Write a single C program to implement Linear and binary search in two different functions. Plot the execution_time/input_size plot for both these functions for at least 10 input instances.

Sure, here is a simple C program that implements both linear and binary search.

#include <stdio.h>
#include <time.h>

// Linear Search Function
int linearSearch(int array[], int size, int element){
    for(int i=0; i<size; i++){
        if(array[i] == element){
            return i;
        }
    }
    return -1;
}

// Binary Search Function
int binarySearch(int array[], int size, int element){
    int low, mid, high;
    low = 0;
    high = size-1;
    // Keep searching until low <= high
    while(low<=high){
        mid = (low + high)/2;
        if(array[mid] == element){
            return mid;
        }
        if(array[mid]<element){
            low = mid+1;
        }
        else{
            high = mid-1;
        }
    } 
    return -1;
}

int main(){
    // Use the clock function to get the start time
    clock_t start, end;
    double cpu_time_used;
    
    int array[] = {1,2,3,4,5,6,7,8,9,10};
    int size = sizeof(array)/sizeof(int);
    
    // Linear Search
    start = clock();
    printf("Found element at index: %d\n", linearSearch(array, size, 5));
    end = clock();
    cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
    printf("Time taken for linear search: %f\n", cpu_time_used);
    
    // Binary Search
    start = clock();
    printf("Found element at index: %d\n", binarySearch(array, size, 5));
    end = clock();
    cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
    printf("Time taken for binary search: %f\n", cpu_time_used);
    
    return 0;
}

This program will print the index of the element if it is found, and -1 if it is not found. It will also print the time taken for each search.

To plot the execution time/input size plot, you would need to run this program with different input sizes and record the time taken for each. You can then use a tool like Excel or a library like matplotlib in Python to create the plot.

Please note that the time taken by these functions will be very small for small input sizes, and may even be reported as 0 by the clock function. You may need to use larger input sizes to see a difference. Also, the binary search function assumes that the input array is sorted.