In spite of the rain, they went out. (complex)

The correct answer is - ক) Though it was raining, they went out.

Simple sentence-এ যদি In spite of ব্যবহৃত হয়, তাহলে Complex sentence করতে হলে Though/Although ব্যবহার করতে হয়।
আবার, Complex sentence-এ Though/Although থাকলে, সেটিকে Simple sentence করতে হলে In spite of বসে।

• Example:
Simple: In spite of his poverty, he is happy.
Complex: Though he is poor, he is happy.

• More examples:
Simple: In spite of the bad weather, we went there.
Complex: Though the weather was bad, we went there.

Simple: In spite of his bad behaviour, people mix with him.
Complex: Though his behaviour is bad, people mix with him.

Simple: In spite of his honesty, he is not happy.
Complex:Though he is honest, he is not happy.
or, Honest as he is, he is not happy.

Simple: In spite of his cruelty, I love him.
Complex: Though he is cruel, I love him.

Other options
খ) Though it rains, they went out.
বাক্যে Tense মিল নেই (present + past)।

গ) Because it was raining, they went out.
বাক্যটি ভুল, কারণ বৃষ্টির কারণে তারা বাইরে যাওয়া উচিত ছিল না।

ঘ) Despite raining, they went out.
"Despite" সাধারণত noun বা pronoun এর সঙ্গে আসে, "raining" এখানে gerund হওয়া সত্ত্বেও formal usage এ কম ব্যবহৃত।

Source: A Passage to the English Language by S M Zakir Hussain.