Find k, if the equations x + y + z = 7,  x + 2y + 3z = 18,  y + kz = 6 are inconsistent

Integrate the following with respect to x. 
\(\frac { { 3x }^{ 2 }-2x+5 }{ { \left( x-1 \right) }\left( x^{ 2 }+5 \right) } \)

Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.

The sum of Rs. 2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (log_e2 = 0.6931)

Using appropriate interpolation formula find the number of students whose weight is between 60 and 70 from the data given below

Weight in lbs	0-40	40-60	60-80	80-100	100-120
No.of.students	250	120	100	70	50

A continuous random variable X has p.d.f
f(x) = 5x⁴, 0\(\le\)x\(\le\)1 
Find a₁ and a₂ such that
i) P[X\(\le\)a₁] = P[X>a₁]   
ii) P[X>a₂] = 0.05

If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals
(a) exactly 3, and
(b) more than 2 individuals will suffer a bad reaction.

A machine produces a component of a product with a standard deviation of 1.6 cm in length. A random sample of 64 componentsvwas selected from the output and this sample has a mean length of 90 cm. The customer will reject the part if it is either less than 88 cm or more than 92 cm. Does the 95% confidence interval for the true mean length of all the components produced ensure acceptance by the customer?

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

Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.