how can I give hsc improvement exam if I have already taken admission for btech
Yes you can do that but there are some different rules for different board
for
CBSC- You can appear for improvement exam in the next year after your first attempt
Different State boards have some different rules Some state boards (e.g., Maharashtra HSC Board) allow improvement attempts within 1–2 years, but rules and subject limits vary. You need to apply to your original school/board office
but also check University criteria