COMMERCIAL MATHEMATICS AND STATISTICS: 2013

2013

H.S. 2nd Year

(COMMERCIAL MATHEMATICS AND STATISTICS)

Full Marks: 100

Time: 3 hours

The figures in the margin indicate full marks for the questions.

1. (a) Simplify: 1

Solution:

(b) For what value of x the matrix 1

Will be singular?

Solution:

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

Solution:

(e) If SD of

be σ, what will be 1

SD of

Solution:

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

(i) Arithmetic mean

(ii) Median

(iii) Mode

Solution:

AM = Affected
Median = Not affected
Mode = Not affected

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

Solution:

(h)

Whether the above statement is true or false? 1

Solution:

2. Answer the following questions: 2x5=10

(a) If

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

Solution:

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

Solution:


3 4 8 10 12	5 4 0 2 4

Solution:

(d) Find x and y, if

Solution:

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

Solution:

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)

Solution:

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

Solution:

Solution:

(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.

Solution:

(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.

Solution:

4. Prove that: 5

Solution:

Solve by using Cramer’s rule:

2x – 3y = 5

4y + 5z = 6

6x + 7z =20

Solution:

5. Using mathematical induction, prove that 5

Solution:

6. Find the coefficient of

Solution:

If in the expansion

The coefficient of

is 160, then find the value of K.

Solution:

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

Solution:


6 2 10 4 8	0 4 2	0 16 16 4 4	9 11 5 8 7	1 3 0	1 9 9 0 1	0 0

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.

Solution:

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

Solution:

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)

Solution:

x	6	4	2
Y	2	3	4
x	1	0	2
Y	0	1	-1

Diagram

$D:\Logo\Statistics Graph\Untitled-3 copy.jpg$

(ii)

Solution:

x	5	0	10
Y	0	3	-3
x	2	1	3
Y	0	2	-2

$D:\Logo\Statistics Graph\Untitled-4 copy.jpg$

(b) Prove that

Solution:

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

Solution:

Marks
29.5 – 39.5 39.4 – 49.5 49.5 – 59.5 59.5 – 69.5 69.5 – 79.5 79.5 – 89.5 89.5 – 99.5	2 13 11 32 7	34.5 44.5 54.5 64.5 74.5 84.5 94.5	0 10 20 30	0 1 2 3	0 32 21
	100