kathám ind. (fr. 2. ka), how? in what manner? whence? (e.g. katham etat, how is that? katham idānīm, how now? what is now to be done? katham mārātmake tvayi viśvāsaḥ, how can there be reliance on thee of murderous mind? katham utsṛjya tvāṃ gaccheyam, how can I go away deserting you? katham buddhvā bhaviṣyati sā, how will she be when she awakes? katham mṛtyuḥ prabhavati vedavidām, whence is it that death has power over those that know the Veda? katham avagamyate, whence is it inferred?);
sometimes merely introduces an interrogation (e.g. katham ātmānaṃ nivedayāmi kathaṃ vātmāpahāraṃ karomi, shall I declare myself or shall I withdraw?) is often found in connection with the particles iva, nāma, nu, svid, which appear to generalize the interrogation (how possibly? how indeed? &c.)
with nu it is sometimes = kimu, or kutas (e.g. kathaṃ nu, how much more! na kathaṃ nu, how much less!) is often connected, like kim, with the particles cana, cid, and api, which give an indefinite sense to the interrogative (e.g. kathaṃ cana, in any way, some how; scarcely, with difficulty; na kathaṃ cana, in no way at all; kathaṃcit, some how or other, by some means or other, in any way, with some difficulty, scarcely, in a moderate degree, a little; na kathaṃcit, not at all, in no way whatever; na kathaṃcid na, in no way not i.e. most decidedly; yathā kathaṃcit, in any way whatsoever; kathaṃcid yadi jīvati, it is with difficulty that he lives; katham api, some how or other, with some difficulty, scarcely a little; katham api na, by no means, not at all), [RV.] &c.
according to lexicographers is a particle implying amazement