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4.   U is a             set that contains all objects.
                   5.  The                of two sets A and B is the set of elements that are in A, in B, or in both A and B.

              B.   State whether the following statement is True or False.

                   1.   Identity matrix is a square matrix where all the diagonal elements are equal to 1 and all
                       the non-diagonal elements are equal to 0.
                   2.   A variance of zero indicates that all the values in a data set are identical.
                   3.   An inner join is just the intersection of two sets.

                   4.   If a matrix has 2 rows and 3 columns then the order of the matrix is 2 x 3.
                   5.   Transpose of a matrix creates a new matrix with number of rows and columns interchanged.


                                                SECTION B (Subjective Type Questions)
              A.   Short answer type questions.
                                                               1
                   1.   The elements a  of a 3x3 matrix are given by =    (– 3i + j). Write the value of elements a  and a .
                                                                                                 21
                                                                                                       32
                                    ij
                                                               2
                   2.   Multiply the following matrices:
                            1   2     3       2     2
                           
                       A =−1     4  −2    B =     1  0  
                           
                            2   0     5       5  −   1
                                                   
                   3.   Calculate the cross products of vectors a = (3, 4, 2) and b = (4, 3, 2).
                   4.   Given that u = (4, 9, 2) and v = (–2, 5, 0), calculate u.v and v.u.
                   5.   Explain the concept of Cartesian Product in relational algebra.

              B.   Long answer type questions.

                   1.   Explain any two similar operations in set theory and relational algebra with examples.
                   2.   Find the standard deviation of the average temperatures recorded over a five-day period last winter: 18, 22, 19, 10, 12.
                   3.   Find the inverse of the following matrices:
                                         1 00 
                                        
                                       
                                        1 00 
                           
                                        
                            4 3
                                              0 
                                         1 1
                                       
                          
                       P =  4 3     S =  1 1  0  
                                        
                           
                            8 7      1 1 1 
                           8 7        1 1 1 
                   4.   Find the mean, mode and median of the following data:
                       7, 16, 12, 35, 51, 10, 80, 71, 16, 9, 11, 16
                   5.   A survey on the heights (in cm) of 50 girls of class XI was conducted at a school and the following data was obtained:
                      Height (cm)     120-130      130-140     140-150      150-160      160-170        Total
                    Number of girls      4            6           12           20           8            50
                   Find the mode and median of the above data.
              C.   Competency-based/Application-based questions:
                   1.     In a city there are two factories A and B. Each factory produces toys for boys and girls. There are three types of
                       toys produced in both the factories, type I, II and III (manual, electric, remote controlled). For boys the number of
                       toys of types I, II and III respectively are 80, 70 and 65 in factory A and 85, 65 and 72 are in factory B. For girls the
                       number of units of types I, II and III respectively are 80, 75, 90 in factory A and 50, 55, 80 are in factory B.

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