Prime Minister Modi did not have the lens cap on while taking photos.

Claim
Father of digital India @RoseTint4 @Swamy39 @PMOIndia @ndtv @RepublicTVs @narendramodi first person in the world took photo with removing the lens cap.
Father of digital India @RoseTint4 @Swamy39 @PMOIndia @ndtv @RepublicTVs @narendramodi first person in the world took photo with removing the lens cap. pic.twitter.com/yXmZ520tZD
— irshad azeez (@irshadazeez7) September 17, 2022
Rating
Explanation
Cheetahs became extinct in India in the year 1952, exactly 70 years ago. There have been many attempts to bring the wild cat back to the Indian wilderness but those attempts got delayed due to various reasons within and outside the country. In the 1970s, when India tried to bring Asiatic Cheetas from Iran, the Iranian Revolution hindered the efforts.
Similarly, in the late 2000s, when the Congress-led UPA-II made a push to bring Cheetahs to India, several legal hurdles further delayed the attempt. After all legal blockades were cleared in 2020, the Cheetahs have been brought to India and were released into the Kuno National Park by Prime Minister Narendra Modi on his birthday on 17th September 2022. During that event, Prime Minister took out an expensive high-end camera to click some photographs of the cheetahs.
An image of the Prime Minister using the expensive camera with the lens cap on has been virally shared on social media by various opposition leaders and supporters of the opposition parties.
ಕ್ಯಾಮರಾ ಲೆನ್ಸ್ ಅನ್ನು ಮುಚ್ಚಿಕೊಂಡು ಫೋಟೋ ತೆಗೆದ ಜಗತ್ತಿನ
ಏಕೈಕ ನಮ್ಮ ನರೇಂದ್ರ ಮೋದಿ.#UnemploymentDay pic.twitter.com/wRZd0Kvtuc— Pavithra Gowda (@PaviGowda123) September 17, 2022
1980 के डिजिटल कैमरे में लेंस कवर नही रहा होगा। pic.twitter.com/XS5XfMHI4I
— Maharashtra Congress Sevadal (@SevadalMH) September 17, 2022
What’s the truth?
First of all, when we started this search, we noticed that the name Nikon in the camera is written backwards which indicated that the image has been reversed, as the name “Nikon” will be written straight in the Nikon brand of cameras.
The second thing we noticed was, that the Nikon camera was allegedly covered using a Canon lens cap, which is not quite possible as the locking mechanism of the lens cap to the lenses between these two brands are incompatible with each other.
So we flipped the image to the correct orientation & reverse image searched it and found that the Gujarat BJP’s Twitter handle uploaded the same pictures on 17th September 2022.
ભારતમાંથી વિલુપ્ત થયેલા અને આફ્રિકાના નામિબિયાથી લવાયેલ ચિત્તાઓને મધ્ય પ્રદેશના કુનો નેશનલ પાર્કમાં માનનીય પ્રધાનમંત્રી શ્રી @narendramodi જીના હસ્તે છોડવામાં આવ્યા. આ સાથે જ પ્રધાનમંત્રીશ્રીએ પાર્કની મુલાકાત લઈને વિવિધ માહિતીઓ મેળવી.#CheetahIsBack pic.twitter.com/8dRvxTRupL
— BJP Gujarat (@BJP4Gujarat) September 17, 2022
Also, we found more pictures from the same location on Union Government’s Press Information Bureau website.

In all these images, we find that these were taken from the same vantage point and one among these pictures has been reversed and photoshopped to have the lens cap on.

Conclusion
In our search, we find that the viral image of Prime Minister Modi using the picture with the lens cap on is fake. The photo is edited and morphed to make the PM look like he is using the camera with his lens closed.