Solve: 2x + 3y = 5, 6x + 5y = 11

Evaluate ഽe^x \(\left( \frac { 1+sinxcosx }{ { cos }^{ 2 }x } \right) dx\)

Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)

Solve: (D²+1)y = 0 when x = 0, y = 2 and when x = \(\frac { \pi }{ 2 } \), y = -2.

Using Lagrange's formula, find the value of y when x = 42 from the following table

x	40	50	60	70
y	31	73	124	159

If a random variable. X has the probability distribution

X	0	1	2	3	4	5
P(X=x)	a	2a	3a	4a	5a	6a

then find F(4)

Suppose that the amount of cosmic radiation to which a person is exposed when flying by jet across USA is a random vertical. having a normal distribution with mean of 4.35m rem and a standard deviation of 0.59m rem. What is the probability that a person will be exposed to more than 5.20 m rem of cosmic radiation of such a flight?

The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with the S.D. of 110 hours. If II is the mean life time of all the bulbs produced by the company, test the hypothesis that μ = 900 hours at 5% level of significance.

Compute Fisher's price index number for the following data.

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
A	10	12	12	15
B	7	15	5	20
C	5	24	9	20
D	16	5	14	5

Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the operators I, II, III and IV.