If \(\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right] \) find x,y and z

Evaluate ഽ sin³ x cos x dx

Find the area bounded by one arc of the curve y = sin ax and the x-axis.

Solve: (x+y)²\(\frac { dy }{ dx } \) = 1

Estimate the population for the year 1995.

year (x)	1961	1971	1981	1991	2001
population in thousands (y)	46	66	81	93	101

If a continuous random variable. X has the p.d.f. f(x) = 4k(x-1)³, 1 ≤ x ≤ 3 then find p[-2 ≤ X ≤ 2]

The standard deviation of a binomial distribution (q +p)¹⁶ is 2. Find its mean.

The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months.

A company market car tyres. Their lives are normally distributed with a mean of 50,000 kms and standard derivation of 2000 kms. A test sample of 64 tyres has a mean life of 51250 km. Can you conclude that the sample mean differs significantly from the population mean? (Test at 5% level).

Find a trend line to the following data by the method of sami-averages.

Years	1980	1981	1982	1983	1984	1985	1986
Sales	102	105	114	110	108	116	112

For the given pay-off matrix, choose the best alternative for the given states of nature under
(i) Maximin (ii) Minimax princple

Alternative	States of Nature
	Good	Fair	Bad
A	100	60	+50
B	80	50	+10
C	40	20	+5

Find the initial basic feasible solution for the following transportation problem by Vogel's approximation method.