Quantitative Techniques Question Paper of MBA Semester 1, Download Question Paper 4

Roll No…….

Total No. of Questions: 07

Paper ID [MB104]

MBA (Sem.-1^st)

QUANTITATIVE TECHNIQUES (MB-104)

Subject Code: MB-104

Time: 3 Hrs.                                                                           Max. Marks: 60

Instruction to Candidates:

1.     Section-A is Compulsory.

2.     Attempt any Four questions from Section-B.

SECTION-A

Q1.    (a) Are the following sets equal A={x ; x is a letter in the word ‘LOYAL’}

                   (b) If log₁₀y=x₂ find the value of 10^2x in terms of y.

                   (c) Without expansion prove that xyz=1,

                   If ­­­­­­­­­­­­­­­­­

                   (d) Using binomial theorem, compute the value of (99).

                   (e) If x₁=50, x₂=27, n₁=9, n₂=5, find the combined mean.

                   (f) Write a note on kurtosis of distribution.

                   (g) Find the chance of a non leap year having 53 Wednesday.

                   (h) If in a Poisson distribution P(I)=P(2), find the value of P(4).

                   (i) Write conditions for the application of x² test.

                   (j) Define probable error of coefficient of correlation.

SECTION-B

Q2.    (a) The present population of a country is 9261000.  If it has been increasing at the rate of 3% annually, using log tables find the population 3 years ago.

          (b) Prove by mathematical induction that n<2”, for all nN.

Q3.    (a) Product of first three terms of a G.P. is 1000. If 6 is added to its second term and 7 added to its third term, it becomes an A.P. Find the G.P.

(b) Score obtained by two batsmen in 10 matches are as follows:

A	30	44	66	62	60	34	80	46	20	38
B	34	46	70	38	55	48	60	34	45	30

Determine who is the most consistent batsman.

Q4.    (a) Find the coefficient of correlation between industrial production and export using

         

Production	55	56	58	59	60	60	62
Export	35	38	38	39	44	43	44

          (b) If  is the angle between two regression lines, then show that

          tan

                   Explain the significance of the formula when r=0, r=1.

Q5.    (a) Fit a straight line trend by least squares method to the following data and calculate short time fluctuations:

         

Year	1985	1986	1987	1988	1989	1990
Production(‘000 tons)	75	83	109	129	134	148

(b) The average whole sale prince in rupees per 20 seers of wheat sold in U.P. is given below. Using 1956 as base year  find the price relatives (simple index numbers) corresponding to all the years.

                   

Year	1953	1954	1955	1956	1957	1958
Price	14.95	14.94	15.10	15.65	16.28	16.53

Q6.    (a) A and B throw alternately with a pair of dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. If a begins, find his chances of winning.

(b) The marks obtained in a certain examination are found to be normally distributed.  If 12.5% of the candidates obtain 60% or more marks, 39% obtain less than 30 marks, find the mean number of marks obtained by candidates. (Given that for A=0.125, x/0=1.15 and for A=0.61, x/0=0.279)

Q7.    (a) If T is an unbiased estimator of show that T² and  are the unbiased estimators of   ² and  respectively.

(b) 9 items of a sample has the following values 45, 47, 50, 52, 48, 47, 49, 53, 51.  Does the mean of these items differ significantly from assumed mean of 47.5. (Given that for v=8, P=0.945 for t=1.8 and P=0.953 for t=1.9)