problem 1)(i) Use matrix multiplication to divide Rs. 30,000 in two parts such that total annual interest at 9% on first part and 11% on the second part amount Rs. 3060.

(ii) Describe Quartile Deviation and Standard Deviation in detail.

problem 2) prepare detailed notes on the following

I) Statistics and Business

II) Statistics and Economics

problem 3) Determine the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangement.

i) do the words start with P.?

ii) do all the vowels always occur together?

iii) do the vowels never occur together?

iv) do the words begin with I and end in P.

problem 4) Draw the histogram and gives curve for given data. Determine the number of workers whose wages lie between Rs. 157 and Rs. 177.

Daily wages             No. of workers      Daily wages                   No of workers
(Rs.)                                                      (Rs.)
115-125                        21                    155-165                             104
125-135                        48                    165-175                                72
135-145                        82                    175-185                                 69
145-155                       167                    185-195                                17

problem 5) Particulars regarding income of two villagers are given below :

                                                 Village X             Village Y             
Number of People                         600                    500              
Average Income (in Rs.)                175                    186
Variance of Income (in Rs.)            100                     081

I) In which village is the variation in income is greater?

II) What is the combined standard deviation of the village X and village Y put together?