1. Where has the सूत्रम् 2-3-71 कृत्यानां कर्तरि वा been used between verses 20-25 of Chapter Three of the गीता?
Answer: The सूत्रम् 2-3-71 कृत्यानां कर्तरि वा has been used to optionally assign a sixth case affix in the form मे (सर्वनाम-प्रातिपदिकम् ‘अस्मद्’, षष्ठी-एकवचनम्) in the following verse –

न मे पार्थास्ति कर्तव्यं त्रिषु लोकेषु किञ्चन |
नानवाप्तमवाप्तव्यं वर्त एव च कर्मणि || 3-22||

Here ‘अस्मद्’ (‘I’) is the doer of the actions (of doing as well as obtaining) denoted respectively by the words ‘कर्तव्य’ and ‘आप्तव्य’ (both of which end in the ‘कृत्य’ affix ‘तव्यत्’/’तव्य’ prescribed by the सूत्रम् 3-1-96 तव्यत्तव्यानीयरः।) Hence ‘अस्मद्’ optionally takes a sixth case affix to give the form मम/मे।
Note: When the sixth case affix is not used, a third case affix is used as per 2-3-18 कर्तृकरणयोस्तृतीया to give the optional form मया।

2. Commenting on the सूत्रम् 2-3-71 the सिद्धान्तकौमुदी says – अत्र योगो विभज्यते। कृत्यानाम्। उभयप्राप्ताविति नेति चानुवर्तते। तेन नेतव्या व्रजं गाव: कृष्णेन। तत: कर्तरि वा। Please explain.
Answer: As per the महाभाष्यम् the सूत्रम् 2-3-71 कृत्यानां कर्तरि वा should be split into two parts – (i) कृत्यानां and (ii) कर्तरि वा । The अनुवृत्ति: of ‘उभयप्राप्तौ’ (from 2-3-66) and ‘न’ (from 2-3-69) comes in to (i). Hence the meaning of (i) becomes – When there is a possibility of using a sixth case affix with both कर्ता (the doer) and कर्म (the object) of an action denoted by a word ending in a ‘कृत्य’ affix, then a sixth case affix cannot be used to denote either of them.
For example –
नेतव्या व्रजं गाव: कृष्णेन The cows should be taken to the cow-pen by Lord Kṛṣṇa. Here ‘व्रज’ as well as ‘कृष्ण’ could have taken a sixth case affix as per 2-3-65 कर्तृकर्मणोः कृति। Now by (i) neither of them can take a sixth case affix. Instead ‘व्रज’ takes a second case affix as per 2-3-2 कर्मणि द्वितीया to give the form व्रजम्, and ‘कृष्ण’ takes a third case affix as per 2-3-18 कर्तृकरणयोस्तृतीया to give the form कृष्णेन। Note: The real purpose of doing the योगविभाग: is to prevent ‘व्रज’ from taking a sixth case affix. The सूत्रम् 2-3-66 उभयप्राप्तौ कर्मणि already prevents ‘कृष्ण’ from taking a sixth case affix. We do not need योगविभाग: of 2-3-71 for that.

The अनुवृत्ति: of ‘कृत्यानाम्’ (from (i)) comes in to (ii). The meaning of (ii) is – A sixth case affix (‘ङस्’, ‘ओस्’, ‘आम्’) is optionally used to denote कर्ता (the doer) of an action denoted by a word ending in a ‘कृत्य’ affix (prescribed in the अधिकार: of 3-1-95 कृत्याः।) e.g. मम सेव्यो हरिः, मया सेव्यो हरिः।

3. Commenting on the सूत्रम् 2-3-71 the तत्त्वबोधिनी says – ‘कर्तृकर्मणो: -‘ इति नित्ये प्राप्ते विभाषेयम्। Please explain.
Answer: In the absence of the सूत्रम् 2-3-71 कृत्यानां कर्तरि वा, a sixth case affix would have always been used (as per the सूत्रम् 2-3-65 कर्तृकर्मणोः कृति) to denote the agent of an action denoted by a word ending in a ‘कृत्य’ affix (since ‘कृत्य’ affixes are a subset of ‘कृत्’ affixes.) But now the सूत्रम् 2-3-71 makes the assignment of a sixth case affix (to denote the agent of an action denoted by a word ending in a ‘कृत्य’ affix) optional.

4. Where has the सूत्रम् 2-3-69 न लोकाव्ययनिष्ठाखलर्थतृनाम्‌ been used in the verse?
Answer: The सूत्रम् 2-3-69 न लोकाव्ययनिष्ठाखलर्थतृनाम्‌ states – A sixth case affix (‘ङस्’, ‘ओस्’, ‘आम्’) is not used (to denote कर्ता (the doer) or कर्म (the object)) of an action denoted by any one of the following –
(i) (a word ending in a substitute in place of) the affix ‘ल्’ (लँट्, लिँट् etc.)
(ii) (a word ending in) the affix ‘उ’ or an affix ending in ‘उ’
(iii) (a word ending in) the affix ‘उक’
(iv) an indeclinable
(v) (a word ending in) a निष्ठा affix (ref. 1-1-26 क्तक्तवतू निष्ठा।)
(vi) (a word ending in) the affix ‘खल्’ or any affix having the same meaning as that of ‘खल्’
(vii) (a word ending in) an affix from the प्रत्याहार: ‘तृन्’ which is formed starting from ‘तृ’ in 3-2-124 लटः शतृशानचावप्रथमासमानाधिकरणे down to 3-2-135 तृन्।

The प्रातिपदिकम् ‘वर्षुक’ used in the verses ends in the affix ‘उक’ (prescribed by 3-2-154 लषपतपदस्थाभूवृषहनकमगमशॄभ्य उकञ्)। Hence the सूत्रम् 2-3-69 न लोकाव्ययनिष्ठाखलर्थतृनाम्‌ prevents the object ‘अप्’ of the agent ‘वर्षुक’ from taking the sixth case affix (which would have applied as per by 2-3-65 कर्तृकर्मणोः कृति)। ‘अप्’ instead takes a second case affix by 2-3-2 कर्मणि द्वितीया to give the form अप:।

Please see answer to easy question 2 below for the derivation of the form अपः (feminine प्रातिपदिकम् ‘अप्’, द्वितीया-बहुवचनम्)।

5. Consider the प्रातिपदिकम् ‘बहुप्रद’ used in the commentary. Can you find the सूत्रम् (which we have seen in a prior comment) that justifies the use of the affix ‘क’ in the derivation of ‘बहुप्रद’? Note that 3-2-3 आतोऽनुपसर्गे कः cannot be used here because the उपसर्ग: ‘प्र’ is present. Hint: The अनुवृत्ति: of ‘क’ goes from 3-2-3 आतोऽनुपसर्गे कः down to 3-2-7 समि ख्यः।
Answer: The सूत्रम् 3-2-6 प्रे दाज्ञः justifies the use of the affix ‘क’ in the प्रातिपदिकम् ‘बहुप्रद’।

बहु प्रददाति = बहुप्रदः।

‘प्रद’ is a कृदन्त-प्रातिपदिकम् (participle form) derived from the verbal root √दा (डुदाञ् दाने ३. १०) preceded by the उपसर्गः ‘प्र’।
The (compound) प्रातिपदिकम् ‘बहुप्रद’ is derived as follows:
बहु + ङस् (ref: 2-3-65 कर्तृकर्मणोः कृति) + प्र दा + क । By 3-2-6 प्रे दाज्ञः – When preceded by the उपसर्गः ‘प्र’ and in composition with a पदम् which denotes the object (of the action), the verbal roots √दा (डुदाञ् दाने ३. १०) and √ज्ञा (ज्ञा अवबोधने ९. ४३) take the affix ‘क’। Note: The affix ‘क’ (prescribed by this सूत्रम्) is an exception to the affix ‘अण्’ prescribed by 3-2-1 कर्मण्यण्।
Note: In the सूत्रम् 3-2-6 प्रे दाज्ञः, the term कर्मणि (which comes as अनुवृत्ति: from the सूत्रम् 3-2-1 कर्मण्यण्) ends in the seventh (locative) case. Hence ‘बहु + ङस्’ (which is the object (कर्म-पदम्) of प्रददाति) gets the उपपद-सञ्ज्ञा here by 3-1-92 तत्रोपपदं सप्तमीस्थम्‌।
= बहु + ङस् + प्र दा + अ । अनुबन्ध-लोप: by 1-3-8 लशक्वतद्धिते and 1-3-9 तस्य लोपः।
= बहु + ङस् + प्र द् + अ । By 6-4-64 आतो लोप इटि च।
= बहु + ङस् + प्रद । We form a compound between ‘बहु + ङस्’ (which is the उपपदम्) and ‘प्रद’ by using the सूत्रम् 2-2-19 उपपदमतिङ्।
In the compound, ‘बहु + ङस्’ is placed in the prior position as per 2-2-30 उपसर्जनं पूर्वम्‌। Note: Here ‘बहु + ङस्’ is the उपपदम् and hence it gets the उपसर्जन-सञ्ज्ञा by 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् – A term denoted by a word (in this case ‘उपपदम्’) ending in a nominative case in a सूत्रम् (in this case 2-2-19 उपपदमतिङ्) which prescribes a compound gets the designation ‘उपसर्जन’।
‘बहु + ङस् + प्रद’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च।
= बहुप्रद । By 2-4-71 सुपो धातुप्रातिपदिकयोः।

6. How would you say this in Sanskrit?
“All of us ought to study the Gīta.” Paraphrase to “The Gīta ought to be studied by all of us.” Use the verbal root √इ (इङ् अध्ययने – नित्यमधिपूर्वः २. ४१) with the उपसर्ग: ‘अधि’ for ‘to study.’
Answer: अस्माभिः सर्वैः गीता अधीतव्या = अस्माभिः सर्वैर्गीताधीतव्या।
अथवा –
अस्माकम् सर्वेषाम् गीता अधीतव्या = अस्माकं सर्वेषां गीताधीतव्या।

Easy questions:
1. Which सूत्रम् prescribes the elision of the letter ‘इ’ in the form अभवत्?
Answer: The सूत्रम् 3-4-100 इतश्च prescribes the elision of the letter ‘इ’ in the form अभवत् – derived from √भू (भू सत्तायाम् १. १). As per 3-4-100 इतश्च – The ending letter of a इकारान्तः (ending in the letter ‘इ’) परस्मैपदम् affix which came in the place of a ङित्-लकारः (लकारः having the letter ‘ङ्’ as a इत्), is elided.

Please see answer to easy question 1 in the following comment for derivation of the form अभवत् – http://avg-sanskrit.org/2012/10/24/जनमेजयः-mns/#comment-5711

2. In the verse can you spot a प्रातिपदिकम् which is used only in the plural (no singular or dual)?
Answer: The feminine प्रातिपदिकम् ‘अप्’ (which occurs in the form अपः (द्वितीया-बहुवचनम्) in the verses) is used only in the plural.
अप् + शस् । By 4-1-2 स्वौजसमौट्छष्टा……..।
= अप् + अस् । By 1-3-8 लशक्वतद्धिते, 1-3-9 तस्य लोपः। 1-3-4 न विभक्तौ तुस्माः prevents the ending letter ‘स्’ of ‘शस्’ from getting the इत्-सञ्ज्ञा।
= अपः । रुँत्व-विसर्गौ by 8-2-66 ससजुषो रुः and 8-3-15 खरवसानयोर्विसर्जनीयः।