Is the prayer valid with a drop of blood on the nose that did not fall during the prayer?

Slight nosebleed does not invalidate the prayer. Al-Baji narrated from Qadi Abu Muhammad the consensus of the Companions that nosebleed absolutely does not invalidate the prayer. Your prayer is valid and you do not need to repeat it, because the blood that came out is slight and is not considered an impurity that invalidates prayer, nor is it excessive blood that nullifies ablution. The preponderant opinion is that blood coming out from an unaccustomed exit does not nullify ablution, even if it is a large amount. One who experiences nosebleed during prayer should remove any accumulated blood immediately, as Saeed ibn al-Musayyab and Salim ibn Abdullah did.