2018

COMMERCIAL MATHEMATICS AND STATISTICS

Full Marks: 100

Pass Marks: 30

Time: 3 hours

The figures in the margin indicate full marks for the questions

- Write down the middle term in the expansion ofwhenis an even number.
- If A is a skew-symmetric matrix, then which of the following is true?

- A is a square matrix.
- for.
- The diagonal elements are all equal to zero.
- All of the above.

- If, then find.
- What do you mean by minorof an elementof determinant?
- AM and HM of two numbers are 10 and 6.4 respectively. Find their GM.
- Fill in the blanks: Mode + _____ = 3 Median.
- Find the coefficient of range for the following data

- If standard deviation ofis 10, then what is the standard deviation of

2. Answer the following questions: 2x5=10

- At what rate of S.I. pa will Rs. 1,500 produce the same interest in 5 years as Rs. 3,125 produce in 3 years at 4% pa?
- If

- In the determinant given below, what are the minor and cofactor of the element ‘3’?

- Find the H. M. of the following series:

- Find the Q. D. (quartile deviation) and Coefficient of Q. D. from following data:

7, 10, 8, 6, 12, 15, 14

3. Compound Interest and Simple Interest on a certain sum of money for 2 years are respectively Rs. 920.25 and Rs. 900. Find the sum and the rate of interest. 3

4. There are 100 students in a class who take at least one of the subjects Commercial Mathematics or Economics. If 75 students take Commercial Mathematics and 60 students take Economics, find the number of students who have taken –

- Both the subjects.
- Only Commercial Mathematics.
- Only Economics. 3

5. Prove that: 3

6. Construct amatrix where 3

7. The mean of 200 observations was 50. Later on, it was found that two observations were misread as 92 and 8 instead of 192 and 88. Find the correct mean. 3

8. Compound Interest for 2nd year on a certain sum at 4% pa is Rs. 25. Find the C.I. for 3rd year. 5

9. What sum will buy an annuity of Rs. 1050 for 4 years, the rate of interest beingpa C. I.? 5

10. Draw the graph of any one of the following inequalities. 5

11. Using mathematical induction prove any one of the following: 5

- for all
- is divisible by 9 for all

12. Find the term independent ofin the expansion of – 5

Or

In the expansion of, the coefficient ofterm is equal to the coefficient ofterm, find.

13. If andfind the values ofand. 5

Or

Ifprove that

14. The following table gives the marks obtained by 100 students. Find the median mark. 5

Marks: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

No. of Students: | 14 | 23 | 27 | 21 | 15 |

15. (a) Prove that: 3+1=4

Use this to prove that

(b) A Polygon has 27 diagonals. Find the number of sides of the Polygon. 4

Or

How many odd numbers of six digits can be formed with the digits 0, 1, 2, 3, 4, 5 each digit occurring only once? 4

16. (a) The mean of five observations is 4.4 and the variance is 8.24. If three of the five observations are 1, 2 and 6, find the other two. 4

(b) Calculate the standard deviation from the data given below: 4

Daily Wages: (in Rs.) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |

No. of Workers: | 3 | 5 | 7 | 10 | 3 | 2 |

17. (a) If a dice and a coin are thrown simultaneously, write down the sample space. 1

(b) What is the probability that a leap year selected at random contains 53 Sundays? 3

(c) A pair of unbiased dice is thrown simultaneously at random. Find the probability of getting. 4

- At least a 6.
- At total of 9 points.

Or

If two cards are drawn at random from a pack of 52 cards, find the probability of drawing – 4

- An Ace and a Queen.
- A Spade and a Heart.

18. (a) What type of correlation exists between the following pairs of variable - 2

Positive / negative / no correlation?

- Atmospheric temperature and sale of woolen garments.
- Colour of Saree and intelligence of lady who wears it.

(b) Calculate Karl Person’s correlation coefficient? 6

X: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Y: | 9 | 8 | 10 | 12 | 11 | 13 | 14 | 16 | 15 |

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