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03521402022
Exam Roll No.
END TERM EXAMINATION
SECOND SEMESTER (BCA] JuLY 2023
Paper Code: BCA-102 Subject: Applied. Mathematics

Time: 3 Hours
(Batch 2021 Onwards) Maximum Marks: 75
Note: Attempt five
compulsory. Select one questions
in
question fromalleach
incluing 0. No. 1 whtch
unit. Scientific Calculator is
allowed.
Q1 Answer the following:
ja) Determine the binomial distribution for whick meon js 4 and variance
is 3. (2.5)
o The probabilities that students A, B, Cand Dsolve a problem are 1/3,
2/5, 1/5 and 1/4, respectively. If all of them try to solve the problem,
what is the probability that the problem will be solved? (2.5)
je Construct forward difference table from the values of x and y gvel
below: (2.5)
X 2 3 4 5
5 11 22 18 2
27
)Prove that AV= A- V, where A and V are forward and backwad
difference operators. (2.5)
e Using Lagrange interpolation, find the unique polynomial of degree 2
such that f(0) = 1, f(1) = 3, f(3) = 55. (2.5)
() What do you mean by Numerical Integration? (2.5)
LgCalculate [ Sin x dx correct to four decimal places with h = i. (2.5)
(h) Define basic feasible solution in Linear Programming Problemn (LPP). (2.5)
) Write a note on unbounded solution of LPP. (2.5)
i) Write a note on slack and surplus variables in LPP. (2.5)
UNIT-I
Q2 af An insurance company insured 2000 scooter drivers, 4000 car drivers
and 6000 truck drivers. The probability of an accident involving a
scooter driver, car driver and truck driver is 0.01, 0.03 and 0.15
respectively. One of the insured person meets with an accident. What
is the probability that he is a truck driver? (6.5)
(b) If Xis a Poisson variae suçh that P(X=2) =9P(X=4) +90P(X=6). Find
the mean and variance of X. (6)
Q3 (a) If the heights of 500 students are normally distributed with mean 68
inches and standard deviation 3 inches. How many students have
heights (i) greater than 72 inches (i) less than equal to 64 inches (iiü)
between 65 and 71 inches? Given P(Zs1.33)=0.4082, P(Zs1l)=0.3413. (6.5)
(b) A continuous random variable X has probability density function. (6)
-00 <x<0
otherwise
0.
Determine the value of k and evaluate P(X > 0).

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UNIT-II
.Bind the missing value of the following table. Explain why the result
Q4 differs from 16? (6)
X 1 2 3 4 5 6 7
2 4 32 64 128
h Find a real rot of the equation x3 - x= 1l using False Position method
upto fifth iteration. (6.5)
lal Obtain a formula to calculate cube root of a natural number N and
Q5 1se it to evaluate cube root of 28. (6)
AEstimate by suitable method of interpolation the number of persons
hose daily income is Rs. 19 but not exceed Rs. 25 from the following
data, (6.5)
Income (In Thousands) 0-99-19 19-2828-37|37-46
No. of persons 50 70 203 406 304

UNIT-III
[3 2 71

06 (a) Find the LU decomposition of the matrix A= |2 3 (6.5)

4 15 6 2

(a) Solve the following system using the Gauss - Seidel iterative method.
Q7
Perform three iterations only. (6.5)
5x-y 3z =3
4x + 7y --2z = 2
6x-3y +9z =9
using Simpson's 1/3 rule and hence obtain the
dx
(b) Evaluate Jby
J0 1+x2
approximate value of n. (6)

UNIT-IV
Q8 Solve the following linear programming problem by using simplex
method: (12.5)
Min Z= xl + 2x2 +3x3
subject to
2x1 - x2 + x3 2 4
xl + x2+2x3 s 8
x2 - x3 2
and x1,x2,x3 2 0

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 (:3]
transportation
Q9 (a) Findthe optimal solution of the following minimization (6.5)
problem:
DI D2 D3 D4 |Supply
S1 11 13 17 14 250

S2 16 18 14 10 300

S3 21 24 13 10 400

Demand 200|225|275|250|
wants
(b) Acomputer centre has 4 expert programmers. The centre
application programmes to be developed. The head of be the computer
programmes to developed,
centre, after studying carefuly the for
estimates the computer time in minutes required by the experts (6)
the application programmes as follows:

|Application Programmes
A B

1 15 18 10

2 14 17
Programmers
3 16 19 17

4 20 14 17

one per
How should the application programmes must be allocated,
programmer, so as to minimize the total time?

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BCA-10