Problem Solving Through Programming In C Week 11
Session: JULY-DEC 2023
Course Name: Problem Solving Through Programming In C
Course Link: Click Here
These are Problem Solving Through Programming In C Assignment 11 Answers
Q1. Interpolation provides a mean for estimating functions
a) At the beginning points
b) At the ending points
c) At the intermediate points
d) None of the mentioned
Answer: c) At the intermediate points
Q2. To solve a differential equation using Runge-Kutta method, necessary inputs from user to the algorithm is/are
a) the differential equation dy/dx in the form x and y
b) the step size based on which the iterations are executed.
c) the initial value of y.
d) all the above
Answer: d) all the above
Q3. A Lagrange polynomial passes through three data points as given below
The polynomial is determined as f(x) = Lo(x). (15.35) + L₁ (x). (9.63) + L₂(x). (3.74). The value of f(x) at x = 7 is
a) 12.78
b) 13.08
c) 14.12
d) 11.36
Answer: b) 13.08
These are Problem Solving Through Programming In C Assignment 11 Answers
Q4. The value of f3.2 0 xex dx by using one segment trapezoidal rule is
a) 172.7
b) 125.6
c) 136.2
d) 142.8
Answer: b) 125.6
Q5. Accuracy of the trapezoidal rule increases when
a) integration is carried out for sufficiently large range
b) instead of trapezoid, we take rectangular approximation function
c) number of segments are increased
d) integration is performedfor only integer range
Answer: c) number of segments are increased
Q6. Solve the ordinary differential equation below using Runge-Kutta4th order method. Step size h=0.2. dy 5 + xy³ = cos(x),y(0) = 3 dx The value of y(0.2) is (upto two decimal points)
a) 2.86
b) 2.93
c) 3.13
d) 3.08
Answer: b) 2.93
These are Problem Solving Through Programming In C Assignment 11 Answers
Q7. Match the following
A. Newton Method 1. Integration
B. Lagrange Polynomial 2. Root finding
C. Trapezoidal Method 3. Differential Equation
D. RungeKutta Method 4. Interpolation
a) A-2, B-4, C-1, D-3
b) A-3, B-1, C-2, D-4
c) A-1, B-4, C-3, D-2
d) A-2, B-3, C-4, D-1
Answer: a) A-2, B-4, C-1, D-3
Q8. The value of fex (lnx) dx calculated using the Trapezoidal rule with five subintervals is (* range is given in output rather than single value to avoid approximation error)
a) 12.56 to 12.92
b) 13.12 to 13.66
c) 14.24 to 14.58
d) 15.13 to 15.45
Answer: c) 14.24 to 14.58
Q9. Consider the same recursive C function that takes two arguments
unsignedintfunc(unsigned int n, unsigned int r) { if (n > 0) return (n%r + func (n/r, r)); else return 0; }
What is the return value of the function foo when it is called as func(513, 2)?
a) 9
b) 8
c) 5
d) 2
Answer: d) 2
These are Problem Solving Through Programming In C Assignment 11 Answers
Q10. What will be the output?
a) 4
b) 8
c) 16
d) Error
Answer: c) 16
Assignment
Question 1
The velocity of a car at different time instant is given as
Time (t) 10 15 18 22 30
Velocity v(t) 22 26 35 48 68
A linear Lagrange interpolant is found using these data points. Write a C program to find the velocity of the car at different time instants. (Taken from test cases)
Solution:
int isa,j;
float b, c, k =0;
for(isa=0; isa < 5; isa++)
{
b=1;
c=1;
for(j=0; j < 5; j++)
{
if(j!=isa)
{
b=b*(a-t[j]);
c=c*(t[isa]-t[j]);
}
}
k=k+((b/c)*v[isa]);
}Question 2
Write a C program to find f b a x² dx using Trapezoidal rule with 10 segments between a and b. The values of a and b will be taken from test cases
Solution:
int id;
float h,x, sum=0;
if(b > a)
h=(b-a)/n;
else
h=-(b-a)/n;
for(id=1;id < n;id++)
{
x=a+id*h;
sum=sum+func(x);
}
integral=(h/2)*(func(a)+func(b)+2*sum);
printf("The integral is: %0.6f\n",integral);
return 0;
}
float func(float x)
{
return x*x;
}These are Problem Solving Through Programming In C Assignment 11 Answers
Question 3
Write a C program to solve the following differential equation using Runge-Kutta method. Step size h=0.3
10dy/dx + 3y³ = x(x + 1), y(0.3) = 5
Find y(x) for different values of x as given in the test cases.
Solution:
while(x0 < xn)
{
m1=func(x0,y0);
m2=func((x0+h/2.0),(y0+m1*h/2));
m3=func((x0+h/2.0),(y0+m2*h/2));
m4=func((x0+h),(y0+m3*h));
m=((m1+2*m2+2*m3+m4)/6);
y0=y0+m*h;
x0=x0+h;
}
printf("y=%.6f",y0);
return (0+0);
}
float func(float x,float y)
{
float m;
m=(x*(x+1)-3*y*y*y)/10;
return m;
}Question 4
Write a C program to check whether the given input number is Prime number or not using recursion. So, the input is an integer and output should print whether the integer is prime or not.
Solution:
int checkPrime(int numBER, int i)
{
if (i == 1)
{
return 1;
}
else
{
if (numBER % i == 0)
{
return 0;
}
else
{
return checkPrime(numBER, i - 1);
}
}
}These are Problem Solving Through Programming In C Assignment 11 Answers
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Session: JAN-APR 2023
Course Name: Problem Solving Through Programming In C
Course Link: Click Here
These are Problem Solving Through Programming In C Assignment 11 Answers
Q1. Interpolation is a process for
a) extracting feasible data set from a given set of data
b) finding a value between two points on a line or curve.
c) removing unnecessary points from a curve
d) all of the mentioned
Answer: b) finding a value between two points on a line or curve.
Q2. Given two data points (a, f (a)) and (b, f(b). the linear Lagrange polynomial f (x) that passes
through these two points are given as
a) f(x) = (x-a/a-b)f(a) + (x-a/a-b)f(b)
b) f(x) = (x/a-b)f(a) + (x/b-a)f(b)
c) f(x) = f(a) + (f(b)-f(a)/b-a)f(b)
d) f(x) = (x-b/a-b)f(a) + (x-a/b-a)f(b)
Answer: d) f(x) = (x-b/a-b)f(a) + (x-a/b-a)f(b)
These are Problem Solving Through Programming In C Assignment 11 Answers
Q3. A Lagrange polynomial passes through three data points as given below
The polynomial is determined as f(x) = L0 (x). (15.35) + L₁ (x). (9.63) + L₂(x). (3.74) The value of f(x) at x = 7 is
a) 12.78
b) 13.08
c) 14.12
d) 11.36
Answer: b) 13.08
Q4. The value of f 1.5 0 xe²x dx by using one segment trapezoidal rule is (upto four decimal places) The value of
Answer: 22.5962
These are Problem Solving Through Programming In C Assignment 11 Answers
Q5. Accuracy of the trapezoidal rule increases when
a) integration is carried out for sufficiently large range
b) instead of trapezoid, we take rectangular approximation function
c) number of segments are increased
d) integration is performed for only integer range
Answer: c) number of segments are increased
Q6. Solve the ordinary differential equation below using Runge-Kutta 4th order method. Step size
h=0.2.
5dy/dx +xy3 = cos(x),y(0) = 3
The value of y(0.2) is (upto two decimal points)
a) 2.86
b) 2.93
c)3.13
d) 3.08
Answer: b) 2.93
These are Problem Solving Through Programming In C Assignment 11 Answers
Q7. Which of the following cannot be a structure member?
a) Another structure
b) function
c) array
d) none of the above
Answer: b) function
Q8. Match the following
A. Newton Method 1. Integration
B. Lagrange Polynomial 2. Root finding
C. Trapezoidal Method 3. Differential Equation
D. Runge Kutta Method 4. Interpolation
a) A-2, B-4, C-1, D-3
b) A-3, B-1, C-2, D-4
c) A-1, B-4, C-3, D-2
d) A-2, B-3, C-4, D-1
Answer: a) A-2, B-4, C-1, D-3
These are Problem Solving Through Programming In C Assignment 11 Answers
Q9. The value of (3 1 ex(In x) dx calculated using the Trapezoidal rule with five subintervals is (* range
is given in output rather than single value to avoid approximation error)
a) 12.56 to 12.92
b) 13.12 to 13.66
c) 14.24 to 14.58
d) 15.13 to 15.45
Answer: c) 14.24 to 14.58
Q10. Consider the same recursive C function that takes two arguments unsigned int func(unsigned int n, unsigned int r)
{if (n >0) retum (n%r + func (n/r, r));
else return 0;
}
What is the return value of the function foo when it is called as func(513, 2)?
a) 9
b) 8
c) 5
d) 2
Answer: d) 2
These are Problem Solving Through Programming In C Assignment 11 Answers
Problem Solving Through Programming In C Programming Assignment
Question 1
The velocity of a car at different time instant is given as
A linear Lagrange interpolant is found using these data points. Write a C program to find the velocity of the car at different time instants. (Taken from test cases)
Solution:
int i,j;
float b, c, k =0;
for(i=0; i<5; i++)
{
b=1;
c=1;
for(j=0; j<5; j++)
{
if(j!=i)
{
b=b*(a-t[j]);
c=c*(t[i]-t[j]);
}
}
k=k+((b/c)*v[i]);
}These are Problem Solving Through Programming In C Assignment 11 Answers
Question 2
Write a C program to find (ba x2dx using Trapezoidal rule with 10 segments between a and b. The values of a and b will be taken from test cases.
Solution:
int i;
float h,x, sum=0;
if(b>a)
h=(b-a)/n;
else
h=-(b-a)/n;
for(i=1;i<n;i++){
x=a+i*h;
sum=sum+func(x);
}
integral=(h/2)*(func(a)+func(b)+2*sum);
printf("The integral is: %0.6f\n",integral);
return 0;
}
float func(float x)
{
return x*x;
}These are Problem Solving Through Programming In C Assignment 11 Answers
Question 3
Write a C program to solve the following differential equation using Runge-Kutta method. Step size h=03
10dy/dx + 3y^3 = x(x+1),y(0.3)=5
Find y(x) for different values of x as given in the test cases.
Solution:
float m1,m2,m3,m4,m,h=0.3;
float x0 = 0.3, y0 = 5;
while (x0 < xn)
{
m1 = func(x0, y0);
m2 = func((x0 + h/2.0), (y0 + m1*h/2));
m3 = func(x0 + h/2.0, (y0 + m2*h/2));
m4 = func((x0 + h), (y0 + m3*h));
m=((m1+2*m2+2*m3+m4)/6);
y0=y0+m*h;
x0=x0+h;
}
printf("y=%.6f",y0);
return 0;
}
float func(float x,float y)
{
float m;
m=(x*(x+1)-3*y*y*y)/10;
return m;
}These are Problem Solving Through Programming In C Assignment 11 Answers
Question 4
Write a C program to check whether the given input number is Prime number or not using recursion. The input is an integer and output should print whether the integer is prime or not. (Note that you have to use recursion).
Solution:
int checkPrime(int num, int i)
{
if (i == 1)
{
return 1;
}
else
{
if (num % i == 0)
{
return 0;
}
else
{
return checkPrime(num, i - 1);
}
}
}These are Problem Solving Through Programming In C Assignment 11 Answers
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