This is a Question Papers of Mumbai University for B.Sc.IT Student of Semester - IV [Quantitative Technology] (Revised Course). [Year - September / 2013] . . . Solution Set of this Paper is Coming soon . . .

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 ( S e p t e m b e r – 2 0 1 3 ) [ 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) Solve the following equations by Gauss elimination method:
2𝑥 + 𝑦 + 𝑧 = 12, 3𝑥 + 2𝑦 + 2𝑧 = 8, 5𝑥 + 10𝑦 − 8𝑧 = 10.
(5)
(B) Use the Runga-Kutta method of second order to find y(0.1) and y(0.2) given
𝑑𝑦
𝑑𝑥
= 𝑦 − 𝑥 𝑎𝑛𝑑 𝑦(0) = 2.
(5)
Q.2 Attempt The Following Question: (15 Marks)
(A) Using Newton-Raphson method obtain a root, correct up to three decimal places of
the equation 𝑠𝑖𝑛 𝑥 = 1 – 𝑥.
(5)
(B) Use Newton’s interpolation formula to find f(2) for the following data:
x 1 3 5 7 9
f(x) 0 24 120 336 720
(5)
OR
(C) Use Lagrange’s interpolation formula to estimate polynomial through (0,1), (1,3),
(4,21).
(5)
Q.3 Attempt The Following Question: (15 Marks)
(A) Evaluate ∫ (4 + 2 sin 𝑥) 𝑑𝑥
𝜋
0
using Trapezoidal Rule. (Take n=6) (5)
(B) Solve the following equations using Gauss-Jordan Method:
2𝑥 − 3𝑦 + 𝑧 = −1, 𝑥 + 4𝑦 + 5𝑧 = 25, 3𝑥 − 4𝑦 + 𝑧 = 2.
(5)
OR (5)
(C) Use Euler’s method to estimate y(0.5) of the equation
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦 + 𝑥𝑦, 𝑦(0) = 1 𝑤𝑖𝑡ℎ ℎ = 0.25.
(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 ( S e p t e m b e r – 2 0 1 3 ) [ 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) An urn contains 6 red and 4 blue balls. 2 balls are drawn at random. If X is number of
blue balls, find the expectation and variance of X.
(5)
(B) In a Poisson Frequency Distribution, frequency corresponding to 3 successes is 2/3
times frequency corresponding to 4 successes. Find the mean and standard deviation
of the distribution.
(5)
OR (5)
(C) A random variable X follows normal distribution with mean 10 and standard deviation
2. Find the following probabilities: (i) P(X>12), (ii) P(X<13.5) and (iii) P(7.5<X<13)
(5)
Q.5 Attempt The Following Question: (15 Marks)
(A) Find the Karl Pearson’s Correlation Coefficient for the following data:
x 8 4 10 2 6
y 9 11 5 8 7
(5)
(B) Fit a regression equation y on x for the following data:
x 3 5 7 9 11
y 9 12 16 14 15
(5)
OR (5)
(C) Fit a second degree equation for the following data:
x 0 1 2 3 4
y 1 1.8 1.3 2.5 6.3
(5)
Q.6 Attempt The Following Question: (15 Marks)
(A) A die is thrown 8000 times and a throw 2 or 6 is observed 3420 times. Can we say that
the die is a fair die?
(5)
(B) It is claimed that the population of a certain item contains 2% defective items. To test
the claim, 300 items were selected and out of which 10 were found to be defective.
Can the claim be accepted at 95 % confidence level?
(5)
OR (5)
(C) In a sample of 45 persons from a City A, 20 are smokers and in another sample of 50
persons from City B, 24 are smokers. Use Z-test to test the claim the proportion of
smokers in the two cities do not differ significantly.
(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 ( S e p t e m b e r – 2 0 1 3 ) [ 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.7 Attempt The Following Question: (15 Marks)
(A) Solve the L.P.P. using Simplex Method:
Maximize z =9600x+11600y+9800z,
Subject to, 𝑥 + 𝑦 + 𝑧 ≤ 100, 5𝑥 + 6𝑦 + 5𝑧 ≤ 400, 𝑎𝑛𝑑 𝑥 ≥ 0, 𝑦 ≥ 0, 𝑧 ≥ 0.
(5)
(B) Use Yate’s correction and test whether A and B are independent. Observed
frequencies are as under:
A Not A Total
B 45 55 100
Not B 60 40 100
Total 105 95 200
(5)
(C) Solve the LPP graphically: Minimize 𝑧 = 𝑥 + 𝑦
Subject To: 2𝑥 + 𝑦 ≥ 12, 5𝑥 + 8𝑦 ≥ 74, 𝑥 + 6𝑦 ≥ 24 𝑎𝑛𝑑 𝑥 ≥ 0, 𝑦 ≥ 0.
(5)