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Calculate the number of singleton subsets of the set M = {a, b, c, d}.

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Free Superintendent Of Survey And Land Records Practice Questions

Kerala Public Service CommissionRecruitment for Superintendent of Survey and Land Records in Kerala Government Service. The role involves managing survey and land records with a pay scale of ₹50,200 – 1,05,300.Direct recruitment2 vacancies available

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Q1. Calculate the number of singleton subsets of the set M = {a, b, c, d}.

  1. 1
  2. 2
  3. 4
  4. 16

Q2. Which of the following statements correctly defines the empty set?

  1. A set containing all possible elements.
  2. A set that contains no elements.
  3. A set that contains exactly one element.
  4. A set that contains only universal elements.

Q3. Which of the following best defines a finite set in elementary set theory?

  1. A set with no elements.
  2. A set with a countable number of elements.
  3. A set with a limited number of elements.
  4. A set with an infinite number of elements.

Q4. Consider the set S = {x | x is a natural number less than 5}. Which of the following is a singleton set related to S?

  1. {3}
  2. {1, 2}
  3. {}
  4. {5}

Q5. Consider the set A = {2, 4, 6, 8}. Which type of set does A represent?

  1. Infinite set
  2. Empty set
  3. Finite set
  4. Universal set

Q6. Consider the set S = {1, 2, 3, ..., 100}. Which of the following statements is true about S?

  1. Set S is infinite because it contains many elements.
  2. Set S is finite and has 100 elements.
  3. Set S is infinite because it contains natural numbers.
  4. Set S is finite but has an unknown number of elements.

Q7. If A = {a} and B = {b} are singleton sets, under what condition are A and B equal?

  1. When a = b
  2. When a ≠ b
  3. When both sets have the same number of elements
  4. When either a or b is an element of the other set

Q8. Given the universal set \( U = \{a, b, c, d\} \) and a set \( B = \{b, d\} \), what is the complement of the empty set \( \emptyset \) with respect to \( U \)?

  1. \( \emptyset \)
  2. \( U \)
  3. \{a, b, c, d, e\} \)
  4. \{b, d\} \)

Q9. Which of the following best describes the union of two sets A and B?

  1. The set of elements common to both A and B
  2. The set of all elements that are in A, or in B, or in both
  3. The set of elements in A but not in B
  4. The set of elements in B but not in A

Q10. Which of the following sets is an example of an infinite set?

  1. The set of all natural numbers
  2. The set of months in a year
  3. The set of vowels in the English alphabet
  4. The set of days in a week

Q11. Given the sets B = {1, 2, 3} and C = {3, 4, 5}, which of the following correctly describes the union of B and C?

  1. {1, 2, 3, 4, 5}
  2. {3}
  3. {1, 2, 4, 5}
  4. {}

Q12. In a survey, the universal set \( U \) represents all land parcels in a district. If \( A \) is the set of parcels surveyed this year and \( \emptyset \) is the empty set, which of the following statements is always true?

  1. \( A \cup \emptyset = \emptyset \)
  2. \( A \cap \emptyset = A \)
  3. \( A \cup \emptyset = A \)
  4. \( A \cap U = \emptyset \)

Q13. Compare the properties of the empty set and the universal set. Which of the following statements is false?

  1. The empty set is a subset of every set, including the universal set.
  2. The universal set is a subset of every set.
  3. The intersection of the universal set with any set \( A \) is \( A \).
  4. The union of the empty set with any set \( A \) is \( A \).

Q14. If a set A is infinite and a set B is finite, which of the following statements is always true?

  1. The union of A and B is finite.
  2. The union of A and B is infinite.
  3. The intersection of A and B is infinite.
  4. The difference B \ A is infinite.

Q15. Which of the following statements correctly defines when two sets A and B are considered equal?

  1. A and B have the same number of elements.
  2. Every element of A is in B and every element of B is in A.
  3. A is a subset of B.
  4. A and B have no elements in common.
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