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
(b) Standard deviation of 1, 2, 3,………n is 1
(Choose the correct answer)
(c) If A is a certain event, what will be the value of P (A). 1
(d) If r is the correlation coefficient, then justify your answer whether 1
is possible(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(f) Define a Skew Symmetric matrix and give an example. 1
(g) 
say true or false. 1
say true or false. 1(h) Which of the following average may have more than one value?
- GM
- AM
- Median
- Mode
2. Answer the following questions: 2x5=10
- A coin and a dice are thrown successively. Write down the sample space obtained.
- Write any two properties of a determinant.
- If A.M. of
is 19, find the value of
.
- Find
and
if
- If
then find
.
3. If
Find
4. Show that:
Or
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
8. Given
And
Find
Or
Given
Show that
9. Using mathematical induction prove any one of the following: 5
10. Draw the graph (any one): 5
11. Find the coefficient of term involving
in the expansion
in the expansion
Or
Find
correct to 5 decimal places.
correct to 5 decimal places. 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 |
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
2Prove that
(b) Find the mode: 1
7, 9, 6, 8, 11, 9, 12, 6, 7, 9
(c) Find Karl Pearson’s Correlation Coefficient 5
X: | 2 | 4 | 5 | 6 | 8 | 11 |
Y: | 18 | 12 | 10 | 8 | 7 | 5 |
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
(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
(b) Evaluate: 2
(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
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.