virtual university of pakistan

#include<iostream.h>
#include<conio.h>
using namespace std;
class Vehicle{
public:

void display();
void setcompany(string a);
void setmodel(string a);
void setenginecapacity(int a);
void setyear(int a);

void getinput();
string getcompany();
string getmodel();
int getenginecapacity();
int getyear();

Vehicle();

Vehicle(string,string,int,int);

~Vehicle();
private:
string company;
string model;
int year;
int enginecapacity;
string company2;
string model2;
int year2;
int enginecapacity2;    
int number,S,C;
};
Vehicle::Vehicle()
{
company=S;
model=C;
year=2011;
enginecapacity=1500;
}
void Vehicle::getinput()
{

cout<<"Enter the number of vehicle :";
cin>>number;
cout<<"Vehicle1"<<endl;
cout<<"Enter the name of vehicle maker company :";
cin>>company;
cout<<"Enter the vehicle model :";
cin>>model;
cout<<"Enter year of registration :";
cin>>year;
cout<<"Enter the engine capacity of the vehicle :";
cin>>enginecapacity;
cout<<endl;

cout<<"Vehicle2"<<endl;
cout<<"Enter the name of vehicle maker company :";
cin>>company2;
cout<<"Enter the vehicle model :";
cin>>model2;
cout<<"Enter year of registration :";
cin>>year2;
cout<<"Enter the engine capacity of the vehicle :";
cin>>enginecapacity2;
cout<<endl;
}




Vehicle::~Vehicle()
{
cout<<"object deleted"<<endl;          
}

void Vehicle::display()
{

cout<<"vehicle 1"<<endl<<"Enter the vehicle maker company :"<<getcompany()<<endl<<"Enter the vehicle model :"<<getmodel()<<endl<<"Enter year of registration :"<<getyear()<<endl<<"Enter the engine capacity of the vehicle :"<<getenginecapacity();
cout<<endl;

cout<<"vehicle 2"<<endl<<"Enter the vehicle maker company :"<<company2<<endl<<"Enter the vehicle model :"<<model2<<endl<<"Enter year of registration :"<<year2<<endl<<"Enter the engine capacity of the vehicle :"<<enginecapacity2;
cout<<endl;
}


void Vehicle::setcompany(string k)
{
company=k;                      
}
void Vehicle::setmodel(string a)
{
model=a;                    
}
void Vehicle::setyear(int a)
{
year=a;                    
}
void Vehicle::setenginecapacity(int a)
{
enginecapacity=a;    
}
string Vehicle::getcompany()
{
return company;  
}
int Vehicle::getenginecapacity()
{
return enginecapacity;  
}
string Vehicle::getmodel()
{
return model;  
}
int Vehicle::getyear()
{
return year;  
}



int main()
{
    Vehicle raousman1;

    raousman1.getinput();
    raousman1.display();
    raousman1.~Vehicle();
   
getch();
}

Q#01: Use mathematical induction to prove that for every integer with . (Note that this inequality is false for and .) Marks = 6
BASIC STEP:
p(4) = 2^n 
2^4 =16 < 24 = 4!

INDUCTIVE STEP:

For this step we assume that p(k) is true for posiive integer k with k>=4
Assume:
2^k < k!
2^k+1 < (k+1)!
2^k+1 = 2.2^k

< 2.k!

< (k+1)k!

= (k+1)!

So p(k+1) is true when p(k) is true.

Q#02: Find the GCD of and using Division Algorithm. Marks = 4
Let a= 4566891 and b=182 . Also, let's introduce the variable "r" for the remainder
Let's evaluate a/b . It turns out that a/b = 25092 remainder 147. What we're are interested in is the remainder.
So let . Now assign the value of "b" to "a" and the value of "r" to "b".
So now a=182 ,b=147 and r=147

Now we must ask ourselves: "Does b=0?". Since b=147 (which is NOT zero), we must start all over and keep going until "b" equals zero.

Let's evaluate a/b . It turns out that a/b= 182/147 = 1 remainder 35. What we're are interested in is the remainder.
So let . Now assign the value of "b" to "a" and the value of "r" to "b".
So now a=147 ,b=35 , and r=35

Now we must ask ourselves: "Does b=0?". Since b=35 (which is NOT zero), we must start all over and keep going until "b" equals to zero

Let's evaluate a/b . It turns out that a/b= 147/35 = 4 remainder 7. What we're are interested in is the remainder.
So let . Now assign the value of "b" to "a" and the value of "r" to "b".
So now a=35 ,b=7 , and r=7

Now we must ask ourselves: "Does b=0?". Since b=7 (which is NOT zero), we must start all over and keep going until "b" equals zero.

Let's evaluate a/b . It turns out that a/b = 35/7 = 5 remainder 0. What we're are interested in is the remainder.
So let . Now assign the value of "b" to "a" and the value of "r" to "b".
So now a=7 ,b=0 , and r=0
Since the value of b is now zero, we can stop the process.
Now the value of "a" in the last row is the GCD of the numbers "a" and "b" 
So this means that GCD(4566891,182)=7.


Q#03: Define a sequence by the formula , for all integers . Show that this sequence satisfies the recurrence relation , with and for all integers . Marks = 5

Question No 1

(a)What is the electric field at the location of the test charge shown below? And what is the direction of electric field? Marks = 5

(b) What are the magnitude and direction of the electric field at point A shown below? Marks = 6

Question No 2

Find the force on the electron in figure shown below and also determine the acceleration of electron? Mention the direction of force and acceleration as well.
Note that mass of electron is 9.1×10-31kg, and the value of charge on electron is (-1.6×10-19 C)
Marks = 7

Question No 3

Is it true to say that electric field lines are the same as electric field vectors. If yes give an example if not explain it. Marks = 6

Question No 4

Suppose you increased the amount of the charge of a test charge, and the force exerted on it
changed. This means the field you were assessing must have changed. Marks = 5

Question No 5

(a) It takes 10.0 J of work by the right-hand wand to separate the charges as shown in figure.
What is the change in potential energy? Marks = 3


(b) Is it true to say that electric potential energy and electric potential are the same?
Either yes or no explain in each case. Marks = 3



Solutions

Q1.a
E=F/q
use this formula to find Electric field.
Q.1.b
E=K.q/r2 (r square)
use this formula to find magnitude.
Q.3