Engineering Mathematics – IV - Gandhi Institute For Education

Prepared by Dr.Binayak Sahu
Sample Questions
Engineering Mathematics – IV
-
by Dr.Binayak Sahu
Gandhi Institute for Education and Technology,
Baniatangi, Bhubaneswar
ALWAYS REMEMBER THE FOLLOWING TIPS :


Never read Mathematics, but write Mathematics :
Do not believe in reading Mathematics. Always adopt pen
and paper for doing Mathematics otherwise you will be
simply deceiving yourself.
Regularity in Mathematics :
The most important thing in the study of mathematics is
regularity in its studies. Do not postpone your daily work
in mathematics.
My dear students, never forget to ask a doubt, if you have any,
write in my e-mail ID: [email protected]
GIET, Baniatangi, Bhubaneswar
Engineering Mathematics – IV
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Prepared by Dr.Binayak Sahu
Engineering Mathematics - IV
1. State the rules of rounding off a decimal number.
2. What is ill conditioning of a system of linear equations? Explain
3. State the conditions under which an experiment will involve
Poisson distribution.
4. What is a standard random variable? What are the mean and
standard deviation of a standard random variable?
5. Find 10 (1  x)(1  2 x 2 )(1  3x3 )(1  4 x 4 ) using h = 1.
6. Estimate y (0.25) and y(0.5) from y  x  y 2 , y(0)  1.1 using
Euler’s method choosing h = 0.25.
7. Sketch F ( x) if f (0)  f (1)  1/ 4 and f (3)  1/ 2.
8. If X is a random variable with mean 50 and standard deviation 5,
find the mean and variance of 25 – 2X.
9. Determine a 95% confidence interval or the mean  of a normal
population with variance  2  16, using a sample of size 196 with
mean 75.
10. If the probability of hitting a target is 0.42 and five shots are fired
independently, what is the probability that the target will be hit at
least twice?
Long type questions:
1.
Find a solution of the equation x 4  x  0.12  0 by using fixed
point iteration method, correct up to three decimal places. You can take
the initial solution x0  1.
GIET, Baniatangi, Bhubaneswar
Engineering Mathematics – IV
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Prepared by Dr.Binayak Sahu
2.
Describe Lagrange Interpolation technique and find the value of f
(0) for the given data.
x:
-2
-1
2
4
5
f (x): - 9
-1
11
23
69
3.
Estimate f (3) if f (1.1)  10,
f (2.3)  5.7,
f (3.9)  25.8
and f (6.7)  78.9 using Newton’s interpolation formula based on divided
differences.
4.
Using Gauss-Seidel iteration method solve the following system of
linear equations correct up to three decimal places.
6 x1  15x2  2 x3  72
x1  x2  54 x3  110
27 x1  6 x2  x3  85
5.
Find the numerical solution y(0.2) for the differential equation
y  x 2  y 2 with the initial condition y(0) = 1 using h = 0.1 by RungeKutta 4th order method.
6.
Find the approximated root of the equation e x sin ( x)  x 2  0
by Newton’s method correct up to 3-decimal places using the initial
approximation x0  3.
2
7.
Evaluate the integral
 e dx
x
which is correct up to 6 decimal
1
places by Simpson’s one third rule.
8.
A box contains r red balls and b black balls. If two balls are drawn
from the box without replacement one after another and the color of the
first ball is unknown, then that is the probability for getting a black ball in
the second draw.
GIET, Baniatangi, Bhubaneswar
Engineering Mathematics – IV
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Prepared by Dr.Binayak Sahu
9.
If a die is rolled 5 times, then what is the probability of getting 6
sixes.
10.
If a probability book having 500 pages contains 300 misprints,
then find the probability that a page of same book contains exactly 2
misprints.
11.
A batch of 200 iron rods consists of 50 oversized rods, 50
undersized rods and 100 rods of desired length. If two rods are drawn at
random without replacement, what is the probability of obtaining (i) two
rods of desired length (ii) exactly one of the desired length (iii) none of the
desired length.
12.
Let X be the random variable denoting the ratio of sales to profits
of some firm. Assume that X has the distribution function
F ( x)  0
= ( x2  4) / 5
=1
13.
if x < 2
if 2  x  3
if x  3
A pressure control apparatus contains three electronic tubes. The
apparatus will not work unless all tubes are operative. If the probability of
failure of each tube during some interval of time is 0.017, what is the
corresponding probability of failure of the apparatus?
14.
Let X (in mm) be the thickness of washers a machine turns out.
Assume that X has the density f ( x)  Kx if 0.9  x  1.1 and f ( x)  0
otherwise. Find K, what is the probability that a washer will have any
thickness between 0.94 mm and 1.03 mm?
GIET, Baniatangi, Bhubaneswar
Engineering Mathematics – IV
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Prepared by Dr.Binayak Sahu
15.
Find the density function of X. Also find the probability that X lies
between 20% to 40% profit range.
16.
The copper content (%) in brass of 10 samples are given below 65,
65, 64, 63, 65, 66, 63, 64, 62, 63
Assuming that the population from which the above samples are drawn is
normal, determine a 99% confidence interval for the mean of the
population.
Given that
( z ) : 0.9
z
: 1.282
17.
0.95
1.645
0.975
1.960
0.99
2.326
0.995
2.576
Find the coefficient of correlation between x and y from the
following data table:
x
5.5
6.5 7.5 8.5 9.5 10.5 11.4
y 10.9 7.8 8.3 6.2 7.1
18.
5.3
4.5
Find the regression line of y (expansion of gelatin [%]) on x
(humidity) of air [%]) using the following data:
(x, y) = (10, 0.8), (20, 1.6) (30, 2.3), (40, 2.8).
GIET, Baniatangi, Bhubaneswar
Engineering Mathematics – IV
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