Section :A (10*1)

1. The roots of the equation

|x−1 1 1

1 x−1 11 1 x−1

|=0

area. 1,2b. -1,2c. 1,-2d. -1,-2

2. Find the non-zero values of x if

|−x 1 0

1 −x 10 1 −x

|=0

a. ±1 b.±√2 c.±√3 d.−√2 ,√3 .

3. Inverse of a diagonal matrix (if it exists) is a a. Skew symmetric matrix b. Non-invertible matrix c.Diagonal matrix d. None of these

4. The system of equations. x + 2y = 5, 4x + 8y = 20 hasa. A unique solution b.No solution c.Infinitely many solutions d.None of these

5. Which of the following provides a measure of central location for the data?a. standard deviationb. meanc. varianced. range

6. The variance of a sample of 169 observations equals 576. The standard deviation of the sample equalsa.13 b.24 c.576 d.28, 461

7. When data are positively skewed, the mean will usually bea. greater than the medianb. smaller than the medianc. equal to the mediand. positive

8. All correlation coefficients share in common the property that they range between

a) +1 and 0 b) +1.00 and -1.00. c) + 0.1 and –0.1 d) +1.96 and -1.96

9. If a researcher is calculating a correlation coefficient using ranked data, he/she will be finding the: a. Pearson correlation b.Spearman correlation c.Point biserial d.Phi10.

Section B (20*1)

11. If A & B are square matrices of size n x n such that A2 – B2 = (A + B). Then which of the following will be always true?

12. Let A = [5 5α α0 α 3 α0 0 5 ] if |A2|=25 , then |α|=

13. IF A = [0 x 16x 5 70 9 x ]

is singular, then the possible values of x are

14. Let , , and Evaluate the (

15. Find the standard deviation of the following set of numbers. 5, 6, 6, 7, 7, 8, 8, 8, 9, 10

16. Compute the Karl Pearson's coefficient of skewness from the following data:

Height (in inches)5859606162636465Number of Persons101830423 52816817. Compute the Karl Pearson's coefficient of skewness from the followingdata :Daily Expenditure (Rs.) : 0-20 20-40 40-60 60-80 80-100No. of families : 13 25 27 19 1618. The following measures were computed for a frequency distribution :

Mean = 50, coefficient of Variation = 35% and Karl Pearson's Coefficient of Skewness = - 0.25.Compute Standard Deviation, Mode and Median of the distribution.

19. The first four central moments of a distribution are 0,2.5,0.7 and 18.75. Examine the skewness and kurtosis of the distribution.20.The first four moments of a distribution are 1,4, 10 and 46 respectively. Compute the moment coefficients of skewness and kurtosis.21. Find the range, mean deviation for the following sample data: 33, 55, 29, 40, 43, 8, 90, 61, 41, 17, 80, 56, 17, 59, 21, 78.22.Find the Mean Deviation of 3, 6, 6, 7, 8, 11, 15, 1623. Determine the standard deviation of the following student test results percentages.92% 66% 99% 75% 69% 51% 89% 75% 54% 45% 69%24. The results of two tests are shown below. Compare the variability of these data sets.Test 1 (out of 15 marks): x = 9 s = 2Test 2 (out of 50 marks): x = 27 s = 825. To find the Correlation of

X Values Y Values60 3.161 3.662 3.863 465 4.1

26. Find Correlation coefficient for X and Y values are given below X= (1, 2, 3, 4, 5) Y= {11, 22, 34, 43, 56}

27. Given that , find det(A).

28. , find adjB.29. The scores of 6 pupils in two subjects: physics and chemistry are given below. Calculate the coefficient of correlation by the rank difference method also called Spearman rho.

30.Find the Correlation Co-efficient ofX Values Y Values

40 3 42 6 43 9 45 544 3 46 7

Section : C (3*10)

1.The following table shows the grouped data, in classes, for the heights of 50 people.

height (in cm) - classes frequency

120 <- 130 2

130 <- 140 5

140 <- 150 25

150 <- 160 10

160 <- 170 8

a) Calculate the mean of the salaries of the 50 people.

b) Calculate the standard deviation of the salaries of the 50 people.2. calculate the correlation coefficient.

X:1361012Y:5 1325414

3. Calculate the first four moments about mean for the following distribution.Also calculate β1 comment upon the nature of skewness.

Marks : 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 '

Frequency : 8 28 35 17 124. The frequency table of the monthly slaries of 20 people is shown below.

salary(in $) frequency

3500 5

4000 8

4200 5

4300 2

a) Calculate the mean of the salaries of the 20 people.

b) Calculate the standard deviation of the salaries of the 20 people5. Calculate the coefficient of variation for each of the following data sets.(a) Stock prices: 8, 10, 9, 10, 11(b) Test results: 10, 5, 8, 9, 2, 12, 5, 7, 5, 86. Compare the variation of the following data sets.Data set A: 35, 38, 34, 36, 38, 35, 36, 37, 36Data set B: 36, 20, 45, 40, 52, 46, 26, 26, 327. Compute Mean deviation from mean and median from thefollowing data:Heightin cms158 159 160 161 162 163 164 165 166No. of

persons15 20 32 35 33 22 20 10 8Also compute coefficient of mean deviation.

8. Let . Find AB and BA.

9. Let , , and

Evaluate the following :

(a) (b)

(c) (d)

10. Given that , show .

Section :D (6*5=30)

1. Factorize each of the following :

2. Factorize the determinant

3.Prove that 4. Compute the first four central moments following data. Also find thetwo beta coefficients.Value 5 10 15 20 25 30 35Frequency : 8 15 20 32 23 17 55. Calculate mean and Standard Deviation of the following frequency distribution of marks.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70

No. of student

5 12 30 45 50 37 21

6. Find the coefficient of skewness from the data given belowSize : 3 4 5 6 7 8 9 10Frequency: 7 10 14 35 102 136 43 8

7. Find Karl – Pearson’ s coefficient of skewness for the givendistribution:X : 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40F : 2 5 7 13 21 16 8 3