First Women's University	Maharshi Karve starts SNDT University in Pune with five students in 1916.
First Woman to hold a Union Cabinet post	Vijaya Lakshmi Pandit
First Woman governor of Independent India	Sarojini Naidu, in charge of United Provinces
First Woman president of UN General Assembly	1953 Vijaya Lakshmi Pandit
First Woman Prime Minister of India	1966 Indira Gandhi
First Woman IPS Officer of India	1972 Kiran Bedi
First Woman to win Nobel Peace Prize	1979 Mother Teresa
First Indian Woman to climb Mount Everest	1984 Bachendri Pal
First Indian Woman to win Booker Prize	1997 Arundhati Roy
First Woman President	2007 Pratibha Patil
First Woman Speaker of Lok Sabha	2009 Meira Kumar
First Indian Woman to become "Miss World"	Rita Faria
First Woman judge in Supreme Court	Mrs. Meera Sahib Fatima Bibi
First Woman Ambassador	Miss C.B. Muthamma
First Woman to climb Mount Everest twice	Santosh Yadav
First Woman President of the Indian National Congress	Mrs. Annie Besant
First Woman Chief Minister of an Indian State	Mrs. Sucheta Kripalani
First Woman chairman of Union Public Service Commission	Roze Millian Bethew
First Woman Director General of Police (DGP)	Kanchan Chaudhary Bhattacharya
First Woman Lieutenant General	Puneeta Arora
First Woman Air Vice Marshal	P. Bandopadhyaya
First Woman chairperson of Indian Airlines	Sushama Chawala
First &Last Muslim Woman ruler of Delhi	Razia Sultan
First Woman to receive Ashoka Chakra	Niraja Bhanot
First Woman to cross English Channel	Arati Saha
First Woman to receive Bharat Ratna	Indira Gandhi
First Woman to receive Gyanpith Award	Ashapurna Devi
First Woman Headmistress in school	Savitribai Phule

- See more at: http://www.onlinegk.com/general-knowledge/first-in-india-(women)#sthash.4PNil1j2.dpuf

The first batsman to score three test century in three successive tests on debut	Mohd. Azharuddin
The first batsman to score double century in One Day International cricket match	Sachin Tendulkar
The first man to have climbed Mount Everest twice	Nawang Gombu
The first President of Indian Republic	Dr. Rajendra Prasad
The first Prime Minister of free India	Pt. Jawaharlal Nehru
The first Indian to win Nobel Prize	Rabindranath Tagore
The first president of Indian National Congress	W.C. Banerjee
The first Muslim President of Indian National Congress	Badruddin Tayyabji
The first Muslim President of India	Dr. Zakir Hussain
The first British Governor General of India	Lord William Bentinck
The first British Viceroy of India	Lord Canning
The first Governor General of free India	Lord Mountbatten
The first and the last Indian Governer General of free India	C. Rajgopalachari
The first man who introduce printing press in India	James Hicky
The first Indian to join the I.C.S.	Satendranath Tagore
The first Indian man in space	Rakesh Sharma
The first Prime Minister of India who resigned without completing the full term	Morarji Desai
The first Indian Commander-in-Chief of India	General Cariappa
The first Cheif of Army Staff	Gen. Maharaj Rajendra Singhji
The first Indian member of the Viceroy's executive council	S.P. Sinha
The first President of India who died while in office	Dr. Zakir Hussain
The first Prime Minister of India who did not face the Parliament	Charan Singh
The first Field Marshal of India	S.H.F. Manekshaw
The first Indian to get Nobel Prize in Physics	C.V. Raman
The first Indian to receive Bharat Ratna award	Dr. Radhakrishnan
The first Indian to cross English Channel	Mihir Sen
The first person to receive Gyanpith award	Sri Shankar Kurup
The first Speaker of the Lok Sabha	Ganesh Vasudev Mavalankar
The first Vice-President of India	Dr. Radhakrishnan
The first Education Minister	Abul Kalam Azad
The first Home Minister of India	Sardar Vallabha Bhai Patel
The first Indian Air Chief Marshal	S. Mukharji
The first Indian Naval Chief	Vice Admiral R.D. Katari
The first judge of International Court of Justice	Dr. Nagendra Singh
The first person to receive Paramveer Chakra	Major Somnath Sharma
The first person to reach Mt. Everest without oxygen	Sherpa Anga Dorjee
The first Chief Election Commissioner	Sukumar Sen
The first person to receive Magsaysay Award	Achrya Vinoba Bhave
The first person of Indian origin to receive Nobel Prize in Medicine	Hargovind Khurana
The first Chinese traveller to visit India	Fahein
The first person to receive Stalin Prize	Saifuddin Kitchlu
The first person to resign from the central cabinate	Shyama Prasad Mukharji
The first foreigner to receive Bharat Ratna	Khan Abdul Gaffar Khan
The first person to receive Nobel Prize in Economics	Amartya Sen
The first Chief Justice of Supreme Court	Justice Hiralal J. Kania