Name of the Organisation : National Institute of Electronics & Information Technology
Examination : C Level Course
Document Type : Sample Question Paper
Year : 2017
Name of the Subject : Mathematical Methods For Computing
Website : http://beta.nielit.gov.in/content/january-2017
Download Sample Question Paper : https://www.pdfquestion.in/uploads/13083-Computing.pdf
C Level Mathematical Methods For Computing Paper
Time: 3 Hours
Total Marks: 100
Related : NIELIT C Level Course Advanced Algorithms Paper 2017 : www.pdfquestion.in/13079.html
Instructions
Note :
1. Answer question 1 and any FOUR from questions 2 to 7.
2. Parts of the same question should be answered together and in the same sequence.
Model Questions
1. a) Events A and B are independent. Examine if the events?A and B are independent?
b) A factory has four independent units A, B, C and D which produces 40%, 30%, 20% and 10% of identical items, respectively. The percentages of defective items produces by these units are 2%, 1%, 0.5% and 0.25% respectively. If an item is selected at random, find the probability that the item is defective.
c) If the probability density function of a continuous random variable is given by < 8, find the mean and variance.
d) Convert the following L.P.P into standard form.
e) Obtain the Laplace transform of the function
f) Two players A and B play tennis games. Their chances of winning a game are in the ratio 3:2 respectively. Find A’s chances of winning at least two chances out of four games played.
g) Find the Fourier series Expansion of the periodic function
2. a) Four boxes A, B, C, D contain fuses. The boxes contain 5000, 3000, 2000 and 1000 fuses respectively. The percentages of fuses in the boxes which are defective are 3%, 2%, 1% and 0.5% respectively. One fuse is selected at random arbitrarily from one of the boxes. It is found to be a defective fuse. Find the probability that it has come from the box D.
3. a) Find the inverse Laplace transform of the following function
b) An irregular six faced dice is thrown 12 times. The expectation that it will give six even numbers is twice the expectation that it will give 5 even numbers. If 1000 sets, each of exactly 12 trials are made, how many sets are expected not to give any even number? (9+9)
4. a) M/s. Mahabir Engineering Works have obtained a large contract for the supply of an alloy steel. The alloy needs three metals, X, Y and Z. The minimum requirement of the metal per week would be 12 units of X, 10 units of Y and 14 units of Z. The metals are available from the dealers who supply them in standardized boxes containing the metals in three different proportions. The boxes are called by code numbers 121, 321 and 115 respectively. Box 121 contains 1 unit of X, 2 units of Y and 1 unit of Z; box 321 contains 3 units of X, 2 units of Y and 1 unit of Z, whereas box 115 contains 1 unit each of X and Y and 5 units of Z. The cost of one box of type 121, 321 and 115, is respectively, Rs.1200, Rs.900 and Rs.1500. Draft its LPP to find no. of boxes of each kind to be bought every week to minimize its cost. Find the dual and give its economic interpretation.
b) A road transport company has one reservation clerk on the time of duty at a time. He handles information of bus schedules and makes reservations. Customer arrive at a rate of 8 per hour and the clerk can service 12 customers on an average per hour. After starting your assumptions, answer the following
i) What is the average number of customers waiting for the service of the clerk?
ii) What is the average time a customer has to wait before getting the service?
iii) The management is contemplating to install a computer system to handle the information and reservations. This is expected to reduce the service time from 5 to 3 minutes. The additional cost of having the new system works out to Rs. 50 per day. If the cost of goodwill of having to wait, its estimated to be 12 paise per minute spent waitingbefore being served. Should the company install the computer system? Assume 8 hours orking day.
6. b) The distributive of the number of road accidents per day in a city is Poisson with mean 4. Find the number of days out of 100 days when there will be
i) no accident
ii) atleast 2 accidents
iii) atmost 2 accidents
iv) between 2 and 5 accidents.