2016
COMMERCIAL MATHEMATICS AND STATISTICS
Full Marks: 100
Pass Marks: 30
Time: 3 hours
The figures in the margin indicate full marks for the questions
- If
then find
.
- If
, express A is tabular form.
- Evaluate:
- Which measure of average is very much affected by extreme values?
- Define scalar matrix with an example.
- Write the 5th term of the following expansion:
- The harmonic mean of 36 and 9 is _____. (Fill in the blank)
- If any two rows of a determinant are interchanged, then the value of the determinant
- Remains unchanged.
- Becomes double.
- Changes by minus sign.
- None of the above.
(Choose the correct answer)
2. Answer the following questions: 2x5=10
- If
then find the value
.
- Using property of determinant, prove that
- A man travelled 40 km at 5 km per hour and then 32 km at 8 km per hour. Find his average speed.
- Find mean deviation about the median of the following data:
Marks: 31, 39, 40, 29, 35
- In the determinant given below, what are the minor and cofactor of the element
?
3. Form a matrix of order
where
3
where 34. The arithmetic mean of samples of sizes 50 and 75 are 75 and
respectively. If the arithmetic mean of 125 observations of both the samples taken together is 66, then find
. 3
respectively. If the arithmetic mean of 125 observations of both the samples taken together is 66, then find. 35. Prove that:
3Or
Solve: 3
6. A person borrowed Rs. 7,500 at the rate of
p.a. SI. After 3 years 6 months he paid Rs. 6,485 and a radio, and cleared up the entire amount to be returned. What is the price of the radio? 3
p.a. SI. After 3 years 6 months he paid Rs. 6,485 and a radio, and cleared up the entire amount to be returned. What is the price of the radio? 37. Two dice are thrown simultaneously. Find the probability of getting an odd number on one die and an even number on the other. 3
8. If 2+2+1=5
Then find
Or
If
5
5 Then prove that
9. Using the mathematical induction, prove any one of the following: 5
10. Draw the graph of any one of the following inequalities: 5
11. If the coefficient of
in
be 160, then find the value of
. 5
inbe 160, then find the value of. 5Or
Prove that the middle term of the expansion
is
is 
12. A committee of 6 is to be formed out of 7 men and 4 ladies. In how many ways can the committee be formed, if it includes –
- At least of 2 ladies;
- At most of 2 ladies? 5
13. Manish buys of bike by giving Rs. 15,000 cash and the balance in 15 equal annual installments of Rs. 10,000 each. If the rate of interest is 16% p.a. compounded annually, how much he should have paid, if he had bought it cash down? 5
Or
The difference between simple and compound interest on a certain sum of money for 3 years @ 5% p.a. is Rs. 76.25. Find the sum, simple interest and the compound interest. 5
14. A computer while calculating
between two variables
and
obtained the following results:
between two variablesandobtained the following results: 
It was however discovered at the time of checking that two pair of observations were not correctly copied. These were taken as
and
, while the correct values were
and
. Find the correct value of
. 5
and, while the correct values wereand. Find the correct value of. 515. (a) Define a sinking fund.
(b) Write down the formula for calculating present value of an immediate annuity if interest is compounded quarterly, stating the meaning of the symbols used.
(c) A washing machine was purchased 3 years ago for Rs. 31,250 and now its depreciated value is Rs. 16,000. Find the rate percent of depreciation. 2+1+5=8
16. (a) Find the arithmetic mean and standard deviation from the data given below: 4+4=8
Weight (kg): | 10-12 | 12-14 | 14-16 | 16-18 | 18-20 | 20-22 | 22-24 |
No. of Items: | 7 | 15 | 18 | 20 | 25 | 10 | 5 |
Or
(b) (1) The mean and standard deviation of a series of 20 items were calculated as 20 kg and 5 kg respectively. But while calculating an item 13 was misread as 30. Find the correct standard deviation. 4
(2) Find the mode of the distribution given below: 4
Family Expenditure (Rs.) | 40-59 | 60-79 | 80-99 | 100-119 | 120-139 |
No. of families: | 25 | 130 | 250 | 70 | 25 |
17. (a) If standard deviation of
be
, then SD of
will be _____. (Fill in the blank) 1
be, then SD ofwill be _____. (Fill in the blank) 1(b) Standard deviation is 5/6 times of quartile deviation. (Write True or False) 1
(c) Show that: 
2
2(d) From the data given below, find the coefficient of quartile deviation: 4
Class Interval: | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |
Frequency: | 2 | 10 | 25 | 16 | 7 |
18. (a) Evaluate: 
1
1(b) In which of the following two cases mode is used? 1
- Sale of ready-made garments.
- Intelligence of students in a class.
(c) 2 cards are drawn simultaneously from a pack of cards. Find the probability of obtaining –
- 1 spade and 1 heart;
- 2 cards of the same colour. 3+3=6
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