiplicative group of cube root of unity the order of  is (1)  4  (2)   3  (3)  2  (4)  1

    • (1)

    • (2)

    • (3)

    • (4)

    Correct Answer
    A. (2)
    Explanation
    In the multiplicative group of cube roots of unity, the order of an element refers to the smallest positive integer 'n' such that the element raised to the power of 'n' equals the identity element (which is 1 in this case). The cube roots of unity are 1, ω, and ω^2, where ω is a complex cube root of unity. When we raise ω to the power of 3, we get ω^3 = (ω^2)^2 = 1. Thus, the order of ω is 3. Similarly, the order of ω^2 is also 3. Therefore, the correct answer is (2) 3.

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  • Current Version
  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Dec 08, 2013
    Quiz Created by
    Padasalai12M
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