Busi Maths Assign02 Dec 2012

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Business Mathematics MMS Sem I 7/12/2012

Assignment Nos. 2 & 3

Note :

(A) Solve all the questions given below as Assignment No. 2

(B) Solve all the questions in the three papers of Business Mathematics

- question papers (copy given) as Assignment No. 3

(C ) Only Handwritten Assignments will be accepted

(D) Submission on 18th Dec., 2012 for all A, B, and C divisions.

Q1. IfA = 2 5 and B = 1 -1 , find A B and B A.

1 3 -3 2

Is AB =BA ?

Q2. If A = 1 -2 3 and B = 2 3 , find AB and show that AB not equal to BA.

-4 2 5 4 5

2 1

Q3. Evaluate A

2

4A 5I, whereA = 1 2 2

2 1 2

2 2 1

And I is the suitable Identity matrix.

Q6. In a certain city there are 50 colleges and 400 schools. Each school and college has 18 peons, 5

clerks and 1 cashier. Each college has, in addition, one section officer and one librarian. The

monthly salary of each of them is as follows:

Peon Rs. 300, Clerk Rs. 500, Cashier Rs. 600, Section officer Rs. 700 and Librarian

Rs. 900.

Using matrix notation, find (i) the total no of posts of each kind in schools and colleges taken

together and (ii) the total monthly salary bill of all the colleges and schools taken together

Q7. Evaluate 1 2 5 Q8 Evaluate 1 1 1


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2 3 1 1 1+x 1

-1 1 1 1 1 1+y

Q10. Show that 1 a b+c

1 b c+a = 01 c a+b

Q11. Differentiate w.r.t. xa) x3 logex b) ex logax c) ex root xd) (x3 + x4) (ex log ex)

e) x/(1 + x) f) x /(a2 + x2)

Q12. Integrate

a) x5 dx b) ax7 dx c) 3x-3 dx d) x1/3 + x1/2 + 2x3/5 dx e)10x + x4 + 3ex dx

Q13. The Inflato tyre company wishes to determine the average mileage of its new PQ tyres. A

random sample of 49 tyres gives a mean of 25000 miles with a std. deviation of 2450 miles. Find a

90% confidence interval for the true mean mileage. (Ans.: 24424.25, 25575.75)

Q14. An examination was given to two classes consisting of 40 and 50 students. In the first class the

mean marks were 74 with a S.D. of 8 while in the second class the mean marks were 78 with a S.D.

of 7. Is it reasonable to regard the two classes as having been obtained from the identical populations

with equal means? (Ans.: |z|= 2.53)

Q15. An examination was given to two classes, each consisting of 49 students. In the first class, the

mean marks were 74 with a S.D of 8; in the second class, the mean marks were 78 with a S.D. of 9.

Test the hypothesis that the difference in mean marks of the two classes is 5. (Ans.: |z|=0.58)

Q16. While throwing 5 unbiased dias 30 times, a person obtained success (securing 6 on the die) 23

times. Can we consider the difference between the observed and the expected results as being

significantly different? (Hint: n= 5 x 30) (Ans.: z=0.437)


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Q17. Out of 200 fans of factory A, 2% were found to be defective while out of 300 fans of factory B,

2.5% were found to be defective. Can u conclude at 5% level of significance that the percentage of

defective fans of factory A is less than that of factory B? (Ans.: z=-1.15)

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Busi Maths Assign02 Dec 2012