## Business Statistics & Mathematics B Com Part 1 Guess Paper 2015

__B.Com Part 1 Business Statistics & Mathematics Important Questions with Different variations 2015__

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## Latest Important Questions for 2016

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**Question # 1**

Weights of 175 male students at a university are given in the following frequency table:

**Weight **118-126 127-135 136-144 145-153 154-162 163-171

**Frequency **20 35 49 32 25 14

Calculate: Karl Pearson’s and Bowley’s Coefficient of skewness.

**Or**

**Wages Rs. No. of workers’ Wages Rs No of workers **

117-124 13 145-152 56

124-131 17 152-159 73

131-138 33 159-166 81

138-145 47 166-173 65

173-180 55

180-187 40

187-194 20

**Required:** Calculate Arithmetic Mean, Harmonic Mean, Standard Deviation and Co-efficient of variation

**Or**

The mid-values of a frequency distribution are given as:

**Mid value **115** **125 135 145 155 165 175 185 195

**Frequency **6 25 48 72 116 60 38 22 2** **

Calculate:

**(i)** A.M

**(ii)** Mode

**(iii)** Coefficient of Skewness

**Question # 2**

**X:** 16, 72, 73, 63. 83. 80. 66, 66, 74, 62

**Y:** 40, 52, 43, 49, 61, 58, 44, 58, 50, 45

**Required:** Calculate coefficient of correlation and comment on the answers.

**Or**

The number of units produced by a process (x) and the cost of producing unit (y) were made as:

Find:

**(i)** The coefficient of correlation

**(ii)** The regression equation of y on x

** **

**Question # 3**

Test for Association

**A1 A2 A3**

**B1** 20 15 30

**B2** 30 1B 35

**B3** 35 20 40

(Tabulated value .of chi-square for 4 degrees of freedom at 5% level of significance = 9.488)

**Or**

Test independence of two classifications in the following contingency table at 5% level of significance:

**Attributes A1 A2 A3 A4**

**B1** 42 72 72 72

**B2** 33 62 82 64

**B3** 37 121 93 90

(The table value of Chi-Square is 12.59)

**Or**

A survey of 1600 families was conducted to observe that high and low income people send their children to private and government school. The following results were obtained:

** School**

** Income Private Government Total**

** **High 494 506 1, 000

Low 162 438 600

Total 656 944 1, 600

Test whether income and type of school are independent at 5% level of significance. (Table value is 3.84)

**Question # 4**

A population consists of six numbers 3, 6. 9. 12, 15, and 18. Consider all possible samples of size three numbers, which can be drawn without replacement from this population.

Find:

**(i)**The mean of the population

**(ii) **The standard deviation of the population.

**(iii)** The mean of the sampling distribution of the means.

**(iv) **The standard error

**Question # 5**

Construct index no for 2002 from the following data taking 2000 as base using

**(i)** Laspeyre’s Index Number

**(ii)** Paasche’s Index Number

**(iii) **Fisher’s Index Number.

**Commodity 2000 2002 **

A Price Quaintly Price Quantity

B 5 100 6 120

C 7 120 10 80

D 10 80 12 80

E 4 50 5 60

F 8 70 8 80

**Or**

The following data gives the prices and quantities of various commodities for the year 1995 and 2002:

**Prices (Rs. Per quintal) Quantities (1000 of quintals) **

**Commodity Prices (Rs. Per Quintal) Quantities (1000 of Quintals)**

1995 2002 1995 2002

A 60 80 270 290

B 40 45 125 140

C 20 25 130 140

D 55 70 270 350

Calculate weighted index number of prices for the year 2002 by taking the year 1995 as base year and using formulae recommended by Laspeyre, Fisher, Paache’s and Marshall.

**Or**

Construct index number of Prices with the help of following data by:

**(a)** Laspeyr’s

**(b)** Paasche’s

**(c)** Fisher’s

**(d)** Marshall Edgeworth Formulae

**Commodity Base Year Current Year **

** Price Quantity Price Quantity**

**A** 6 140 8 150

**B** 10 160 12 180

**C** 16 80 20 110

**D** 20 100 24 120

**Or**

Compute index number for 2012 from the following taking 2008 as the base and using formulae recommended by:

**(i)** Lasperyre’s

**(ii)** Paasche’s

**(iii)** Marshall’s and

**(iv) **Fisher’s

** A B C**

**Year Price Qty Price Qty Price Qty **

2008 5.0 80 3.6 90 3.1 20

2012 8.7 100 5.7 95 4.6 30

**Question # 6**

If

Calculate: **(i)** A – 3B **(ii)** AB

**Or**

**Or**

**Question # 7**

Solve the following simultaneous equations

2x + y = – 7

3x+2y = -12

**Or**

Solve the quadratic equation 6×2 – 5x – 6 =0

**Or**

Solve the following: X^{2} + 5x = 50

**Or**

Solve for X the equation:

**Or**

Solve the following system of equations:

9x + 15y = 123

15x + 93y = 201

**Or**

Solve for x and y:

4x – 3y = 10

5x -7y = 6

** **

**Question # 8**

The 54^{th} and 4^{th} terms of an A.P are -61 and 64 respectively. Show that the common difference is – 2.5 and 23 term is 16.5.

**Or**

The first term, of an AP is 5, the last term 45 and the sum 400. Find number of terms and common difference in the series.

**Or**

Show that the sum of the series

0.53 + 0.0053 + — 53 + 0.000053 +…… to infinity is 53/99

**Or**

Show that the sum of geometric series of 6 terms;

1/3, -1/9, 1/27, -1/81 …………… is 182/729

** **

**Question # 9**

Find out the compound amount and compound interest at the end of 3 years on a sum of Rs 20, 000, borrowed at 6 % compounded annually

**Or**

A 90 days Rs. 4, 000. 7% interest bearing note dated April 4, was discounted on May 4, at a discount rate of 8%. What was the discounted value of the note? (Take 360 days in the year)

**Or**

Mohsin had it note tor Rs. 1.5000 with an interest rate of 6%. The note an, dated January 12, 2003 and maturity date was 90 days after date On January 27, 2003, he took the note to his bank, loch discounted it at a discount rate of 7%. How much .did he receive? (Take 360 days in the year)

**Or**

A property changed hands 3 times and at each time the loss to the seller was 10%. If in the last transaction the loss was Rs. 202.50. Find out the original value of the property.

**Or**

The difference between the simple and compound interest on a certain sum is Rs. 31 for three years at 10% p.a. Find out the sum.

**Or**

A company offers two alternatives for the payment of salary for the post of a high executive.

Either one may receive Rs.2,40, 000 per year or Rs. 100 in the first month, Rs.200 in the second month, Rs.400 in the third month and so on. Which of the two alternatives should he prefer?

**Or**

Find the compound interest on Rs.4500 in 3 years. If the rate of interest is 4% for the 1^{st} year, 5% for the 2^{nd} year and 6% for the 3^{rd} year

**Or**

Find the accumulated value of Rs. 5, 000 invested at the end of each quarter for 5 years at 8% compounded quarterly.

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