Friday, March 16, 2018

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

(Choose the correct answer)
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.
  1. All graduates.
  2. Exactly 1 graduate.