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5. Which of these is not a valid type of matrix?
a. Column matrix b. Zero matrix
c. Random matrix d. Square matrix

B. Fill in the blanks.
1. The is the most widely used measure of central tendency and is generally considered
the best measure.
2. In models like linear regression or neural networks, the and biases are vectors.
3. join returns all records from the right table, and the matching records from the left table.
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.

C. State whether these statements are 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 3 × 3 matrix are given by = (– 3i + j). Write the value of elements a and a .
ij
2 21 32
2. Add the following matrices and find the transpose of the sum
 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 and 12.

3. Explain how the concept of ‘joins’ helps in combining data from different sources. Give one example also.
4. Find the mean, mode and median of the following data:
7, 16, 12, 35, 51, 10, 80, 71, 16, 9, 11 and 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.

Mathematics for AI 147