Solve the following equations by using Cramer’s rule
 2x + 3y = 7; 3x + 5y = 9

Integrate the following with respect to x.
\(\frac { 1 }{ { \sin }^{ 2 }x{ \cos }^{ 2 }x } [Hint:\sin ^{ 2 }+{ \cos }^{ 2 }x=1]\)

The demand and supply function of a commodity are p_d = 18− 2x − x² and p_s = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.

Solve yx²dx + e ^{− x}dy = 0

Using graphic method, find the value of y when x = 48 from the following data:

x	40	50	60	70
y	6.2	7.2	9.1	12

State the properties of distribution function.

Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?

Write short note on sampling distribution and standard error.

An Enquiry was made into the budgets of the middle class families in a city gave the following information.

Expenditure	Food	Rent	Clothing	Fuel	Rice
Price(2010)	150	50	100	20	60
Price(2011)	174	60	125	25	90
Weights	35	15	20	10	20

What changes in the cost of living have taken place in the middle class families of a city?

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below.
Determine the allocation that minimizes the overall processing cost.

(cost is in Rs. per unit)