1. Where has the प्रातिपदिकम् ‘श्रद्धा’ been used in Chapter Twelve of the गीता?
Answer: The प्रातिपदिकम् ‘श्रद्धा’ has been used in the form श्रद्धया (तृतीया-एकवचनम्) in the following verse of Chapter Twelve of the गीता –
श्रीभगवानुवाच |
मय्यावेश्य मनो ये मां नित्ययुक्ता उपासते |
श्रद्धया परयोपेतास्ते मे युक्ततमा मताः || 12-2||

2. Commenting on the वार्तिकम् ‘श्रदन्तरोरुपसर्गवद् वृत्तिः’ the लघुशब्देन्दुशेखर: (which is a commentary by नागेश: on the सिद्धान्तकौमुदी) says – तत्र श्रतोऽङ्विधावेव। अन्त:शब्दस्याङ्किविधिणत्वेष्विति भाष्ये स्पष्टम्। तेन ‘अन्तर्धा’, ‘अन्तर्धि:’, ‘अन्तर्णयति’ इत्यादिसिद्धि:। Please explain.
Answer: With regard to the वार्तिकम् ‘श्रदन्तरोरुपसर्गवद् वृत्तिः’ it has been clearly stated in the महाभाष्यम् that ‘श्रत्’ should be treated as a उपसर्ग: only in the situation where the affix ‘अङ्’ is to be used. And ‘अन्तर्’ should be treated as a उपसर्ग: only in the following three situations – i) where the affix ‘अङ्’ is to be used – giving अन्तर्धा i) where the affix ‘कि’ is to be used – giving अन्तर्धि: and iii) where the substitution ‘ण्’ (in place of ‘न्’) is to be made – for example अन्तर्णयति।

3. Derive the प्रातिपदिकम् ‘स्पृहा’। Hint: भिदादेराकृतिगणत्वादङ्।
Answer: The प्रातिपदिकम् ‘स्पृहा’ is derived from the verbal root √स्पृह (स्पृह ईप्सायाम् १०. ४१०) as follows:
स्पृह + णिच् । By 3-1-25 सत्यापपाशरूपवीणातूलश्लोकसेनालोमत्वचवर्मवर्णचूर्णचुरादिभ्यो णिच्।
= स्पृह + इ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-7 चुटू, 1-3-9 तस्य लोपः।
= स्पृह् + इ । By 6-4-48 अतो लोपः। Note: As per 7-3-86 पुगन्तलघूपधस्य च, the affix ‘णिच्’ would do a गुण: substitution in place of the letter ‘ऋ’ of the अङ्गम् ‘स्पृह्’। But this does not happen because as per 1-1-57 अचः परस्मिन् पूर्वविधौ, the लोप: done by 6-4-48 has स्थानिवद्-भाव: (it behaves like the item it replaced – the letter ‘अ’) when it comes to an operation (गुण:) that would be performed to the left of it. Hence as far as 7-3-86 is concerned, the उपधा of the अङ्गम् is the letter ‘ह्’ and hence it cannot apply.
= स्पृहि । ‘स्पृहि’ gets धातु-सञ्ज्ञा by 3-1-32 सनाद्यन्ता धातवः।

स्पृहि + अङ् । By 3-3-104 षिद्भिदादिभ्योऽङ् – Following verbal roots which have the letter ‘ष्’ as a marker and the verbal roots enumerated in the list √भिद् (भिदिँर् विदारणे ७. २) etc the affix अङ् is used to denote in the feminine gender either (i) the sense of the verbal root as having attained to a completed state or (ii) any कारक: except the agent of the action, provided the word so derived is a proper name.
Note: The verbal roots √भिद् (भिदिँर् विदारणे ७. २) etc are not listed together in the धातु-पाठ:। Instead गणपरिपठितेषु भिदादिषु निष्कृष्य प्रकृतयो गृह्यन्ते – the final forms ‘भिदा’ etc are listed in the भिदादिगण: in the गण-पाठ:। From these forms we have to extract the verbal roots √भिद् (भिदिँर् विदारणे ७. २) etc to which the affix अङ् is prescribed by this सूत्रम्।
Note: स्पृहा is considered to be in the भिदादिगण: (even though it is not specifically listed there) because the भिदादिगण: is a आकृतिगण: – which is a class or group of words in which some words are actually mentioned and room is left to include others which are found undergoing the same operations.
= स्पृहि + अ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम् and 1-3-9 तस्य लोपः। Note: 1-1-5 क्क्ङिति च prevents 7-3-84 सार्वधातुकार्धधातुकयोः from applying.
= स्पृह् + अ । By 6-4-51 णेरनिटि।
= स्पृह । ‘स्पृह’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च।

Note: Since this प्रातिपदिकम् is used in the feminine gender we have to add the appropriate feminine affix (स्त्रीप्रत्यय:)।
स्पृह + टाप् । By 4-1-4 अजाद्यतष्टाप्‌।
= स्पृह + आ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-7 चुटू, 1-3-9 तस्य लोपः।
= स्पृहा । By 6-1-101 अकः सवर्णे दीर्घः।

4. Where has the सूत्रम् 3-2-83 आत्ममाने खश्च been used in the verses?
Answer: The सूत्रम् 3-2-83 आत्ममाने खश्च has been used in the form शूरमानिनाम् (प्रातिपदिकम् ‘शूरमानिन्’, पुंलिङ्गे षष्ठी-बहुवचनम्)।

शूरमात्मानं मन्यते = शूरमानी।

The derivation of the प्रातिपदिकम् ‘शूरमानिन्’ is as shown in the following post – http://avg-sanskrit.org/2012/11/07/

5. Which सूत्रम् justifies the use of the affix घञ् in the प्रातिपदिकम् ‘सार’?
Answer: The सूत्रम् 3-3-17 सृ स्थिरे justifies the use of the affix घञ् in the प्रातिपदिकम् ‘सार’ derived from the verbal root √सृ (सृ गतौ १. १०८५, सृ गतौ ३. १८).
Please see the following post for derivation of the प्रातिपदिकम् ‘सार’ – http://avg-sanskrit.org/2013/03/07/सारम्-mas/

6. How would you say this in Sanskrit?
“Knowledge comes only to him who has faith in the teacher’s words.” Paraphrase to “Knowledge comes only to him whose faith in the teacher’s words exists.” Use the verbal root √इ (इण् गतौ २. ४०) with the उपसर्ग: ‘उप’ for ‘to come (near.)’
Answer: गुरोः वचनेषु यस्य श्रद्धा वर्तते तम् एव ज्ञानम् उपैति = गुरोर्वचनेषु यस्य श्रद्धा वर्तते तमेव ज्ञानमुपैति।

Easy questions:

1. Which सूत्रम् prescribes the substitution ‘त’ in the form तिष्ठत?
Answer: The सूत्रम् 3-4-101 तस्थस्थमिपां तांतंतामः prescribes the substitution ‘त’ in the form तिष्ठत – derived from the verbal root √स्था (ष्ठा गतिनिवृत्तौ १. १०७७).

The विवक्षा is लोँट्, कर्तरि प्रयोग:, मध्यम-पुरुषः, बहुवचनम्।
स्था + लोँट् । By 3-3-162 लोट् च – The affix लोँट् follows a धातुः when used in the sense of command/request.
= स्था + ल् । अनुबन्ध-लोपः by 1-3-2 उपदेशेऽजनुनासिक इत्, 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।
= स्था + थ । By 3-4-78 तिप्तस्झिसिप्थस्थमिब्वस्मस्तातांझथासाथांध्वमिड्वहिमहिङ्, 1-3-78 शेषात् कर्तरि परस्मैपदम्।
= स्था + त । As per 3-4-85 लोटो लङ्वत्‌ – लोँट् is treated like लँङ्, and hence the following two operations take place in the case of लोँट् as they do in the case of लँङ् –
i) the substitution by ताम् etc. (ref 3-4-101) and ii) the elision of the letter ‘स्’ (ref 3-4-99).
By 3-4-101 तस्थस्थमिपां तांतंतामः – The तिङ्-प्रत्ययाः ‘तस्’, ‘थस्’, ‘थ’ and ‘मिप्’ of a लकारः which is a ङित् (has the letter ‘ङ्’ as a इत्), are replaced by ‘ताम्’, ‘तम्’, ‘त’ and ‘अम्’ respectively (ref: 1-3-10 यथासंख्यमनुदेशः समानाम्)।
= स्था + शप् + त । By 3-1-68 कर्तरि शप्‌।
= स्था + अ + त । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-8 लशक्वतद्धिते, 1-3-9 तस्य लोपः।
= तिष्ठ + अ + त । By 7-3-78 पाघ्राध्मास्थाम्नादाण्दृश्यर्त्तिसर्त्तिशदसदां पिबजिघ्रधमतिष्ठमनयच्छपश्यर्च्छधौशीयसीदाः।
= तिष्ठत । By 6-1-97 अतो गुणे।

2. Where has the सूत्रम् 7-3-102 सुपि च been used in the commentary?
Answer: The सूत्रम् 7-3-102 सुपि च has been used in the form द्वाभ्याम् (प्रातिपदिकम् ‘द्वि’, पुंलिङ्गे तृतीया-द्विवचनम्)।

Please refer to answer to easy question 1 in the following comment for derivation of the form द्वाभ्याम् – http://avg-sanskrit.org/2013/01/08/स्थास्नुः-mns/#comment-14487
http://avg-sanskrit.org/2013/01/08/स्थास्नुः-mns/#comment-14487