Module - 1

1. If A is a symmetric matrix, then Transpose of A is:

A. -A
B. A
C. 2A
D. 3A

2. The complement of set A, denoted by A', represents the set of elements:

A. Not in set A
B. In both set A and set B
C. In either set A or set B
D. In the universal set

3. If A ⊂ B and B ⊂ C, what can we conclude?

A. A = C
B. C ⊂ A
C. B = C
D. A ⊂ C

4. Which of the following set is finite?

A. X={1, 2, 3, …}
B. X={1,2 3,…, 500}
C. X= {x: x=4n+1, n is a natural number}
D. X= {x: x is a prime number}

5. The set that contains all possible subsets of a given set is called the:

A. Subset
B. Power set
C. Union
D. Intersection

6. Transpose of a row matrix is:

A. Row matrix
B. Column matrix
C. Square matrix
D. Diagonal matrix

7. The set that contains all the elements common to two or more sets is called a:

A. Subset
B. Power Set
C. Union
D. Intersection

8. If two sets have no elements in common, they are said to be:

A. Disjoint Sets
B. Equivalent sets
C. Power sets
D. Complementary sets

9. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is:

A. {1, 2, 3, 4, 5}
B. {1, 2}
C. {3}
D. {4, 5}

10. The rank of a matrix is always less than or equal to:

A. The maximum element in the matrix
B. The sum of the elements in the matrix
C. The minimum element in the matrix
D. The smaller of the number of rows and columns of the matrix

11. The cardinality of the power set of {x: x∈N, x≤10} is ______.

A. 1023
B. 1024
C. 2043
D. 2048

12. In a group of 80 people, 37 like cold drinks and 52 like hot drinks and each person likes at least one of the two drinks. Find How many people like both coffee and tea?

A. 3
B. 9
C. 15
D. 22

13. If A = {x | x is a prime number less than 10} and B = {x | x is an even number less than 10}, what is the intersection of sets A and B?

A. {2, 3, 5, 7}
B. {2}
C. {4, 6, 8}
D. {2, 4, 6, 8}

14. If [2p+q p-2q]=[4 -3], then 3p+4q is:

A. 5 
B. 7
C. 9
D. 11

15. Order of a row matrix is of the form ______.

A. 1 x n
B. n x 1
C. 2 x n
D. n x 2

16. Which of the following is true about the transpose of a matrix product (AB)^T, where A and B are matrices?

A. (AB)^T = A * B
B. (AB)^T = A^T * B^T
C. (AB)^T = B^T * A^T
D. (AB)^T = A^T + B^T

17. The rank of a 3x3 matrix with first row [2 1 3], second row [4 -2 6], and third row [1 5 -1] is:

A. 1
B. 2
C. 3
D. Undefined