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McGill University

Computers in Engineering

308-208B

Final Exam

Wednesday April 21st, 1999

9.00 am - 12.00 noon.

Examiner: Prof. G. Ratzer

Associate Examiners: C. K. Kim, S. Li

Faculty CALCULATORS are allowed. This is a multiple-choice exam to be answered using the red and white sheets for questions 1 to 16. Select what you consider to be the BEST answer of the answers provided for each of these questions. Questions 17 and 18 are to be written on this exam paper, which must be returned. This exam consists of 13 pages.

 

QUESTION 1.

What is the output of this FORTRAN 90 program:

program question1

implicit none

integer :: I,J,K

real :: A,B,C

A = 2.1E1 + 4

B = 37/7

C = 37.0/7.0

I = 2.2 + MOD(78,5)

J = 89/4*4+2-1*2

K = C

PRINT *,I,J,K,A,B,C

stop

end program question1

1) 6 5 5.0000 25.0000 5 5

2) 5 88 5 25.0000 5.00000 5.28571

3) 6 5 5.0000 25.0000 5 5.28571

4) 5 5 5 6.10000 5.00000 5.28571

5) 6 88 5 25.0000 5.00000 5.28571

QUESTION 2

What is the output of this FORTRAN 90 program?

program question2

implicit none

integer :: i, y(5)

real :: a(5),x(5)

do i=1, 5

x(i) = i+1

y(i) = i - 1 + MOD(i, 2)

end do

do i=1, 5

a(i) = x(y(i))

end do

write (*,*) (a(i),i=1,5)

do i=1, 5

a(y(i)) = x(i)

end do

write (*,*) (a(i),i=1,5)

stop

end program question2

1) 3. 2. 4. 4. 6.

2. 5. 4. 3. 6.

2) 3. 2. 4. 4. 6.

2. 2. 5. 4. 6.

3) 2. 2. 4. 4. 6.

3. 2. 5. 4. 6.

4) 3. 2. 3. 2. 3.

5. 6. 3. 2. 3.

5) 2. 4. 4. 2. 6.

3. 2. 4. 5. 6.

QUESTION 3.

program question3

implicit none

integer :: i, nterm

real :: x,term, s

read (*,*) x

read (*,*) nterm

s = 1

term = 1

do i=1, nterm

term = term * i * 1.0 / x

s = s + term

end do

write (*,*) s

stop

end program question3

What does the above FORTRAN 90 program calculate?

(where ! is the symbol for FACTORIAL):

1) 1 + 1!/x + 2!/(x**2) + 3!/(x**3) + 4!/(x**4) + .....

2) 1 + 1/x + 2/(x*2) + 3/(x*3) + 4/(x*4) + ....

3) 1 + x/1! + x/2! + x/3! + x/4! + ....

4) x**n/x!

5) None of the above

QUESTION 4.

PROGRAM HALF_ADDER

IMPLICIT NONE

LOGICAL :: A, B, SUM, CARRY

PRINT *, "ENTER LOGICAL INPUTS A AND B: "

READ *, A, B

SUM = (A .OR. B) .AND. .NOT. (A .AND. B)

CARRY = A .AND. B

PRINT *, "CARRY, SUM =", CARRY,SUM

STOP

END PROGRAM HALF_ADDER

For the above FORTRAN 90 program and the entered input values shown, which is the INCORRECT output.

1) ENTER LOGICAL INPUTS A AND B:

T T

CARRY, SUM = T F

2) ENTER LOGICAL INPUTS A AND B:

T F

CARRY, SUM = F T

3) ENTER LOGICAL INPUTS A AND B:

F T

CARRY, SUM = F T

4) ENTER LOGICAL INPUTS A AND B:

F F

CARRY, SUM = F F

5) NONE OF THE ABOVE

 

QUESTION 5.

What will the following program print?

Program Question5

implicit none

real :: I, J, K, L

integer :: A, B, C

interface ! You can ignore this

subroutine THIS (U, V) ! interface section

implicit none

integer, intent(in out) :: U

integer, intent(in) :: V

end subroutine THIS

subroutine THAT ( X,Y )

implicit none

real, intent(in out) :: X

real, intent(in) :: Y

end subroutine THAT

end interface ! ELF90 wants it

!

! Program begins

!

I=12

A=7

B = 27

C = 4

K = 4.0

J = 4.0

L = 0.0

CALL THIS(B,C)

CALL THAT(J,K)

CALL THAT(L,3.0)

WRITE (*,*)A,B,C

WRITE (*,*)I,J,K,L

Stop

End Program Question5

!

SUBROUTINE THIS (U,V)

implicit none

integer, intent(in out) :: U

integer, intent(in) :: V

integer :: A

U = V**2

A = A+U+V

RETURN

END SUBROUTINE THIS

SUBROUTINE THAT (X,Y)

implicit none

real, intent(in out) :: X

real, intent(in) :: Y

real :: I

X= Y**3

I= I+X+Y

RETURN

END SUBROUTINE THAT

 

1) 7 16 4

12.0 64.0 4.0 27.0

2) 27 16 4

12.0 4.0 64.0 27.0

3) 7 27 4

12.0 64.0 4.0 27.0

4) 7 16 64

12.0 64.0 4.0 27.0

5) None of the above

 

QUESTION 6.

What is the output of the following C program?

#include<math.h>

#include<stdio.h>

#define N 15

main()

{

int i,j,line,a[N];

for (i=2;i<N;i++) a[i]=i;

for (i=2;i<sqrt(N);i++)

for (j=i+1;j<N;j++)

{

if (a[i]!=0&&a[j]!=0)

if (a[j]%a[i]==0)

a[j]=0;

}

printf("\n");

for (i=2,line=0;i<N;i++)

{

if (a[i]!=0)

{printf("%5d",a[i]);

line++;}

if (line==10)

{printf("\n");

line=0;}

}

}

1) 1 3 5 7 9 11

2) 2 4 6 8 10 12

3) 2 3 5 7 9 11

4) 2 3 5 7 11 13

5) 2 3 5 8 13 15

 

QUESTION 7.

Consider the following C program.

Given the input string: abcdef

what is the output?

#include<stdio.h>

main()

{

char str[100];

printf("input string:\n");

scanf("%s",str);

x(str);

printf("%s\n",str);

}

 

x(str)

char str[];

{

char t;

int i;

int j;

for (i=0,j=strlen(str);i<strlen(str)/2;i++,j--)

{

t=str[i];

str[i]=str[j-1];

str[j-1]=t;

}

}

 

 

1)abcdef

2)bcdefa

3)fedcba

4)cdefba

5)defcba

 

QUESTION 8.

What is the output of the following C program?

#include <stdio.h>

char input[] = "SSSWILTECH1\1W\1WALLMP1";

main()

{

int i,c;

for( i=1; (c=input[i]) !='\0'; i++) {

switch(c) {

case 'a': putchar('i'); continue;

case '1': break;

case 1 : while( (c=input[++i]) !='\1' && c !='\0' );

case 9 : putchar('S');

case 'E': case 'L': continue;

default: putchar(c); continue;

}

putchar(' ');

}

putchar('\n'); return;

}

1) SSWITCH SWAMP

2) SSWITCH WWAMP

3) SSWITCH WAMP

4) SWITCH WWAMP

5) None of the above

QUESTION 9.

What will the following C program print?

#include<stdio.h>

#define N 6

#define M 8

int function1(int);

void main(void){

int m[N]={5,6,3,8,2,1};

int i,j;

for(i=0,j=2;i<=5;i++,j--){

if(m[i] < 5 && j < 0)

m[i] = m[i] + 5;

else

m[i] += 5;

if(m[i] <= M-1)

m[i] -= function1(*(m+i));

printf("%d ",m[i]);

}

}

int function1(int x){

int m[M]={9,5,3,7,1,3,3,0};

return m[x];

}

1) 11 12 13 14 15

2) 10 8 13 14 3 2

3) 10 11 8 13 7 3

4) 10 11 9 12 8 5

5) None of the above

 

QUESTION 10.

What will the following C program print?

#include<stdio.h>

#define N 5

main()

{

int i,j,a[N][N];

for (i=1;i<N;i++)

{ a[i][i]=1;

a[i][1]=1;

}

for (i=3;i<N;i++)

for (j=2;j<=i-1;j++)

a[i][j]=a[i-1][j-1]+a[i-1][j];

for (i=1;i<N;i++)

{for (j=1;j<=i;j++)

printf("%6d",a[i][j]);

printf("\n");

}

printf("\n");

}

1)1

1 1

1 2 1

1 2 2 1

2)1

1 2

1 3 1

1 4 4 4

3)1

1 2

1 3 1

1 4 4 1

4)1

1 1

1 2 1

1 3 3 1

5)None of above

 

QUESTION 11.

Using the Newton-Raphson method to find the approximation to the root of a function F(x), if the initial value of x is 2 and

F(x) = 2(x*x*x)+3(x*x)+152, what is the value of x after 1 iteration?

 

1) x = 108

2) x = -3

3) x = 36

4) x = -4

5) None of the above.

QUESTION 12.

Given input data GA,D,A,G,L,A2,A1,A3,A4,Z,ZA,E in order -

fill up the following hash table. When a new identifier gets hashed into a full bucket, we use the simplest solution to find the next closest unfilled bucket. Assume the hash table is used circularly. The Hash function f(x)= order of alphabet of the 1st character of x that is it converts the first letter of the input from A-Z to 1-26.

 

-----------------------------------------------

1 2 3 4 5 6 7 8 9 10 11 12 13 - 26

-----------------------------------------------

1) A A2 A1 D A4 A3 GA G E L Z ZA

-----------------------------------------------

2) A A1 A2 A3 A4 D G GA E L Z ZA

-----------------------------------------------

3) A A1 A2 D A4 A3 G GA ZA E L Z

-----------------------------------------------

4) A A2 A1 D A3 A4 GA G ZA E L Z

-----------------------------------------------

5) None of the above

 

QUESTION 13.

Which of the following triangularized matrices represent a

solution of this system of linear equations?

x + 2y + z = 9

2x + 3y - 2z = 7

4x + 4y + z = 18

1) 1 0 0 2

0 1 0 0

0 0 1 1

2) 1 0 1 1

0 1 0 2

0 0 1 1

3) 1 0 0 2

0 1 0 -1

0 0 1 3

4) 1 0 0 1

0 1 0 3

0 0 1 2

5) 1 0 0 1

0 1 1 2

0 0 1 1

 

 

 

 

 

QUESTION 14.

Which of the following Statements are TRUE.

  1. Secant method (used for root finding) converges quickly to a
  2. root almost as quickly as Newton-Raphson method) but requires

    computation of the derivative f'(x) which may be costly.

  3. The trapezoidal rule takes 2 function evaluations per panel,
  4. but uses only n+1 evaluations of f(x) where n is the number of

    panels used in the approximation

  5. The pseudocode evaluates the integral from XMin to Xmax using

The trapezoidal rule

PanelWidth = (XMax - XMin) / NumberPanels

Sum = f(XMin)/2

X = X_Min + PanelWidth

for k = 1 , NumberPanels

Sum = Sum + f(X)

X = X + PanelWidth

end of for loop

Sum = Sum - f(XMax)/2

Estimate = PanelWidth*Sum

d) Simpson's rule is usually a much better approximation than the

Midpoint, but not as good as Trapezoidal rule.

Select the "best" answer.

1) a and b

2) b and c

3) a, b and c

4) b, c and d

5) None of the above

 

QUESTION 15.

Consider the following statements:

a) The Runge-Kutta method to estimate a differential equation is

very much better than Euler's method.

b) This pseudo-code implements the Euler algorithm:

x <-- 0

y <-- y0

while ( x <= xf )

y <-- y + h*f(x)

x <-- x + h

c) Given the differential equation y' = 3*y + 2x - 1 on

the interval [0, 0.8], and 2.12 is the value of y at x=0.4

using Euler's method with h=0.2 and initial value of

y=1 (i.e. y(0) = 1 ).

Which of the above statement(s) is(are) false?

1) b only

2) a and b

3) a and c

4) a only

5) None of them

QUESTION 16.

On your IBM computer marked sheet fill in circle ONE = 1

(This is to prove that you are still awake and got this far in

the exam!!)

QUESTION 17.

Write a "C" program which tests the first thousand integers (from 1 to 1,000 inclusive) to see if they are PERFECT numbers. A PERFECT number is one, where its factors add up to the number.

Your program should count and print how many perfect numbers are in the range 1 to 1,000 and add them up. Your output should look like this:-

__________________________________________________________________

Program to count and total the PERFECT numbers between 1 and 1,000

Perfect number 1 is 1 factors are 1

Perfect number 2 is 6 factors are 1 2 3

Perfect number 3 is 28 factors are 1 2 4 7 14

. . . .

. . . .

There are ?? perfect numbers and their total is ?????

__________________________________________________________________

Write your "C" program below and on the back of the page.

QUESTION 18.

Write a FORTRAN 90 program

SUBROUTINE Quad(a,b,n,pointm,trap,simp)

which uses a single loop to find the Midpoint (pointm), the trapezoidal (trap), and Simpson's (simp) rules approximations to the integral of a function f(X) (supplied) from a to b using n intervals.

Note you only have to write the SUBROUTINE, not the main program or function f. Try to minimize the number of function evaluations.

Write your program neatly below or on the backs of pages: