Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech EEE (Electrical And Electronics Engineering) 2020 March 5th Sem Numerical And Statistical Methods Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Electronics & Electrical Engg.) (2012 to 2017)/(EE) (2012
Onwards)/(Electrical & Electronics Engg.) (2011 Onwards)
(Sem.?5)
NUMERICAL AND STATISTICAL METHODS
Subject Code : BTEE-505
M.Code : 70558
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. Do all the questions :
a. The area of cross-section of a rod is desired upto 0.2% error. How accurately should
the diameter be measured?
b. The mean of the binomial distribution is 20 and standard deviation is 4. Calculate n,
p, q
c. Point out the inconsistency, if any, in the following statement
??The regression equation of y on x is 2y + 3x = 4 and the correlation coefficient
between x and y is 0.8??.
d. Write Newton-cote's quadrature formula.
e. Find the eigen vector corresponding to the eigen value 1 of the matrix
5 4
1 2
? ?
? ?
? ?
.
f. If 2 percent of the books bound at a certain bindery have defective bindings.
Determine the probability that five of 400 books bound by this bindery will have
defective bindings.
g. What is the difference between the Gauss-elimination and Gauss-Seidel methods.
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1 | M-70558 (S2)-713
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Electronics & Electrical Engg.) (2012 to 2017)/(EE) (2012
Onwards)/(Electrical & Electronics Engg.) (2011 Onwards)
(Sem.?5)
NUMERICAL AND STATISTICAL METHODS
Subject Code : BTEE-505
M.Code : 70558
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. Do all the questions :
a. The area of cross-section of a rod is desired upto 0.2% error. How accurately should
the diameter be measured?
b. The mean of the binomial distribution is 20 and standard deviation is 4. Calculate n,
p, q
c. Point out the inconsistency, if any, in the following statement
??The regression equation of y on x is 2y + 3x = 4 and the correlation coefficient
between x and y is 0.8??.
d. Write Newton-cote's quadrature formula.
e. Find the eigen vector corresponding to the eigen value 1 of the matrix
5 4
1 2
? ?
? ?
? ?
.
f. If 2 percent of the books bound at a certain bindery have defective bindings.
Determine the probability that five of 400 books bound by this bindery will have
defective bindings.
g. What is the difference between the Gauss-elimination and Gauss-Seidel methods.
2 | M-70558 (S2)-713
h. Let X be the random variable such that P(X = ?2) = P (X = ?1), P(X = 2) = P(X=1)
and P(X > 0) = P(X < 0) = P(X = 0). Obtain the probability mass function of X and its
distribution functions.
i. Discuss the order of the convergence of the Newton's method for nonlinear equation
f (x) = 0.
j. Write the normal equation for the curve y = a + bx, for n points by the method of least
squares.
SECTION-B
2. Perform six iterations of the bisection method to find the root of the equation cos x = xe
x
correct to four decimal places.
3. Solve the equations 27x + 6y ?z = 85, x + y + 54z = 110, 6x + l5y + 2z = 72 by Gauss-
Seidel method.
4. Using Newton's divided difference formula, find the missing value from the table :
X 1 2 4 5 6
Y 12 15 5 ---- 9
5. The amount of time, in hours, that a computer functions before breaking down is a
continuous random variable with probability density function given by :
100
; 0
( )
0 ; 0
x
e x
f x
x
?
?
?
?
?
?
?
? ?
?
.
What is the probability that a computer will function between 50 and 150 hours before
breaking down?
6. A sample analysis of examination results of 500 students was made. It was found that 220
had failed, 170 had secured a third class, 90 was placed in second class and 20 got a first
class. Are these figures commensurate with the general examination result which is in a
ratio of 4:3:2:1 for the various categories respectively? The table value of chi-square for 3
d.f. at the 5% level of significance is 7.81.
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Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Electronics & Electrical Engg.) (2012 to 2017)/(EE) (2012
Onwards)/(Electrical & Electronics Engg.) (2011 Onwards)
(Sem.?5)
NUMERICAL AND STATISTICAL METHODS
Subject Code : BTEE-505
M.Code : 70558
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. Do all the questions :
a. The area of cross-section of a rod is desired upto 0.2% error. How accurately should
the diameter be measured?
b. The mean of the binomial distribution is 20 and standard deviation is 4. Calculate n,
p, q
c. Point out the inconsistency, if any, in the following statement
??The regression equation of y on x is 2y + 3x = 4 and the correlation coefficient
between x and y is 0.8??.
d. Write Newton-cote's quadrature formula.
e. Find the eigen vector corresponding to the eigen value 1 of the matrix
5 4
1 2
? ?
? ?
? ?
.
f. If 2 percent of the books bound at a certain bindery have defective bindings.
Determine the probability that five of 400 books bound by this bindery will have
defective bindings.
g. What is the difference between the Gauss-elimination and Gauss-Seidel methods.
2 | M-70558 (S2)-713
h. Let X be the random variable such that P(X = ?2) = P (X = ?1), P(X = 2) = P(X=1)
and P(X > 0) = P(X < 0) = P(X = 0). Obtain the probability mass function of X and its
distribution functions.
i. Discuss the order of the convergence of the Newton's method for nonlinear equation
f (x) = 0.
j. Write the normal equation for the curve y = a + bx, for n points by the method of least
squares.
SECTION-B
2. Perform six iterations of the bisection method to find the root of the equation cos x = xe
x
correct to four decimal places.
3. Solve the equations 27x + 6y ?z = 85, x + y + 54z = 110, 6x + l5y + 2z = 72 by Gauss-
Seidel method.
4. Using Newton's divided difference formula, find the missing value from the table :
X 1 2 4 5 6
Y 12 15 5 ---- 9
5. The amount of time, in hours, that a computer functions before breaking down is a
continuous random variable with probability density function given by :
100
; 0
( )
0 ; 0
x
e x
f x
x
?
?
?
?
?
?
?
? ?
?
.
What is the probability that a computer will function between 50 and 150 hours before
breaking down?
6. A sample analysis of examination results of 500 students was made. It was found that 220
had failed, 170 had secured a third class, 90 was placed in second class and 20 got a first
class. Are these figures commensurate with the general examination result which is in a
ratio of 4:3:2:1 for the various categories respectively? The table value of chi-square for 3
d.f. at the 5% level of significance is 7.81.
3 | M-70558 (S2)-713
SECTION-C
7. a. Evaluate
6
2
0
1
dx
x ?
?
dx by using Trapezoidal rule.
b. Apply Runge-Kutta fourth order method to find the approximate value of y for x =
0.2.
Given that
dy
dx
= x + y, and y = 1 where x = 0.
8. a. Find the coefficient of correlation and obtain the lines of regression from the given
data
X 62 64 65 69 70 71 72 74
Y 126 125 139 145 165 152 180 208
b. Samples of sales in similar shops in two rooms are taken for a new product with the
following results :
Town Mean sales Variance Size of samples
A 57 5.3 5
B 61 4.8 7
Is there any evidence of difference in sales in the two towns? Use 5% level of
significance for testing this difference between the mean of two samples.
Use t
10
(0.05) = 2.228
9. The results of a survey on the sales of a product (Y) as a function of time period (X) are
summarized as below :
X Y
Mean 40 125
Standard deviation 2.5 16
Correlation coefficient (r) 0.85
a. Fit a regression line of Y on X and estimate the value of Y when X is 45.
b. Fit a regression line of X on Y and estimate the value of X when Y is 135.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 21 March 2020