Avik Das asked 6 years ago
Let, n be any natural no. Then prove that, it has a nonzero multiple whose representation in (base 10) contains only digits 0 and 1
Avik Das answered 6 years ago
We know that, there are only n distinct numbers modulo n. Let us consider the set S={1,11,111,1111,…} whose largest no. contains (n+1) digits. Then we must get atleast 2 no.s in “S” whose modulo n are same. So, if we subtract those two no.s, the new no. will be divisible by n and that no. will contains digits 0 and 1 only.
Hence, proved
Electronic systems are something we are surrounded with. We use cell phones, computers, fitness sensors, navigation systems and video games like a natural thing, medical equipments. But without electronic systems, none of the electronics surrounding us would have worked.Department of Electronics teaches the conception of electronics device, circuits and applications in various field and do research into further development of this technology. Student will enable to understand the ‘Today’s and tomorrow’s’ requirements for advanced communication solutions, energy efficiency, and storage capacity etc.
Keeping in view, the most rapidly developing subject in twentieth century, it has been decided to intend electronics as one of the subject in undergraduate B.Sc. curriculum. Accordingly appropriate academic curricula in electronics have been framed keeping the relevence of the subject and the utility of the course under consideration. Inclusion of electronics as one of the elective subjects was first made from the academic year 2009. The entire responsibility of running the course was commenced by the Dept. of Physics. Some of the faculty members of the Physics department namely, Dr. S. Bardhan Roy, Dr. M. Purokait, Dr. D. Das and a few Part-time teachers conducted the course successfully. However due to lack of teaching faculty the course of electronics as pass subject was however suspended from the academic year 2012.
Finally the course has started in the session 2014 after Dr. Sourav Chattopadhyay joined the institute as a full time Electronics faculty. Along with Dr. S. Chattopadhyay, the course has been carried out with help of Dr. D Das, Dr. J C. Mahato, Mr. S. Bhunia, Dr. S. Sarkar and Mr. A. Ray of Department of Physics. At present the Dept. of Electronics is offering generic elective course for students under CBCS syllabus.
At the very beginning :Dr. S. Bardhan Roy, Dr. M. Purokait, Dr. D. Das : Their untiring efforts at excellence and unflagging spirit of service have made the Dept. what it is today.
At present :Dr. Sourav Chattopadhyay and Mr. Tanmay Biswas of Electronics Department and Dr. D Das, Dr. J C. Mahato, Mr. S. Bhuia, Dr. S. Sarkar and Mr. A. Ray of Dept. Of Physics.
The course is designed such way that the students will be able to understand the logics behind the electronic device operation, how to implicate and design any king of instrument including. They would be able to understand the practical problems and way to overcome such designing problems and they may also be to deal with new kind of instrumentation/circuit designing. As it is a growing field lots of research scope are there in this field and students will be able to think independently afterthe course.
R&D projects are evolved in identified thrust areas by comprising of leading faculty Dr. S. Chattopadhyay,. Appraised projects are processed. Regarding the present research activities of the department, Dr. S. Chattopadhyay has got research grant from Science and Engineering research board (SERB), Department of Science and Technology (DST) and West Bengal Higher Education Department (WBHED).Broad area of research of the departmentis on nano-semiconductor devices, flexible device for medical applications, and energy devices.
The Department of History came into existence in the year 1960 and started functioning w.e.f. the academic session 1960-61. Initially, the college obtained affiliation in History to the B.A. Pass standard only (vide Calcutta University letter no: C-2306/160 [affl.] dated 23.05.1960). Honours course in History was introduced in the academic session 1961-62.
The Department in its formative Phase:
The early years of the Department saw the involvement of some eminent professors of History of the stature of Dr. BinoyBhushanChoudhury, Dr. Sushil Choudhury and Dr. SekharBandyopadhyay both as teachers and advisors. In addition to these historians of repute, full-time teachers whose names are given below rendered valuable services to this department in the first three decades of its existence (from 1961 to the 1980s):
Shri Kalyan Sen retired after 32 years of service in this Dept. (1965-1996), in June 1996. The department sustained a major loss in the pre-mature death of one of its brilliant faculty members, Dr. Abhijit Mukherjee in August 2009. Dr. Mukherjee had joined the Department in January 1986.
Present Strength of the Department:
Three of the permanent faculty presently serving the Department joined in the 1990s. Shri Arup Biswas (ex-student) and Dr. Chnadra Bhushan Roy joined the Department in the year 1990 and Shri Susobhan Sengupta (ex-student) in October, 1999.
Dr. Rajesh Biswas joined the Dept in March 2017 and obtained Ph.D. degree from Jadavpur University in June, 2018.
Dr. Krishna Kumar Sarkar joined the Dept as Guest faculty in February 2014. He obtained Ph.D. degree from Jadavpur University in August, 2018 and is presently a Post-Doctoral Fellow at Jadavpur University.
Awards and Recognition:
The late Dr. Prafulla Kr. Das won the Griffith Memorial Prize of Calcutta University in 1975. Probably no other full-time faculty of the college had earned such a recognition before Dr. Das.
The late Dr. Abhijit Mukherjee was privileged to attend the 20th International Congress of History of Science as an INSA delegate in July 1997 at Liege, Belgium.
Dr. Chandra Bhushan Prasad Roy was given honorary appointment to the “Research Board of Advisors”, American Biographical Institute, North Carolina, USA, in the year 2005.
Role of the Department in multi-dimensional activities of the College:
All the full time teachers of the Department have been and are actively involved in various activities—cultural, sports, social services etc. of the college for decades. It would not be an exaggeration to say that in the post-Silver Jubilee era, this Department has been playing a key role in providing all sorts of assistance to the college administration in launching, managing, controlling and completing various academic programmes and extension activities:
iii) Member, College Exam Cell since 2014.
Nestling close to lush bougainvillea sprays that are a delight to the eye, the Department of English has a beautiful setting, with the inner and outer walls of its classrooms displaying portraits of the greats of English literature—Shakespeare, Milton and George Bernard Shaw et al. The Dept. breathes an ambience of homeliness and warmth its students feel on their pulses the moment they set foot on its precincts.
The Dept. of English was born one of the firstlings of the College in 1960. Legend has it that from the beginning, the Dept. was the blue-eyed boy of Swami Lokeswarananda who had himself studied Honours in English in his student days. He saw to it that the Dept. had teachers of proven excellence on its teaching staff. Incredible as it might sound, he could persuade even Dr. Subodh Chandra Sengupta, a Shakespeare scholar of international stature, to teach in the Dept. for a few months. During its early years, thanks wholly to Swami Lokeswaranandaji’s dynamic initiative, the Dept. faculty was an impressive array of scholarly and dedicated teachers. In the early 1960s, between 1960 and 1964 to be precise, Dr. Satyendranath Roy ( D. Phil. Oxon ), Dr. Sarojendranath Roy (Ph.D. London), Sri Sourindranath Mitra (the first Head of the Dept.), Sri Sudhangshu Sekhar Mandal, Sri Kshitindra Chandra Ghosal, Sri Ajit Nath Nandi, Sri Akshay Kr. Dey, Sri Nirad Bandhu Mukherjee (formerly of JU), Sri Binoy Chowdhury joined the Dept. and immensely contributed to its steady burgeoning. The Dept. owes profound debts of gratitude to them. The Dept. is also indebted, in no small measure, to Sri Dilip Kumar Sanyal, Sri Dwijadas Banerjee (first enrolled student of the College; later Director, Rabindra Bhaban, VB), Dr. Binoy Banerjee (alumnus, ex-Professor, NBU), Prof. Harijiban Ghosh (ex-Principal, Holkar College, Madhya Pradesh), Sri Prasanta Pal, Sri Adhip Kr. Ghosh Dastidar, Sri Prasanta Banerjee, Sri M. N. De, Dr. Parbaticharan Chakraborty (alumnus; ex-Professor, BU), Sri Cowas de Tambuli, Sri Amitava Mitra (formerly of IIT, Kharagpur), Dr. Swapan Chakraborty (now Director, The National Library, Kolkata), Sri Sushil Mukherjee (formerly Principal, Scottish Church College), Prof. Ashok Mukherjee (formerly of Presidency College), Sri Kapila Chatterjee, Dr. R. K. Sen (D. Litt., CU), Dr. Amrit Sen (VB) and Dr. Amlan Dasgupta GU) for their contribution to the enrichment of the Dept. in their capacities as full-time or guest teachers. At present, ‘1 the faculty has 5 full-timers and 7 Guest lecturers.
A special word must be said about Sri Kshitindra Chandra Ghosal, the longest-serving Head of the Dept. (1962-83). More than anybody else before or since, he contributed to the Dept.’s consolidation into its present position of importance in the academic hierarchy of the College. A scholar equally at home with English and Bengali literature, a strict disciplinarian and an uncompromising perfectionist, he spared no pains to maintain a high standard of work culture in the Dept. and commanded the respect of his students as well as his colleagues. The Shakespeare Gallery, The Sophocles Gallery and the Language Laboratory bear testimony to his creative genius and his exceptional organisational skill. It was under his leadership that the Dept. hosted a 5-day State-Level Seminar on Humanities subjects under the UGC-sponsored COHSSIP (College Humanities and Social Sciences Improvement Programme) scheme, in July 1978. It was a grand success, indeed! On Sri Ghosal’s retirement, the mantle of headship fell on Sri Sudhangshu Sekhar Mandal who ably sustained the legacy handed down to him. Sri Satiprasad Maiti took over as HOD in 1998. The four other members of Team English are : Sri Satyaki Pal, Sri Dipaksankar Chakraborty, Sri Sajal Bhattacharya and Sri Arya Ghosh. The Dept. boasts the richest seminar library of the college with a collection of nearly 5000 books. Students borrow books at regular intervals and the faculty, sees to it that the library delivers to full potential. The faculty is student-friendly, supportive and easy of access. The students of the Dept. have been, over the years, taking the lead in the cultural affairs of the College. They are all agog when it comes to the periodical publication of the Department’s Wall-magazine ‘Image’. The Dept. has recently set up a Film Theatre where students can view film versions of the novels and dramas prescribed for study in their curriculum, besides other critically acclaimed movies. Much as the faculty might wish, the Dept. went without a first class in the University exams over a long stretch of years. Then in 2003, Sri Shishir Roy, the Dept.’s wonder boy, broke the jinx. He not only secured 1st class but also won the 1st position. He repeated the performance in his M.A. Five of the Dept.’s students have secured 1st class since—a remarkable achievement, given that first classes in English do not come thick and fast and were until recently almost the exclusive preserve of only two or three colleges under the University of Calcutta. We are also proud of a distinguished alumntA of the Dept., Swami Purnatmananda, ex-Editor, UDBODHAN. Seminar lectures, Symposia, workshops and talks by scholars well-known to the English-teaching academia, have always been a high spot of the Dept. In 2006, the Dept. had the proud privilege of hosting a UGC-Sponsored National-Level Seminar—the first ever in the college—on ‘Indian Poetry in English : The Problem of Canon’, with Prof. Nirmal Kumar Bhattacharya, Director, Sahitya Akademi, New Delhi, in the Chair. Among the speakers were the late Prof. (Dr.) Niranjan Mohanty of Visva Bharati, and Sri Ranjit Hoskote, stalwart art critic and poet. The seminar was rounded off by a brainstorming one-to-one interface between Sri Amit Chowdhury, a stalwart novelist in English and Dr. Swapan Chakraborty, one-time teacher of the Dept., then Prof. of JU and now Director, The National Library, Kolkata. The whole event was really a big draw. In 2009, the English Department Alumni Association in sync. with the Dept. successfully hosted a talk by Sri Amitav Ghosh, a front-ranking novelist in English and winner of many accolades. 2010 saw the iconic Indian playwright in English, Sri Mahesh Dattani, visit the Dept. and give a heart-warming talk that held a capacity audience spell-bound. The attainment of Autonomous Status in 2008 and, by happy co-incidence, the introduction of the P.G. course in the Dept. in 2009 have no doubt set the Dept. firmly on the road to a further expansion of its activities. Some of the old boys of the Dept. including Prof. P. C. Chakraborty, Dr. Tirthankar Das Purakayastha, and Dr. Subhajit Sengupta—the Dept. cannot thank them enough—have come forward, in a remarkable gesture of solidarity, to help the Dept. grapple with the challenges the twin developments of 2008-09 have thrown its way. New horizons unfold before the Dept.
The Department of Mathematics came into being in 1960. Fifty years down the line, it has had much to feel happy about. It has had a faculty committed to the cause of excellence and also students—scores of them—who have brought glory to it by their brilliant academic performance. During the period 1985-2010 alone, several 1st classes apart, 7 students of the Dept. stood 1st in the 1st class in Calcutta University exams, one of them securing the First position among all the science graduates of the University (1997). This speaks volumes. From 2009 the Dept. restructured its syllabus and focus to the then requirement of Academic Autonomy granted to our college by the UGC. Naturally from this period onward our boys have been writing the examinations conducted by our college, whence their success and achievements may be found as reflected in several pan India entrance examinations, like that of IIT, ISI, IISc, TIFR, IIEST, IISER, CMI, HCU, ISM, CU, JU, RKM-VERI etc towards progression into higher studies. The department takes much pride in the fact that the faculty lists of a good many number of these Institutes of our country, where higher studies and research in mathematics is undertaken, now features quite a few names of our ex-students.
The Department started with eight to ten boys on its rolls. These boys, already into their second year at Dinabandhu Andrews College (Garia), decided to forgo a precious year of their career and join the fledgling Department of Mathematics here. The first faculty comprised four teachers Sri Baidyanath Basu, Sri Sudarsan Das, Sri Rasik Chandra Chakraborty and Sri Gobindadev Bhattacharya. Sri Gobindadev Bhattacharya was the first Head of the Dept. The Dept. was soon joined by Dr. Yudisthir De, Dr.Nanipada Bhanja, and a little later by Sri Makhanlal Nag who succeeded Sri G. Bhattacharya as HOD and served as Vice-Principal of the College till his retirement in 1979. The Dept. moved from strength to strength as years rolled by. From the very beginning the Dept. had the privilege of having some well-known teachers agree to teach here part-time, thanks largely to the initiative taken by Dr. Bikas Chandra Sanyal, the then Prof-in-charge of our College, whose great mentor was Swami Lokeswaranandaji himself. The Dept. will and does gratefully remember Sri Ramkrishna Ghosh (St. Xavier’s College), Sri Hemendra Kanta Ganguli (formerly of Scottish Church College) and Sri Murari Mohan Roy Choudhury (formerly of Presidency College and CU) and Sadhan K. Mapa (Presidency College) and Sri Nalini Ranjan Roy (Dept. of Pure Maths. C.U.) for their services to and affection for the Dept. They were the boost the Dept. needed for forging ahead in vigour. In continuation of this tradition the Dept. gratefully acknowledges the academic help and selfless service rendered by a number of eminent scholars in recent years. The list includes Prof. (Dr.) M.N. Mukherjee (Dept. of Pure mathematics, CU) and Sri Samar Ghosh, IAS (ex Chief Secretary Govt. of WB) among others. No annals of the growth and development of the Dept. can do without a loving and respectful remembrance of Dr.Sudarsan Das who joined the Dept. in 1961 and was its Head till his retirement in 1995. He was an outstanding teacher the memory of whose unique style of exposition left an indelible mark on the minds of his students. His students loved him and held him in the highest esteem. Affable, soft-spoken, affectionate, he served the Dept. with exemplary dedication. He was a good actor and directed many plays put on the boards during college functions. His superannuation in 1995 marked the end of an era in the history of the Dept.
The role of vanguard towards our journey moving ahead was thereafter taken by Dr. Yudhushir De (1995-1996), Dr.Nanipada Bhanja (1996-1998) and then by Dr. Bijoy Kumar Bera, an alumnus of our Dept. (1971-1974) who joined the service in 1979. Dr. Bera headed the Dept. from 1998 to 2010 and played a significant role in sustaining the upward mobility of the Dept. and enhancing its reputation. Post retirement (2010), he has been appointed Deputy Controller of Examinations of our College and the Dept. is still receiving his invaluable guidance and active participation in teaching as well. Dr. Nurul Islam, another alumnus (1974-1977) of this dept. joined the service in 1982 andtook the baton of Headship from Dr. Bera 2010. Actively engaged in UGC-DST-sponsored research projects, Dr. Islam has successfully co-guided two students towards their Doctoral degrees,one each from CU and JU. Two others, registered as Doctoral students at CU are doing their research under his guidance at present. After his retirement in 2016, he is now actively involved with the Dept. as Prof. N.N. Biswas Chair Professor. From 2016 he also holds the coveted post of Co-ordinator of the Vivekananda Centre for Research, the research wing of our College, recognized by CU. With a heavy heart, the Dept. acknowledges the peerless service rendered by one of its relatively recent faculties, Sri Partha Pratim Basu, who joined in 1999 and whose sudden untimely demise in 2019 left all of us shocked. Apart from scholastic reasons, he will be remembered by his students and colleagues alike for his jovial and ever youthful student friendly nature,that was loved by one and all. The present faculty of three full time members, Dr. Parthasarathi Mukhopadhyay (1997 – ) and Dr. Pulak Samanta (2019 – ), headed since 2016 by yet another alumni (1982-1985) Dr. Nanigopal Mandal (1997- ) has been putting in their best efforts to keep up the tradition of excellence set up by their predecessors. In this endeavour the Dept. gets useful support from some Guest faculties like Mr. Dipak Roy and Mr.Biswadip Pal, who is presently holding a Chair Professor post created out of an endowment in the memory of Prof. N.N. Biswas. Dr. Parthasarathi Mukhopadhyay has a lot of solid achievements to his credit. He visited Bangkok, Hongkong, Berlin, Madrid and Budapest (Hungary) on invitation to present talks/papers. Both Dr. Mukhopadhyay and Dr.Mandal have several books on mathematics to their credit. Several ex-pupils of the Dept. are occupying top faculty positions in institutions of higher education in our country. Mention must be made in this connection of Dr. Imran Habib Biswas (TIFR, Bengaluru), Dr.Ujjal Koley (TIFR, Bengaluru), Dr. SanjoyPusti (IIT Mumbai), Dr. SumanKundu (Vanderbilt University, Nashville), Dr. AshishMondal (IIT Kanpur), Prof. Pravash Roy (CURetd.), Professor Saktipada Ghorai (IIT, Kanpur), Dr.Ranjit Dhar (Ex-Registrar, Vidyasagar University), Dr. Sunil Kumar Maity (Dept. of Pure Maths. CU), Dr.Anjan Bhunia (VisvaBharati) and Professor Prakash Chandra Mali (JU). The students of the Dept., apart from their pursuit of academic excellence, have always shown a keen interest in the different co-curricular and extra-curricular activities of the department in particular and the college as a whole.The Dept. does not rest on its laurels. It continues its efforts at further excellenceand looks forward to a brighter future in the current CBCS regime, to which it has geared up under the dynamic leadership of Dr. Mandal.
The Department of Physics was opened in Ramakrishna Mission Residential College, Narendrapur and affiliated to Calcutta University offering Honours degree course from the very beginning of the college (in the year 1960). Prof. K. P. Ghosh from Scottish Church College joined this college as the Head of the department. Then, around the same time, joined many senior professors, namely Shri Abalakanta Choudhuri from Bankura Christan College, Sri Bhabani Bhattacharya from Surendranath College, Sri Kulada Prasad Roy Choudhury from Burdwan Raj College and Sri Himangshu Bimal Dey from Rajshahi University. They worked hard in shaping the department and developing the laboratory for performing various UG experiments. The department was further upgraded to its present form by Dr. J. N. Chakraborty, Prof. P. Sengupta, Prof S. Chakraborty, and Dr. A. K. Tewari, who acted as HOD in various periods of time. The role of Dr. S. Bardhan Roy and the Lab-attendant Sri Rakhal Chandra Pal in setting-up the UG experiments is also praiseworthy.
The seminar lectures by famous professors like Prof. S. N. Ghoshal, Shyamal kr Sengupta, B. B. Baliga, Prof. S. K. Chakraborty and many other such eminent persons were arranged every year for the enrichment of students and faculty members. The department has a high-profile academic record with a large number of students securing first class every year. The students got top ranks in university examinations in most of the years, till it received its autonomous status from Calcutta University in 2009. The students have been doing well in various Master’s and Ph.D. entrance examinations consistently in every year. The post-graduate course in Physics was started in the year 2006. We have at present Condensed Matter Physics as Special paper and Astrophysics as an Elective paper. Most of the theoretical classes in Astrophysics are being taken in collaboration with Indian Centre for Space Physics, Kolkata. Right now, the faculty consists of Dr. Debabrata Das, Dr. Malay Purkait, Dr. Kaushik Sarkar, Dr. Jagadish Chandra Mahato, Sri Swapan Bhunia and Sri Amit Ray and Dr. D. K. Basak. Professors from different colleges, universities, research institutes as well as eminent retired professors from different universities take classes in physics department as Guest Professors regularly, both in the UG and PG sections. Regarding the research activities of the present faculty members of the department, Dr. M. Purkait has received research grants from CSIR, SERB, WBDST and UGC; Dr. D. Das has received minor research projects from UGC and Dr. J. C. Mahato has recently got research grants from WBDST. Dr. M. Purkait has been doing the research works in the field of Atomic Collision Physics and he has been guiding several research scholars. Dr. K. Sarkar, Dr. J. C. Mahato and Sri S. Bhunia are also engaged in research works in various fields. They have been publishing research papers in national and international journals regularly.
The Department of Chemistry of Ramakrishna Mission Residential College, Narendrapur, came into existence in July, 1960. The then Secretary of the Ashrama, Swami Lokeswarananda was dreaming of a degree college, motivated by the ideals of Swami Vivekananda. The main objective of this college was to instil the man-making and character-building ideas of Swamiji in the minds of students and make them complete citizens and nation-builders.
Guided by the Secretary, Swami Lokeswaranandaji, Sri Bikash Chandra Sanyal, a famous alumnus of the Ashrama, went all out in search of suitable teachers for the college. Fortunately, a group of highly talented teachers who had been teaching elsewhere joined our college. Among them Prof. Deb Kumar Mitra was appointed Head of the Department. In the meantime, Prof. Asim Gupta, Prof. Dipak Guha, Dr. P. B. Sarkar, Prof. Ramesh Chandra Sen, Prof. Bijoykali Goswami, Dr. S. M. Dasgupta (retired from CGCRI) joined the Department one after another. Some retired teachers taught part-time in the Department.
Prof. Basudev Barman, an ex-student of the Ashrama, joined the faculty and worked for some time. Professor-Emeritus Dr. Pratul Chandra Rakshit, an outstanding scholar and teacher respected and adored by all, joined the college at the beginning of 1967. He brought a new lease of life to the Department with his illuminating method of teaching and continued his honorary service to the last of his life. Other erudite teachers, Prof. Sushil Chandra Nag and Dr. Kanai Lal Roy, made their mark in teaching their respective subjects. All the teachers and professors and also non-teaching staff worked hard with unswerving commitment and dedication.
Research activities by the teachers were encouraged by the authorities. But the heavy teaching load and inadequate infrastructure stood in the way of active research. Despite limited resources, a number of teachers earned their doctorate degrees working in the college laboratories. Notable of them are Dr. Haraprasad Samaddar, Dr. Hrisikesh Chatterjee and Dr. Dinabandhu Mandal.
The college of yesteryears was like a sapling planted by the then Secretary. Now it has grown big and blossomed in full with research and other activities going on in full swing to keep up with the modern developments of science and technology. The present group of teachers are fully devoted and committed to their duties and obligations. They work hard to improve their own performance as teachers as also to infuse their students with dynamism.
The faculty was headed from 1998 to 2012 by Dr. Arogyavaram Saha whose admission to the degree of Doctor of Sciente (D.Sc.) of the University of Calcutta in 1989 added immensely to the prestige of the College in general and the Dept. of Chemistry in particular. Ever since his joining the Dept. in 1976, he has been an invaluable asset for it. Another distinguished member of the faculty worthy of special mention is Dr. Prasanta Ghosh who was awarded the prestigious Humboldt Research Fellowship (Germany) in 2000 and who has been successfully supervising research projects, under the aegis of CSIR, UGC and DST, for the award of Ph.D. degrees.
The Dept. duly acknowledge the services of Sri Samar Kumar Chakraborty (a long-service HOD), Sri Prabhat Kumar Mondal (PRS) and Dr. Santosh Kr. Maji to the Dept. over a long period of time.
Over the years, the results of the Department boys in university exams have been highly satisfactory. The Department is poised for a great expansion of its activities with the introduction of the P. G. course, a well-equipped research wing and of course, the recent grant of autonomy to the College by the UGC and the University of Calcutta in 2008-09.
