Statement 1: Linear search is based on the sequential approach and binary search is based on the divide and conquer approach.

The first statement is true.

Linear Search: Linear search is a simple search algorithm that sequentially checks each element in a list until a match is found or the end of the list is reached. It starts from the beginning of the list and compares each element with the target value. If a match is found, the search is successful, otherwise, it continues to the next element. This process continues until the target value is found or the end of the list is reached.

It is called a sequential approach because it goes through each element in a linear manner, one by one, until the desired element is found.

Binary Search: Binary search is a more efficient search algorithm used for searching elements in sorted lists or arrays. It follows a divide and conquer approach. In binary search, the list is divided into two halves repeatedly until the target element is found or the search space is reduced to zero.

The algorithm starts by comparing the target value with the middle element of the list. If the target value is equal to the middle element, the search is successful. If the target value is less than the middle element, the search continues in the left half of the list. If the target value is greater than the middle element, the search continues in the right half of the list. This process is repeated until the target value is found or the search space is reduced to zero.

Binary search is based on the divide and conquer approach because it divides the search space into smaller subproblems and solves them recursively.

Statement 2: Binary search algorithm takes more than a linear search algorithm.

The second statement is false.

Binary search is generally more efficient than linear search, especially for large lists or arrays. In linear search, the average case time complexity is O(n) where n is the number of elements in the list. On the other hand, binary search has an average case time complexity of O(log n) which is significantly faster than linear search.

The reason for this efficiency is that binary search reduces the search space by half with each comparison, while linear search goes through each element one by one. Therefore, binary search takes fewer comparisons and has a logarithmic time complexity.

In conclusion, statement 1 is true as linear search is based on the sequential approach and binary search is based on the divide and conquer approach. However, statement 2 is false as the binary search algorithm is generally faster than a linear search algorithm.