The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is Rs. 840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is Rs. 570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is Rs. 630. Find the cost of each book by using Cramer’s rule.

Evaluate the following integrals as the limit of the sum:
\(\int _{ 1 }^{ 3 }{ xdx } \)

Find the consumer’s surplus and producer’s surplus for the demand function p_d = 25 − 3x and supply function p_s = 5 + 2x.

Solve: (D² − 2D + 1)y = e^2x + e^x

Calculate the value of y when x = 7.5 from the table given below

x	1	2	3	4	5	6	7	8
y	1	8	27	64	125	216	343	512

A continuous random variable X has the following probability function

Value of X = x	0	1	2	3	4	5	6	7
P(x)	0	k	2k	2k	3k	k2	2k2	7k2+k

(i) Find k
(ii) Ealuate p(x<6), p(x\(\ge \)6) and p(0)
(iii) If P(X\(\le\)x).\(\frac{1}{2}\), then find the minimum value of x.

Forty percent of business travellers carry a laptop. In a sample of 15 business travelers,
(i) what is the probability that 3 will have a laptop?
(ii) what is the probability that 12 of the travelers will not have a laptop?
(iii) what is the probability that atleast three of the travelers have a laptop?

The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with mean I.Q 100 and standard deviation 15? (Test at 5% level of significance)

Construct the cost of living index number for 2011 on the basis of 2007 from the given data using family budget method.

Commodities	Price		Weights
	2007	2011
A	350	400	40
B	175	250	35
C	100	115	15
D	75	105	20
E	60	80	25

A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

Assign the programmers to the programme in such a way that the total computer time is least.