Using modern radio-carbon techniques, fossils unearthed from the ruins of the Mohenjodaro-Harappa civilization can be accurately dated with near zero chances of error.A. Using modern radio-carbon techniques, fossils unearthed from the ruins of the Mohenjodaro-Harappa civilization can be accurately dated with near zero chances of error. -> who is using modern radio-carbon techniques, is it fossils unearthed or a scientist. Incorrect.
B. Fossils unearthed from the ruins of the Mohenjodaro-Harappa civilization can be accurately dated, using modern radio-carbon techniques with near zero chances of error. -> We need a modifier for "using modern..." Incorrect.
C. Dating fossils unearthed from the ruins of Mohenjodaro-Harappa civilization accurately, scientists can use modern radio-carbon techniques. -> Incorrect, as scientists can date fossils...using modern radio-carbon techniques.
D. Using modern radio-carbon techniques, fossils unearthed from the ruins of Mohenjodaro-Harappa civilization can be accurately dated by a scientist with near zero chances of error. -> Same as A.
E. Using modern radio-carbon technique, scientists can date fossils unearthed from the ruins of Mohenjodaro-Harappa civilization accurately with near zero chances of error. -> It is better.
So, I think E.