This document appears to be a quantitative technology question paper from October 2016 containing 7 questions with multiple parts to each question. The questions cover a range of quantitative and statistical topics including: solving equations numerically using methods like Newton Raphson, Gauss Jordon, false position; evaluating integrals using techniques like trapezoidal rule, Simpson's rule; correlation and regression; probability distributions; hypothesis testing; and linear programming. The paper is 3 hours long and contains both theoretical and problem-solving questions across these quantitative topics.

1. Q u a n t i t a t i v e T e c h n o l o g y
Q u e s t i o n P a p e r ( O c t o b e r – 2 0 1 6 ) [ R e v i s e d C o u r s e ]
1 | Page
M u m b a i B . S c . I T S t u d y
F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e
– Kamal T.
Time: 3 Hours Total Marks: 100
N.B.: (1) All Questions are Compulsory.
(2) For Q.2 to Q.7, Part (a) is Compulsory and attempt any one part from (b) and (c).
(3) All Questions carry equal marks.
(4) Figures to right indicate full marks.
(5) Use of Non-programmable Scientific Calculator is allowed.
Q.1 Attempt Any One From The Following Question: (10 Marks)
(A) Find the root of the equation 𝑓(𝑥) = 3𝑥 − 𝑐𝑜𝑠𝑥 − 1 = 0 by using Newton Raphson’s
method with initial value 𝑥0 = 1. (upto five iteration)
(5)
(B) Solve the following equations by using Gauss Jordon method correct upto three
decimal places 𝑥 + 2𝑦 + 6𝑧 = 22, 3𝑥 + 4𝑦 + 𝑧 = 26, 6𝑥 − 𝑦 − 𝑧 = 19.
(5)
Q.2 Attempt The Following Question: (15 Marks)
(A) Find a real root of the equation 𝑥3
− 2𝑥 − 5 = 0 by method of false position correct
upto to three decimal places.
(5)
(B) Evaluate ∫ √sin 𝑥 + cos 𝑥 𝑑𝑥
1
0
taking 5 sub intervals in trapezoidal rule. (5)
(C) Find 𝑓(7) by Lagrange’s formula.
Age (x) 0 2 5 8 10 12
Weight (y) 7.5 10.25 15 16 18 21
(5)
Q.3 Attempt The Following Question: (15 Marks)
(A)
Evaluate ∫
𝑠𝑖𝑛2 𝑥
5+4cos 𝑥
𝜋
0
𝑑𝑥 by taking 5 ordinates by Simpson’s (
1
3
)
𝑛𝑑
𝑟𝑢𝑙𝑒.
(5)
(B) Use Taylor’s series method top solve the equation
𝑑𝑦
𝑑𝑥
= 𝑥2
𝑦 − 1; 𝑦(0) = 1. Find
y(0.03) by taking h=0.01.
(5)
(C) 𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦 + 𝑥𝑦 With y(0)=2 estimate y(2) by Euler’s method taking h=0.5. (5)

2. Q u a n t i t a t i v e T e c h n o l o g y
Q u e s t i o n P a p e r ( O c t o b e r – 2 0 1 6 ) [ R e v i s e d C o u r s e ]
2 | Page
M u m b a i B . S c . I T S t u d y
F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e
– Kamal T.
Q.4 Attempt The Following Question: (15 Marks)
(A) The following data represents the demand (x) and supply (y) both in thousands of units
of a certain commodity during first seven months of 2010.
Months 1 2 3 4 5 6 7
Demand (x) 1 2 3 4 5 6 7
Supply (y) 2 4 7 6 5 6 5
Find the regression equation and hence the correlation coefficient. Also estimate the
supply when the demand is 8,000.
(5)
(B) Compute the coefficient of correlation for the following data:
X 7 9 8 5 6 3 4 1 2
Y 18 20 19 21 24 26 25 23 27
(5)
(C) Find standard deviation and variance of the data given below:
X 10 20 30 40 50 60 70 80 90 100
Y 12 19 31 38 46 44 37 23 13 7
(5)
Q.5 Attempt The Following Question: (15 Marks)
(A) A random variable X follows Poisson Distribution with mean =2.5. Find (i) P(X-3), (ii)
P(X≤2), (iii) P (X≥1), (iv) P(1≤X≤3).
(5)
(B) In a certain city 20% of person’s are vegetarians. If 5 persons from the city are
chosen at the random, find the probability that, (i) None is Vegetarian (ii) at least one
is vegetarian.
(5)
(C) In a certain lottery, one prize of Rs. 1000/- three prizes of Rs. 500/- each five prizes of
Rs. 100/- each and 10 prizes of Rs. 50/- each are to be awarded to 19 tickets drawn
from the total number of 10000 tickets sold at prize of Rs. 1/- per ticket. Find the
expected net gain, to the person buying a particular ticket.
(5)

3. Q u a n t i t a t i v e T e c h n o l o g y
Q u e s t i o n P a p e r ( O c t o b e r – 2 0 1 6 ) [ R e v i s e d C o u r s e ]
3 | Page
M u m b a i B . S c . I T S t u d y
F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e
– Kamal T.
Q.6 Attempt The Following Question: (15 Marks)
(A) Following are two samples from two different populations. Can we say that the two
population have same mean.
Sample I: 25, 32, 30, 34, 24, 14, 32, 24, 30, 31, 35, 25
Sample II: 44, 34, 22, 10, 47, 31, 40, 30, 32, 35, 18, 21, 35, 39, 22.
(5)
(B) 300 out of 550 people in a survey were mean and 220 out of 400 were found to be
men in an another survey. Does this survey represented the same population?
(5)
(C) A manufacturer claims that 10% of his product is defective. A sample of 300 items
selected at random had 32 defective items. Test his claim at 1% level of significance.
(5)
Q.7 Attempt The Following Question: (15 Marks)
(A) A manufacturer of furniture makes two products chairs and tables. Processing of these
products is done on two machines A and B. A chair requires 2 hours on machine A and
6 hours on machine B. A table requires 5 hours on machine A and no time on machine
B. Time available per day on machine A and B are 16 and 30 hours respectively. Profits
earned from a chair and a table are Rs.50 and Rs.250 respectively. Formulate the LPP
and solve graphically to maximize the profit.
(5)
(B) A sample from normal population is as under: 12, 9, 8, 7, 8, 9, 12, 11, 15, 12, and 16.
On the basis of above values can we say that the variance of population is 2.5? Use 5%
level of significance.
(5)
(C) A sample of size 16 from Normal population has Standard Deviation 12. Can we say
that population standard deviation is 10? Given level of significance is 5%.
(5)