Model Test Paper 4 CMA Foundation Syllabus 2016

Paper 4 – Fundamentals of Business Mathematics andStatistics

Time Allowed: 3 Hours Full Marks: 100

The figures in the margin on the right side indicate full marks.

This question paper has two sections.

Both the sections are to be answered subject to instructions given against each.

Section – A

I.(a) Choose the correct answer (9 × 2 = 18)(1) If 3, x, 27 are in continued proportion then x = _____

(1) If 3, x, 27 are in continued proportion then x = _____

(a) ±6

(b) ±9

(c) ±7

(d) None of these

(2) At what rate p.a. S.I. will a sum of money double itself in 25 years?

(a) 4%

(b) 3%

(c) 5%

(d) 6%

(3) Compute C.I. on ` 2500 for 1 year at 12% compounded six months –

(a) 309

(b) 390

(c) 300

(d) 290

(4) A.M. of two integral numbers exceeds their G.M. by 2 and the ratio of the numbers is 1 : 4.

Find the numbers.(a) 5, 20

(b) 1, 4

(c) 2, 8

(d) 4, 16

(5) Set of even positive integers less than equal to 6 by selector method.

(a) {x/x<6}

(b) {x/x=6}

(c) {x/x≤6}

(d) None

(6) If log

10= 0.3010 log^{2}10= ___________^{2}(a) 0.3322 (b) 3.2320 (c) 3.3222 (d) 5

(7) If np3 = 120 then n = ___

(a) 8 (b) 4 c) 6 (d) None of these(8) If rc12=8 find cr22

(a) 213 (b) 321 (c) 231 (d) None of these

(9) If one roots of the equation x2 – 3x + m = 0 exceeds the other by 5 then the value of M is

equal to ______

(a) -6 (b) -4 (c) 12 (d) 18

I. (b) State whether the following statements are true or false (6 × 1 = 6)(1) If 15% of x = 20% of y then x : y = 4 : 3

(2) If the terms -1 + 2x, 5, 5+x are is an A.P. then x is 4

(3) The statement “Equivalent sets are always equal” is true or false

(4) The logarithm of one to any base is zero

(5) nco = 1 is true of false

(6) The degree of the equation 3×5 + xyz2 + y3 is 3

II. Answer any four questions. Each question carries 4 marks (4 × 4 = 16)(1) Monthly income of two persons Ram and Rahim are in the ratio 5 : 7 and their monthly

expenditure are in the ratio 7 : 11. If each of them saves Rs. 60/months. Find their monthly

income.

(2) Which is better investment – 3% per year compounded monthly (or) 3.2% per simple

interest (given that (1.0025)12 = 1.0304)

(3) Insert 4 arithmetic means between 4 and 324.(4) Prove that

log 3 3 + log 8 -log 125 3

log 6-log 5 2

(5) A question paper is divided into three groups A, B, C which contains 4, 5 and 3 questions

respectively. An examine is required to answer 6 questions taking atleast 2 from A, 2

From B, 1 From C. in how many ways he can answer.(6) Solve 2x-1 + x-½ = 6.

Section – B

III. (a) Choose the correct answer (12 × 2 = 24)(1) If the co-efficient of correlation between x and y is 2/3 and the standard deviation of x is 3 and standard deviation of y is 4, the covariance between x and y will be________

(a) 3

(b) 6

(c) 7

(d) 8(2) Which of the following measures of averages divide the observation into two parts

(a) Mean

(b) Median

(c) Mode

(d) Range(3) The mode for the series 3, 5, 6, 2, 6, 2, 9, 5, 8, 6 is ……………..

(a) 5.1

(b) 5

(c) 6

(d) 8(4) If Median = 12, Q1 = 6, Q3 = 22 then the co-efficient of Quartile Deviation is______

(a) 33.33

(b) 60

(c) 66.67

(d) 70(5) For the observations 6, 4, 1, 6, 5, 10, 4, 8 range is

(a) 10

(b) 9

(c) 8

(d) None(6) Harmonic mean is used for calculating

(a) Average Growth Rate of variables

(b) Average speed of journey

(c) Average rate of increase in net worth of a company

(d) All the above 1 to 3(7) For the regression equation of Y on X, 2x + 3y + 50 = 0. The value of bxy is

(a) 2/3

(b) -2/3

(c) -3/2

(d) None(8) Two regression lines coincide when

(a) r=0

(b) r = 2

(c) r = +1 or -1

(d) None(9) x =

31/6 –y/6 is the regression equation of(a) y on x

(b) x on y

(c) both

(d) none

(10) If an unbiased coin is tossed twice, the probability of obtaining at least one tail is

(a) 0.25

(b) 0.50

(c) 0.75

(d) 1.00

(11) Two dice are thrown together. The probability that „the event the difference of nos.

shown is 2‟ is

(a) 2/9

(b) 5/9

(c) 4/9

(d) 7/9

(12) If y = a + bx, then what is the co-efficient of correlation between x and y?

(a) 1

(b) -1

(c) 1 or -1 according as b > 0 or b < 0

(d) None of these

III. (b) State whether the following statements are true or false (12 × 1 = 12)(1) Harmonic mean is based on all the items in a series

(2) Median is a mathematical averag

(3) Co-efficient of variation = Co-efficient of variation/Mean×100

(4) Range is the value of difference between mode and median

(5) If a coin is tossed, then probability of getting two heads is zero

(6) If an unbiased coin is tossed once, then the two events head and tail are mutually exclusive

(7) 10th Percentile is equal to 9th Decile.

(8) Mean deviation can never be negative

(9) The value of correlation co-efficient lies between 0 & 1

(10) Bivariate data are the data collected for two variables

(11) When all value s are equal, then standard deviation would be zero

(12) As the sample size increase, range tends to decrease

IV.Answer any four questions. Each question carries 6 marks(4 × 6 = 24)

(1) Draw histogram and frequency polygon of the following data:

Wages (Rs.)50-5960-6970-7980-8990-99100-109110-119No. of Employees81016141052

(2) Find the median and median-class of the data given below:

Class-boundariesFrequency15-25425-351135-451945-551455-65065-752

(3) The marks obtained by 6 students were 24, 12, 16, 11, 40, 42. Find the Range. If the highestmark is omitted, find the percentage change in the range.

(4) Compute rank correlation from the following table

X415434420430424428Y330332328331327325

(5) Given:Covariance between X and Y = 16 ,Variance of X = 25 ,Variance of Y = 16(i) Calculate co-efficient of correlation between X and Y,

(ii) If arithmetic means of X and Y are 20 and 30 respectively, find regression equation of Y on X.

(iii) Estimate Y when X = 30.

(6) What is the chance that a leap year, selected at random will contain 53 Sundays?