1. Where has the प्रातिपदिकम् ‘एक’ been used in the first five verses of Chapter Three of the गीता?
Answer: The प्रातिपदिकम् ‘एक’ been used in the following verse in the form एकम् (नपुंसकलिङ्गे, द्वितीया-एकवचनम्)।
व्यामिश्रेणेव वाक्येन बुद्धिं मोहयसीव मे |
तदेकं वद निश्चित्य येन श्रेयोऽहमाप्नुयाम्‌ || 3-2||

2. Commenting on the affix कन् the सिद्धान्तकौमुदी says बाहुलकान्न कस्येत्संज्ञा। Please explain.
Answer: Shouldn’t the letter ‘क्’ in the affix कन् get the designation इत् by 1-3-8 लशक्वतद्धिते? Yes, normally it should. But if it did it would be elided by 1-3-9 तस्य लोपः and we would not get the desired form ‘एक’। Hence we take recourse to the mention of बहुलम् (variously) in the सूत्रम् 3-3-1 उणादयो बहुलम् in order to prevent the letter ‘क्’ from getting the designation इत्। The महाभाष्यम् states that one of the reasons for पाणिनि: mentioning बहुलम् in the सूत्रम् 3-3-1 is – कार्यसशेषविधेश्च तदुक्तम् – (and) among the operations which take place on applying these affixes (उण् etc) some have not been enumerated. In our present example, the mention of बहुलम् gives us the license to assume that – even though not explicitly stated – letter ‘क्’ in the affix कन् get not the designation इत्। This is what is meant by the statement बाहुलकान्न कस्येत्संज्ञा।

3. Which उणादि-प्रत्यय: is used to derive the प्रातिपदिकम् ‘भीम’? (Search the following document for ‘भीम’ – http://avg-sanskrit.org/notes-for-saturday-class/उणादिप्रकरणम्/)
Answer: The उणादि-प्रत्ययः ‘मक्’ by 1-145 भियः षुग्वा is used to derive the प्रातिपदिकम् ‘भीम’।

The प्रातिपदिकम् ‘भीम’ is derived from the verbal root √भी (ञिभी भये ३. २).

भी + मक् । By the उणादि-सूत्रम् 1-145 भियः षुग्वा – The affix ‘मक्’ comes after the verbal root √भी (ञिभी भये ३. २) with the optional augment ‘षुक्’। In the present example we’re considering the case where the optional augment ‘षुक्’ is not attached. Note: As per 3-4-74 भीमादयोऽपादाने – (The affixes occurring in a few) words such as ‘भीम’ etc are in the ablative sense. बिभेत्यस्मादिति भीम:। He from whom one is afraid is भीम:।
= भी + म । अनुबन्ध-लोप: by 1-3-3 हलन्त्यम् and 1-3-9 तस्य लोपः। Note: 7-2-8 नेड् वशि कृति – as well as 7-2-10 एकाच उपदेशेऽनुदात्तात्‌ – prevents the affix ‘मक्’ from taking the augment ‘इट्’ here. Note: 1-1-5 क्क्ङिति च prevents 7-3-84 सार्वधातुकार्धधातुकयोः from applying.
= भीम । ‘भीम’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च।

4. Can you spot the affix ‘ड’ in the verses?
Answer: The affix ‘ड’ is applied to derive the स्त्रीलिङ्ग-प्रातिपदिकम् ‘प्रजा’ used in the form प्रजाः (द्वितीया-बहुवचनम्)।
Please see the following post for the derivation of the form प्रजाः – http://avg-sanskrit.org/2012/11/12/प्रजाः-fap/

5. How would you say this in Sanskrit?
“The truth is only one but lies could be many.” Use the प्रातिपदिकम् ‘अनृत’ in the neuter for ‘lie.’
Answer: सत्यम् एकम् एव अस्ति परन्तु अनृतानि बहूनि भवेयुः = सत्यमेकमेवास्ति परन्त्वनृतानि बहूनि भवेयुः।

6. How would you say this in Sanskrit?
“Hold the book with one hand and write with the other (hand.)”
Answer: एकेन हस्तेन पुस्तकम् धारय अन्येन च (हस्तेन) लिख = एकेन हस्तेन पुस्तकं धारयान्येन च (हस्तेन) लिख ।
अथवा –
एकेन हस्तेन पुस्तकम् धारयित्वा अन्येन (हस्तेन) लिख = एकेन हस्तेन पुस्तकं धारयित्वान्येन (हस्तेन) लिख ।

Easy questions:

1. Where has the affix ‘णल्’ been used in the verses?
Answer: An affix ‘णल्’ is seen in the form विवेश derived from the verbal root √विश् (तुदादि-गणः, विशँ प्रवेशने, धातु-पाठः # ६. १६०).
Please see answer to question 4 in the following comment for derivation of the form विवेश – http://avg-sanskrit.org/2012/09/20/कृत्यम्-nas/#comment-4501

2. How would you say this in Sanskrit?
“I have only one car.” Paraphrase to “Only one car of mine exists.” Use the verbal root √वृत् (वृतुँ वर्तने १. ८६२) for “to exist.”
Answer: मम एकम् एव वाहनम् वर्तते = ममैकमेव वाहनं वर्तते ।