1. Which सूत्रम् prescribes the placement of the term ‘धूप’ in the prior position in the compound धूपदीपकैः?
Answer: The सूत्रम् 2-2-34 अल्पाच्तरम्‌ prescribes the placement of the term ‘धूप’ in the prior position in the compound धूपदीपकैः (पुंलिङ्ग-प्रातिपदिकम् ’धूपदीपक’, तृतीया-बहुवचनम्)।

धूपश्च दीपकाश्च = धूपदीपकाः – incense and lights

धूप सुँ + दीपक जस् । By 2-2-29 चार्थे द्वन्द्वः।

The derivation of the compound प्रातिपदिकम् ’धूपदीपक’ is similar to the derivation of the compound प्रातिपदिकम् ‘रामलक्ष्मण’ as shown in the following post – https://avg-sanskrit.org/2016/02/15/रामलक्ष्मणौ-mnd

2. Where has the सूत्रम् 8-1-4 नित्यवीप्सयोः been used in the verses?
Answer: The सूत्रम् 8-1-4 नित्यवीप्सयोः has been used in the formation द्वारि द्वारि। As per the सूत्रम् 8-1-4 नित्यवीप्सयोः – To express repetition of action or pervasion of a thing by a property or action, a पदम् (ref. 1-4-14) is duplicated.

In the present example, the पदम् ‘द्वारि’ (‘at the entrance’) has been duplicated to express pervasion by the action ‘अलङ्कृता’ (‘adorned’).

3. In the verses can you spot a compound composed using the वार्तिकम् (under 2-1-60 क्तेन नञ्विशिष्टेनानञ् in the सिद्धान्तकौमुदी) शाकपार्थिवादीनां सिद्धये उत्तरपदलोपस्योपसंख्यानम्?’
Answer: The compound गन्धजलैः (नपुंसकलिङ्ग-प्रातिपदिकम् ’गन्धजल’, तृतीया-बहुवचनम्) is composed using the वार्तिकम् (under 2-1-60 क्तेन नञ्विशिष्टेनानञ् in the सिद्धान्तकौमुदी) शाकपार्थिवादीनां सिद्धये उत्तरपदलोपस्योपसंख्यानम्।

गन्धमिश्रं जलम् = गन्धजलम् – scented water

Note: गन्धमिश्रम् itself is a तृतीया-तत्पुरुष: compound explained as follows – गन्धेन मिश्रम् = गन्धमिश्रम् – infused with scent. The compound गन्धमिश्रम् is derived using the सूत्रम् 2-1-31 पूर्वसदृशसमोनार्थकलहनिपुणमिश्रश्लक्ष्णैः।

अलौकिक-विग्रह: –
गन्धमिश्र सुँ + जल सुँ । By 2-1-57 विशेषणं विशेष्येण बहुलम्‌।
By 1-2-43 प्रथमानिर्दिष्टं समास उपसर्जनम् – the term ‘गन्धमिश्र सुँ’ gets the designation उपसर्जनम् because in the सूत्रम् 2-1-57 (which prescribes the compounding) the term विशेषणम्‌ ends in the nominative case. Hence the adjective ‘गन्धमिश्र सुँ’ is placed in the prior position in the compound as per the सूत्रम् 2-2-30 उपसर्जनं पूर्वम्‌।
Note: ‘गन्धमिश्र सुँ + जल सुँ’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 to apply in the next step.
= गन्धमिश्र + जल । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= गन्धजल । By the वार्तिकम् – शाकपार्थिवादीनां सिद्धये उत्तरपदलोपस्‍योपसंख्‍यानम् – In order to explain compounds like शाकपार्थिव:, an additional provision is made to allow for the elision of the latter member of a compound (which itself is the prior member of the final compound.) In the present example, the latter member ‘मिश्र’ of the compound ‘गन्धमिश्र’ is elided in order to explain the compound ‘गन्धजल’।
Note: A compound composed using this वार्तिकम् is referred to as a शाकपार्थिवादिसमास: or a मध्यमपदलोपिसमास:।
As per the सूत्रम् 2-4-26 परवल्लिङ्गं द्वन्द्वतत्पुरुषयोः, the compound प्रातिपदिकम् ’गन्धजल’ is neuter since the latter member ‘जल’ of the compound is neuter. The compound declines like वन-शब्द:।

4. From which verbal root is the form उप्ताम् (स्त्रीलिङ्गे द्वितीया-एकवचनम्) derived?
Answer: The प्रातिपदिकम् ‘उप्ता’ used in the form उप्ताम् is derived from the verbal root √वप् (डुवपँ बीजसन्ताने | छेदनेऽपि १. ११५८) as follows –

वप् + क्त । By 3-2-102 निष्ठा, 1-1-26 क्तक्तवतू निष्ठा। Note: The affix ‘क्त’ has been used कर्मणि (to denote the object) here as per 3-4-70 तयोरेव कृत्यक्तखलर्थाः।
= वप् + त । अनुबन्ध-लोप: by 1-3-8 लशक्वतद्धिते and 1-3-9 तस्य लोपः। Note: 7-2-10 एकाच उपदेशेऽनुदात्तात्‌ prevents the affix ‘त’ from taking the augment ‘इट्’ which would have been done by 7-2-35 आर्धधातुकस्येड् वलादेः। The affix ‘क्त’ is a कित् (has the letter ‘क्’ as a इत्)। This allows 6-1-15 to apply in the next step.
= उ अ प् + त । By 6-1-15 वचिस्वपियजादीनां किति – The verbal roots √वच् (वचँ परिभाषणे २. ५८), √स्वप् (ञिष्वपँ शये २. ६३) and also the nine verbal roots beginning with √यज् (यजँ देवपूजासङ्गतिकरणदानेषु १. ११५७) take सम्प्रसारणम् (ref. 1-1-45) when followed by an affix which is a कित्।
= उप् + त । By 6-1-108 सम्प्रसारणाच्च।
’उप्त’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च।

Now we have to add the appropriate feminine affix (स्त्रीप्रत्यय:) to get the feminine प्रातिपदिकम् ‘उप्ता’।
उप्त + टाप् । By 4-1-4 अजाद्यतष्टाप्‌।
= उप्त + आ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-7 चुटू, 1-3-9 तस्य लोपः।
= उप्ता । By 6-1-101 अकः सवर्णे दीर्घः।

5. In which compound in the commentary has the affix ‘कप्’ been used?
Answer: The affix ‘कप्’ has been used in the compound नि:सारितरजस्कानि (प्रातिपदिकम् ’निःसारितरजस्क’, नपुंसकलिङ्गे प्रथमा-बहुवचनम्)।

नि:सारितं रजो येषां तानि (महामार्गादीनि) = निःसारितरजस्कानि (महामार्गादीनि) – those (highways etc) whose dirt was removed/cleaned.

नि:सारित सुँ + रजस् सुँ । By 2-2-24 अनेकमन्यपदार्थे ।
The adjective ‘नि:सारित सुँ’ is placed in the prior position in the compound as per the सूत्रम् 2-2-35 सप्तमीविशेषणे बहुव्रीहौ।
Note: ‘नि:सारित सुँ + रजस् सुँ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 to apply in the next step.
= नि:सारित + रजस् । By 2-4-71 सुपो धातुप्रातिपदिकयोः।
= नि:सारितरजस् + कप् । By 5-4-154 शेषाद्विभाषा – Following a बहुव्रीहि: compound for which no other समासान्त: operation has been prescribed and which is composed using a rule in the अधिकार: of शेष: (which runs from 2-2-23 शेषो बहुव्रीहिः to 2-2-24 अनेकमन्यपदार्थे) the तद्धित: affix कप्‌ is optionally prescribed and this affix becomes the ending member of the compound.
= नि:सारितरजस् + क । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम् and 1-3-9 तस्य लोपः। Note: ‘नि:सारितरजस्’ has the designation पदम् here as per 1-4-17 स्वादिष्वसर्वनामस्थाने। This allows 8-2-66 to apply in the next step.
= नि:सारितरज: + क । रुँत्व-विसर्गौ by 8-2-66 ससजुषो रुः and 8-3-15 खरवसानयोर्विसर्जनीयः।
= नि:सारितरजस्क । By 8-3-38 सोऽपदादौ।

6. How would you say this in Sanskrit?
“The Lord is pleased even by only fruits and flowers offered with devotion.” Use the adjective प्रातिपदिकम् ‘केवल’ for ‘only.’ Use a causative form of the verbal root √ऋ (ऋ गतिप्रापणयोः १. १०८६, ऋ गतौ ३. १७) for ‘to offer.’
Answer: भगवान् भ्क्त्या अर्पितैः केवलैः फलपुष्पैः अपि प्रसीदति = भगवान् भ्क्त्यार्पितैः केवलैः फलपुष्पैरपि प्रसीदति।

Easy questions:
1. In which other words (besides फलपुष्पाक्षताङ्कुरैः) in the verses has the सूत्रम् 7-1-9 अतो भिस ऐस् (use in step 7) been used?
Answer: The सूत्रम् 7-1-9 अतो भिस ऐस् has also been used in the forms गन्धजलैः (नपुंसकलिङ्ग-प्रातिपदिकम् ’गन्धजल’, तृतीया-बहुवचनम्), पूर्णकुम्भैः (पुंलिङ्ग-प्रातिपदिकम् ’पूर्णकुम्भ’, तृतीया-बहुवचनम्) and धूपदीपकैः (पुंलिङ्ग-प्रातिपदिकम् ’धूपदीपक’, तृतीया-बहुवचनम्)।
The derivation of these forms is similar to the derivation of the form फलपुष्पाक्षताङ्कुरैः from the प्रातिपदिकम् ’फलपुष्पाक्षताङ्कुर’ as shown in the post.

2. Why doesn’t the सूत्रम् 7-1-9 अतो भिस ऐस् apply in the word दध्यक्षतफलेक्षुभिः? (Which condition is not satisfied?)
Answer: The सूत्रम् 7-1-9 अतो भिस ऐस् doesn’t apply in the word दध्यक्षतफलेक्षुभिः because the प्रातिपदिकम् ’दध्यक्षतफलेक्षु’ ends in the letter ‘उ’ and not the letter ‘अ’।
As per the सूत्रम् 7-1-9 अतो भिस ऐस् – Following a अङ्गम् ending in the letter ‘अ’, the affix ‘भिस्’ is replaced by ‘ऐस्’।