Is it permissible to do Hajj on behalf of one person and ‘Umrah on behalf of another in the same year?

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Check below answers in case you are looking for other related questions:
If his family offer an udhiyah on his behalf whilst he is on Hajj, does he have to offer another udhiyah?
They form rings around the women in tawaaf and the Ka’bah is not to their left

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Related Answers:
He is not sure whether his father’s Hajj was valid; can he do Hajj on his behalf after his death?
Pilgrims who are not residents of Makkah should shorten their prayers in Mina, ‘Arafah and Muzdalifah
Is it permissible for the pilgrim in ihram to put a bandage on his knee because it is hurting him?
If his family offer an udhiyah on his behalf whilst he is on Hajj, does he have to offer another udhiyah?
They form rings around the women in tawaaf and the Ka’bah is not to their left

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