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Name
Reg No A
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
07 THRISSUR CLUSTER
FIRST SEMESTER M.TECH. DEGREE EXAMINATION DEC 2017
CHEMICAL ENGINEERING
PROCESS CONTROL
07MA6009 MATHEMATICS
Time:3 hours Max.Marks: 60
Answer all six questions. Part of each question is compulsory.
Answer either part or part of each question
(Statistical tables are allowed.)
Q.no. Module 1 Mar
ks
1a Show that the vectors − and form a
basis for With respect to this basis find the representation of the vector
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Answer b or c
b In the space of all polynomials in of degree at most 2 over show that
1
−1 ∈ is an inner product. Find an orthonormal
basis for using this inner product by Gramschmidt orthogonolization process.
5
c Show that the following system of simultaneous equations has a unique solution.
Hence find the solution by Gaussian elimination method.
− − − 3
5
Q.no. Module 2 Mar
ks
2a Show that

4
Answer b or c
b Show that 1


− 5
c Reduce the following quadratic from into Canonical form by an orthogonal
Reduction and hence determine its definiteness
−
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Q.no. Module 3 Marks
3a Find regression line of Y on X from the following data. Use it to predict the value
of Y when X 5
X 1 4 6 8 10
Y 1 8 10 15 19
4
Answer b or c
b Calculate the correlation coefficient between X and Y
X 8 1 5 4 7
Y 3 4 0 2 1
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c Solve the simultaneous equations


−


0
Given 0 when 0.
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Q.no. Module 4 Marks
4a In a certain experiment, the error made in determining the specific gravity of a
substance is a random variable having uniform density whose value lies in the
interval (0.025,0.025). What is the probability that such error will be between
0.010 and 0.015?
4
Answer b or c
b If the probability that an individual suffers a bad reaction from an injection is
0.001, find the probability that out of 2000 individuals exactly 3 more than 2
individuals suffer from a bad reaction.
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c In a certain examination, the percentage of candidates passing and getting
distinction were 60 and 10 respectively. Estimate the average marks obtained by
the candidates if the minimum marks for pass is 40 and that for distinction is 80
respectively. Assume that the distribution of marks is normal.
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Q.no. Module 5 Marks
5a A random sample of size 100 is taken from a population with standard deviation 5.
If the sample mean is 21, construct a 95% confidence interval for the population
mean.
5
Answer b or c
b The manufacturer claims that the iron bar made by him has a mean breaking 7
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strength of 180 kg. Five bars made by the same manufacturer are randomly chosen
and found to have a mean breaking strength of 169 kg with a standard deviation of
5 kg. Can we accept the manufacturer's claim at 0.01 level of significance.
c If 6 determinations of specific heat of iron have a standard deviation of 0.0086, test
the standard deviation is 0.01 at level of significance
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Q.no. Module 6 Marks
6a Obtain the least squares fit of a straight line to the following data
X 0 1 2 3 4
Y 2 4 3 7 9
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Answer b or c
b The following are the number of mistakes made in 5 successive days for 3
technicians working for a photographic laboratory
Technician 1 6 14 10 8 11
Technician 2 14 19 12 10 14
Technician 3 10 12 7 15 11
Test at level of significance whether the differences among the 3 sample means
can be attributed to chance.
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c The measurements of breaking strengths of each of 3 kinds of linen threads by
means of 4 different instruments are as follows
Measuring Instrument
A B C D
Thread 1 20 21 20 22
Thread 2 24 26 27 24
Thread 3 25 23 22 24
Perform an analysis of variance at level of significance
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