lets analyze the options one by one....
1> Clearly binary search can be implemented if the array is sorted. Hence search can be performed in O(logn).
2>Lets take an example first..
Consider an array with elements 1234567. Now, suppose the array is rotated by 2 then the new array will be 3456712. Here k is 2. As, k is known to us finding the pivot point is easy it will be just = (n-1)-k ;where n is the size of the array. Here it is 4. Now, to search for an element divide the array in two subarrays . Now compare the number with the 0th element, if the number is greater than the 0th element then apply binary search in left subarray to pivot else apply binary search to right subarray...Hence searching can be performed in O(logn).
3>Here k is not known. Hence the pivot point is not known, if we can get the pivot point then we can apply the same method as above.
Now cosider the above example. The pivot point has the property that the pivot point element is the only element whose next element is smaller than it in the array.Hence we can find the pivot in O(logn) applying binary search like seaching. and the rest are same as above Hence the total complexity becomes O(logn)+O(logn)=O(logn).
Hence 1,2 and 3 are correct options