# COMMERCIAL MATHEMATICS AND STATISTICS: 2017

2017
(COMMERCIAL MATHEMATICS AND STATISTICS)
Full Marks: 100
Pass Marks: 30
Time: 3 hours
The figures in the margin indicate full marks for the questions
1. (a) In the determinant given below, find the cofactor of the element – 7. 1
Solution:
(b) Standard deviation of 1, 2, 3,………n is 1

Ans.
(c) If A is a certain event, what will be the value of P (A). 1
Ans: 1 (one)
(d) If r is the correlation coefficient, then justify your answer whether 1
is possible
Ans. Possible, because r is less than – 1
(e) If “is divisible by 5” is a mathematical statement says whether is true or false. 1
Ans: True
(f) Define a Skew Symmetric matrix and give an example. 1
Ans. A square matrixis said to be skew symmetric if
E.g.
(g) say true or false. 1
Solution:
(h) Which of the following average may have more than one value?
1. GM – GM cannot be calculated when any observation is zero or negative.
2. AM
3. Median – Medium have two value (AM is the best average and SD is the best measure of dispersion)
4. Mode
2. Answer the following questions: 2x5=10
1. A coin and a dice are thrown successively. Write down the sample space obtained.
Solution:
1. Write any two properties of a determinant.
2. If A.M. ofis 19, find the value of.
Solution:
1. Find andif
Solution:
1. If then find.
Solution: Same as 2012 Paper
3. If
Find
Solution:
4. Show that:
Solution: Same as 2014 Paper

Or
Solution:

5. Calculate Mean Deviation about Median and its coefficient from the following data. 3
 Weight (kg): 45 53 36 73 64
Or
Find Quartile Deviation and its coefficient from the following data.
 Marks: 10 13 14 19 28 30 27 17 21
6. The difference in Simple Interest on Rs. 2050 at 4% p.a. and on Rs. 1650 at the same rate and for the same period is Rs. 232. Find the time. 3
7. There are 30 tickers numbered from 1 to 30. 1 ticket is drawn at random. Find the probability that the number on the ticket is divisible by 4 or 5. 3
Solution:
8. Given
And
Find
Solution:
Or
Given
Show that
Solution:
9. Using mathematical induction prove any one of the following: 5
Solution:
Solution:
10. Draw the graph (any one): 5
(ii) Solution: Same at 2013
11. Find the coefficient of term involvingin the expansion
Solution:
Or
Findcorrect to 5 decimal places.
Solution:
12. A machine depreciates at the rate of 10% p.a. If the original value of the machine is Rs. 5810 and its scrap value is Rs. 2250, for how many years was the machine in use. 5
13. The median marks for a group of 100 students having the following distribution is 30. Find the missing frequencies. 5
 Marks Frequency 0-10 10-20 20-30 30-40 40-50 50-60 10 ? 25 30 ? 10

Solution:
 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 10 25 30 10 10
14. A man borrows Rs. 10,000 under the condition that he will repay with compound interest @ 5% p.a. by annual installments of Rs. 1000 each. In how many years will be debt be paid off? 5
15. (a) If 2
Prove that
(b) Find the mode: 1
7, 9, 6, 8, 11, 9, 12, 6, 7, 9
Solution:
(c) Find Karl Pearson’s Correlation Coefficient 5
 X: 2 4 5 6 8 11 Y: 18 12 10 8 7 5

Solution:
 2 4 5 6 8 11 0 2 5 16 4 1 0 4 25 18 12 10 8 7 5 8 2 0 64 4 0 4 9 25 0 0

16. Find Arithmetic Mean and Standard deviation from the data given below: 4+4=8
 Height (cm) No. of students 115-125 125-135 135-145 145-155 155-165 165-175 4 5 6 3 1 1

17. (a) How many words may be formed by using the letters of the word DAUGHTER if the vowels never come together? 5
Solution:
(b) Find who is the more consistent worker – A or B 3
 Worker A Worker B Average time (minutes) Standard Deviation (minutes) 30 6 25 4
18. (a) Prove that: 2
Solution:
(b) Evaluate: 2
Solution:
(c) Two cards are drawn together from a pack of cards at random. Find the probability of drawing. 4
1. 2 red cards.
2. 1 king and 1 queen
Solution:
Or
There are 20 employees in an office out of which 5 are graduates, 3 persons are selected at random. Find the probability of selecting.