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
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 matrix
is said to be skew symmetric if
is said to be skew symmetric if
E.g. 
(g) 
say true or false. 1
say true or false. 1
Solution:
(h) Which of the following average may have more than one value?
- GM – GM cannot be calculated when any observation is zero or negative.
- AM
- Median – Medium have two value (AM is the best average and SD is the best measure of dispersion)
- Mode
2. Answer the following questions: 2x5=10
- A coin and a dice are thrown successively. Write down the sample space obtained.
Solution:
- Write any two properties of a determinant.
- If A.M. of
is 19, find the value of
.
Solution:
- Find
and
if
Solution:
- 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 involving
in the expansion
in the expansion
Solution:
Or
Find
correct to 5 decimal places.
correct 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
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
- 2 red cards.
- 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.
- All graduates.
- Exactly 1 graduate.