Grade 11 : Mathematics - Sets (Set 4) | Concept of Maths

Question 1

1. Two sets \(A\) and \(B\) have \(m\) and \(n\) elements respectively. If the total number of subsets of \(A\) is 48 more than the total number of subsets of \(B\), then the values of \(m\) and \(n\) are:

A) \(m = 7, n = 6\)

B) \(m = 6, n = 3\)

C) \(m = 6, n = 4\)

D) \(m = 5, n = 2\)

Answer

Correct Answer: C

Question 2

2. In a survey of 100 students, 40 like Mathematics, 35 like Physics, and 30 like Chemistry. 15 like Math and Physics, 12 like Physics and Chemistry, 10 like Math and Chemistry, and 5 like all three. How many students like none of these subjects?

A) 23

B) 27

C) 15

D) 32

Answer

Correct Answer: B

Question 3

3. If \(U = \{1, 2, 3, \dots, 10\}\), \(A = \{x \in U : x \text{ is a prime number}\}\), and \(B = \{x \in U : x \text{ is a factor of 12}\}\), find \((A \cap B)'\).

A) \(\{1, 4, 6, 8, 9, 10\}\)

B) \(\{2, 3\}\)

C) \(\{5, 7, 1, 4, 6\}\)

D) \(\{1, 4, 5, 6, 7, 8, 9, 10\}\)

Answer

Correct Answer: D

Question 4

4. Let \(A = \{x \in \mathbb{R} : x^2 - 5x + 6 = 0\}\) and \(B = \{x \in \mathbb{R} : x^2 - 7x + 12 = 0\}\). What is the Symmetric Difference \(A \Delta B\)?

A) \(\{2, 4\}\)

Question 5

5. If the Cartesian product \(A \times B\) consists of 6 elements and three of them are \((1, 4), (2, 6), (3, 4)\), then the set \(B\) is:

A) \(\{1, 2, 3\}\)

B) \(\{4, 5, 6\}\)

C) \(\{4, 6\}\)

D) \(\{1, 4, 6\}\)

Answer

Correct Answer: C

Question 6

6. Consider the intervals \(A = (-3, 5]\) and \(B = [2, 8)\). The intersection \(A \cap B\) is represented as:

A) \((-3, 8)\)

B) \([2, 5]\)

C) \((2, 5)\)

D) \([2, 5)\)

Answer

Correct Answer: B

Question 7

7. Let \(S = \{x \in \mathbb{Z} : \frac{x+2}{x-1} \in \mathbb{Z}\}\). How many elements are in the set \(S\)?

A) 2

B) 3

C) 5

D) 4

Answer

Correct Answer: D

Accepted Answer

Correct Answer: A

Grade 11 : Mathematics - Sets (Set 4) | Concept of Maths

Grade 11 : Mathematics - Sets (Set 4) | Concept of Maths

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5. If the Cartesian product \(A \times B\) consists of 6 elements and three of them are \((1, 4), (2, 6), (3, 4)\), then the set \(B\) is:

6. Consider the intervals \(A = (-3, 5]\) and \(B = [2, 8)\). The intersection \(A \cap B\) is represented as:

7. Let \(S = \{x \in \mathbb{Z} : \frac{x+2}{x-1} \in \mathbb{Z}\}\). How many elements are in the set \(S\)?

Grade 11 : Mathematics - Sets (Set 4) | Concept of Maths

1. Two sets \(A\) and \(B\) have \(m\) and \(n\) elements respectively. If the total number of subsets of \(A\) is 48 more than the total number of subsets of \(B\), then the values of \(m\) and \(n\) are:

2. In a survey of 100 students, 40 like Mathematics, 35 like Physics, and 30 like Chemistry. 15 like Math and Physics, 12 like Physics and Chemistry, 10 like Math and Chemistry, and 5 like all three. How many students like none of these subjects?

3. If \(U = \{1, 2, 3, \dots, 10\}\), \(A = \{x \in U : x \text{ is a prime number}\}\), and \(B = \{x \in U : x \text{ is a factor of 12}\}\), find \((A \cap B)'\).

4. Let \(A = \{x \in \mathbb{R} : x^2 - 5x + 6 = 0\}\) and \(B = \{x \in \mathbb{R} : x^2 - 7x + 12 = 0\}\). What is the Symmetric Difference \(A \Delta B\)?

Grade 11 : Mathematics - Sets (Set 4) | Concept of Maths

Grade 11 : Mathematics - Sets (Set 4) | Concept of Maths

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5. If the Cartesian product \(A \times B\) consists of 6 elements and three of them are \((1, 4), (2, 6), (3, 4)\), then the set \(B\) is:

6. Consider the intervals \(A = (-3, 5]\) and \(B = [2, 8)\). The intersection \(A \cap B\) is represented as:

7. Let \(S = \{x \in \mathbb{Z} : \frac{x+2}{x-1} \in \mathbb{Z}\}\). How many elements are in the set \(S\)?