option C is the right answer here,

alternate is the right spelling

which means; 

(used about two types of events, things, etc.) happening or following regularly one after the other

(दो प्रकार की परिस्थितियों, वस्‍तुओं आदि के लिए प्रयुक्त) बारी-बारी से, पहले के बाद दूसरा और फिर पहला—ऐसा क्रम

alternate periods of sun and showers

other three options are spelt correctly