Note: Attempt all the questions and send it to the coordinator of the study centre, you are attached with.

1. Using matrix inversion method, solve the following system of equations
2x-y+2z=6
x-2y+3z=6
3x-3y-z=-6

2. A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or a bolt

3. Find the area under the standard normal curve, which lies
a. To the left of z= 0.94
b. To the right of z= - 0.65
c. To the right of z= 1.76
d. Between z= - 0.34 and z= 0.62

4. In a random sample of 200 persons of a town, 120 are found to be tea drinkers. In a random sample of 500 persons of another town, 240 are found to be tea drinkers. Is the proportion of tea drinkers in the two towns equal? Use 0.01 level of significance.

5. What is a time-series? Mention its important components. How a time series can be analyzed.