2013

H.S. 2nd Year

(COMMERCIAL MATHEMATICS AND STATISTICS)

Full Marks: 100

Time: 3 hours

1. (a) Simplify: 1

(b) For what value of x the matrix 1

Will be singular?

(c) Evaluate: 1

X

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

(e) If SD of be Ïƒ, what will be 1

SD of

(f) Which of the following is affected by extreme values? 1

(i) Arithmetic mean

(ii) Median

(iii) Mode

(g) Write down the formula of amount (A) on principal (P) for (n) years @ r% p.a. compounded monthly. 1

(h) Whether the above statement is true or false? 1

2. Answer the following questions: 2x5=10

(a) If cov (x, y) =0.9, then find the value of r.

(b) Find mean deviation about median of the following data: Wt (kg) 3, 4, 8, 10, 12

(c) In the determinant given below, what are the minor and cofactor of the element – 2?

(d) Find x and y, if

=

(e) Find the weighted AM of 1,2,3,4 with corresponding weights 4, 3, 2, and 1 respectively.

3. Answer any five parts of the following: 3x5=15

(a) If

A = {2, 4, 5, 6}

B = {3, 4, 6, 9, 10}

C = {2, 6, 7, 10}

Find

(i)

(ii)

(b) Form a matrix A of order 3x2, where

(c) Prove that

=

(d) AM and GM of any two positive numbers are 10 and 8 respectively. Find the two numbers.

(e) Two dice are thrown simultaneously. Find the probability of getting an odd number on one dice and an even number on the other.

(f) Each side of a square field is of length 100 meters. A cyclist covers the four sides at speed of 50 meters, 20 meters, 10 meters, and 25 meters per hour respectively. Find his average speed.

4. Prove that: 5

Or

Solve by using Cramer’s rule:

2x – 3y = 5

4y + 5z = 6

6x + 7z =20

5. Using mathematical induction, prove that 5

6. Find the coefficient of in

Or

If in the expansion

The coefficient of is 160, then find the value of K.

7. How many numbers less than 700 may be formed by using the digits 3,4,5,6,7,8? 5

8. Find r from the following data: 5

X : 6 2 10 4 8

Y : 9 11 5 8 7

9. A man deposited Rs. 400 every year in a fund at 3% p.a. compounded annually. After some years he received Rs. 4,064 as amount from the fund. Find the number of years. 5

10. There are 20 pens out of which 5 are defective, 3 pens are picked at random. Find the probability of selecting:

(i) all defective pens;

(ii) exactly I defective pen. 5

Or

2 cards are drawn from a pack of cards. Find the probability of getting 2 cards of same colour.

11. Write down the definition of sinking fund and perpetuity/ The difference between simple and compound interest on a certain sum of money for 3 years at 5% p.a. is Rs. 213.50. Find the principal, simple interest and compound interest. 8

12. (a) Draw the graph of the following linear inequalities. 4+4=8

(i)

Or

(ii)

(b) Prove that

13. (a) From the following data , find and if AM of the following distribution is 72.5 marks :

Marks | No. of Students |

30-39 40-49 50-59 60-69 70-79 80-89 90-99 | 2 3 11 32 7 |

Total =100 |

(b) Write two demerits of mode.

14. (a) If mean deviation for a group of 50 items is 16.2, what will be their SD? 1

(b) Write four properties of a good measure of dispersion. 2

(c) From the following data, find standard deviation and CV. 5

X : | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

Y : | 2 | 7 | 11 | 15 | 10 | 4 | 1 |

Or

Find quartile deviation from the following data:

Height (in cm) | Frequency |

25-35 35-45 45-55 55-65 65-75 | 2 10 25 16 7 |