Sanskrit ṛ-stems · pitṛ, mātṛ, dātṛ

	pitṛ Masculine kinship · “father”
Nom.	pitā	pitarau	pitaraḥ
Acc.	pitaram	pitarau	pitṝn
Ins.	pitrā	pitṛbhyām	pitṛbhiḥ
Dat.	pitre	pitṛbhyām	pitṛbhyaḥ
Abl.	pituḥ	pitṛbhyām	pitṛbhyaḥ
Gen.	pituḥ	pitroḥ	pitṝṇām
Loc.	pitari	pitroḥ	pitṛṣu
Voc.	pitar	pitarau	pitaraḥ

Coral marks the strong stem pitar- — used in nom. sg., acc. sg., nom./acc./voc. dual, nom./voc. pl., loc. sg., voc. sg. The weak stem pitṛ- / pit- fills every other cell. Note the unique ablative/genitive sg. pituḥ (with unexpected -u-) and gen. pl. pitṝṇām (long ṝ + retroflex ṇ).

	mātṛ Feminine kinship · “mother”
Nom.	mātā	mātarau	mātaraḥ
Acc.	mātaram	mātarau	mātṝḥ
Ins.	mātrā	mātṛbhyām	mātṛbhiḥ
Dat.	mātre	mātṛbhyām	mātṛbhyaḥ
Abl.	mātuḥ	mātṛbhyām	mātṛbhyaḥ
Gen.	mātuḥ	mātroḥ	mātṝṇām
Loc.	mātari	mātroḥ	mātṛṣu
Voc.	mātar	mātarau	mātaraḥ

Coral marks the single cell that distinguishes the feminine from the masculine: acc. pl. mātṝḥ (long ṝ + visarga), where the masculine has pitṝn (with -n). Every other cell is identical to the masculine kinship paradigm — including the odd abl./gen. sg. mātuḥ.

	dātṛ Masculine agent · “giver”
Nom.	dātā	dātārau	dātāraḥ
Acc.	dātāram	dātārau	dātṝn
Ins.	dātrā	dātṛbhyām	dātṛbhiḥ
Dat.	dātre	dātṛbhyām	dātṛbhyaḥ
Abl.	dātuḥ	dātṛbhyām	dātṛbhyaḥ
Gen.	dātuḥ	dātroḥ	dātṝṇām
Loc.	dātari	dātroḥ	dātṛṣu
Voc.	dātar	dātārau	dātāraḥ

Coral marks where the agent subtype diverges from kinship: the strong stem of agent nouns is dātār- with long ā, not short a. So you get dātāram, dātārau, dātāraḥ where pitṛ would have pitaram, pitarau, pitaraḥ. Nom. sg. dātā, abl./gen. sg. dātuḥ, loc. sg. dātari, voc. sg. dātar — all identical to kinship.

1. The rule

ṛ-stems form a small but frequent class of agent and kinship nouns (Whitney §369–375; MacDonell §101). They use a strong/weak stem alternation: the strong stem surfaces in the nominative and accusative (sg./du./pl., except acc. pl.), the locative singular and the vocative; the weak stem fills every other cell. Kinship nouns use the short-vowel strong stem (pitar-), agent nouns the long-vowel strong stem (dātār-). Feminine and masculine kinship nouns decline identically except in acc. pl., where the feminine takes visarga (mātṝḥ) and the masculine takes -n (pitṝn).

2. How to remember

i Kinship vs. agent = short a vs. long ā in the strong stem. pitar-, mātar-, bhrātar-, svasar-, duhitar-, naptar- (kinship) — short. dātār-, kartār-, vaktār- (agent) — long. Same endings, different stem vowel. Memorise which words are kin and which are agents, then decline them identically.
ii Nom. sg. ends in -ā. Identical for both subtypes: pitā, mātā, bhrātā, dātā, kartā. The ṛ of the stem disappears entirely here — the longest-vowel form of the whole paradigm.
iii Abl./Gen. sg. is -uḥ. pituḥ, mātuḥ, dātuḥ — a unique ending in the nominal system. The ṛ becomes u before -ḥ in this one slot. Learn it by rote.
iv Gen. pl. lengthens and retroflexes: pitṝṇām, mātṝṇām, dātṝṇām — long ṝ and retroflex ṇ. This is the strongest cue that you're in an ṛ-stem paradigm.
v Acc. pl. distinguishes gender in kinship. Masc. pitṝn (with -n), fem. mātṝḥ (with visarga). The same split you have seen in agni/gati and bhānu/dhenu.

3. Exercise — all three paradigms

Three paradigms, 72 forms. Watch the short-a / long-ā split in the strong stem between kinship and agent nouns.

	pitṛ Masculine kinship · “father”
	Singular	Dual	Plural
Nom.
Acc.
Ins.
Dat.
Abl.
Gen.
Loc.
Voc.

	mātṛ Feminine kinship · “mother”
	Singular	Dual	Plural
Nom.
Acc.
Ins.
Dat.
Abl.
Gen.
Loc.
Voc.

	dātṛ Masculine agent · “giver”
	Singular	Dual	Plural
Nom.
Acc.
Ins.
Dat.
Abl.
Gen.
Loc.
Voc.

0 / 72 correct