Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.

If f'(x) = 8x³ -2x², f(2) = 1, find f(x)

The marginal cost at a production level of x units is given by C '(x) = 85 +\(\frac{375}{x^2}\). Find the cost of producing 10 in elemental units after 15 units have been produced?

Solve: x dy +y dx = 0

When h = 1, find Δ (x³).

Two eggs are drawn at random without replacement from a bag containing two bad eggs and eight good eggs. Find the probability of getting two bad eggs?

A continuous random variable. X has the p.d.f. defined by \(f(x)=\left\{\begin{array}{l} C e^{-a x}, \quad 0<x<\infty \\ 0, \quad \text { elsewhere } \end{array}\right.\) Find the value of C if a> 0

If the mean of the binomial distribution is 20 and standard deviation is 4, then find the number of events.

A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)

Construct the cost of living index for 2003 on the basis of 2000 from the following data using family budget method.

Item	Price(Rs.)		Weights
Food	2000	2003	30
Rent	200	280	30
Clothing	150	120	20
Fuel & lighting	50	100	10
Miscellaneous	100	200	20

For the given pay-off matrix, find the optimal decision under the minimax principle.