Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

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 \(\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx } \)

A company produces 50,000 units per week with 200 workers. The rate of change of productions with respect to the change in the number of additional labour x is represented as 300 - 5x^2/3. If 64 additional labours are employed, find out the additional number of units, the company can produce.

Solve 3e^xtan ydx +(1 + e^x)sec²ydy = 0 given y(0) = \(\frac { \pi }{ 4 } \)

Using Newton’s formula for interpolation estimate the population for the year 1905 from the table:

Year	1891	1901	1911	1921	1931
Population	98.752	1,32,285	1,68,076	1,95,690	2,46,050

If f (x) is defined by f(x)=ke^-2x,  0\(\le\)x<\(\infty\) is a density function. Determine the constant k and also find mean.

One fifth percent of the the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective and two defective blades respectively in a consignment of 1,00,000 packets (e^–0.2 =.9802)

An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at 5% level of significance.

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities	Price		Quandity
	2000	2010	2000	2010
Rice	38	35	6	7
Wheat	12	18	7	10
Rent	10	15	10	15
Fuel	25	30	12	16
Miscellaneous	30	33	8	10