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True Discount and Banker's Discount problems tricks in Hindi | fast track formulae for problem solving.


TRUE DISCOUNT 1). वास्तविक बट्टा = मिश्रधन - वर्तमान धन
2). यदि ब्याज की दर r% वार्षिक , समय t व वर्तमान धन (pw) है, तो वास्तविक बट्टा = PW×r×t/100
3). यदि r% तथा समय t के बाद देय धन A है, तो तत्काल धन pw = 100×A/(100+r.t)
4). यदि देय धन A पर r% व समय t दिए गए है, तो वास्तविक बट्टा = A.r.t /(100+r.t)
5). यदि किसी निश्चित समय के पश्चात निश्चित वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व समान समय व दर के लिए साधारण ब्याज (SI) हैं, तो देय धन A =      SI × TD/(SI - TD)
6). यदि t समय पश्चात r% वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व साधारण ब्याज (SI) है , तो -  SI - TD = TD×r×t/100
7). t वर्ष बाद r% चक्रवृद्धि दर पर देय धन A का तत्काल धन (PW) = A/(1+r/100)^t   व वास्तविक बट्टा = A - PW
BANKER'S DISCOUNT1). महाजनी बट्टा = शेष समय (समाप्त न हुए समय) के लिए बिल पर ब्याज = बिल की राशि × दर × शेष समय /100
2). महाजनी लाभ = महाजनी बट्टा - वास्तविक बट्टा
3). यदि बिल का मान / अंकित मूल्य A है, समय t व दर r% है, तो महाजनी बट्टा = A×r×t/100

Analyzing the Preamble to the Constitution of India


  • Generally considered as “The Soul of Constitution", the Preamble to the Constitution is a brief introductory statement which captures the broader objectives that our Constitution seeks to promote and establish through its inherent composition. It is based on the "Objective Resolution" proposed by Pandit Jawahar Lal Nehru on 13 December, 1946. After long discussions, these objectives were adopted by Constituent Assembly on 22 January, 1947. In the present article, I've attempted to analyze the deeper meanings of Preamble by understanding the broader terms like- Sovereign, Socialist, Secular, Democratic, Republic etc. and in addition to this, I've also endeavored to discuss about amendments in Preamble.


WE, THE PEOPLE OF INDIA, having solemnly resolved to constitute India into a SOVEREIGN SOCIALIST SECULAR DEMOCRATIC REPUBLIC and to secure to all its citizens

JUSTICE, social, economic and political;
LIBERTY of thought, expression, belief, faith and worship;
EQUALITY of status and of opportunity;
and to promote among them all FRATERNITY
assuring the dignity of the individual and the unity and integrity of the Nation;


On a broader spectrum, the Preamble reflects the critical structure of political system and the significance of our Constitution by setting out definitive principles and rules that guide the nation. It is adopted by Constituent Assembly on 26 November, 1949 and came into effect on 26 January, 1950 which is celebrated as Republic Day.
In Preamble, the people of India are solemnly resolved to constitute India into a SOVEREIGN SOCIALIST SECULAR DEMOCRATIC REPUBLIC. Let's understand the comprehensive meanings of these definitive terms.

SOVEREIGN- The term "Sovereign" in Indian Preamble implies that India is neither a dependency nor a dominion of any other nation but an independent state. Being a Sovereign state, India is free to conduct its internal and external affairs independently. In simple words, India is neither under the control of nor dependent on any external power.

SOCIALIST- The term "Socialist" in Indian Preamble indicates the democratic socialist pattern of India. Under "Democratic Socialism", both private and government sectors can co-exist in India in order to terminate ignorance, sickness and poverty etc. As Supreme Court remarks- " Democratic Socialism aims to end poverty, ignorance, disease and inequality of opportunity. Indian Socialism is a blend of Marxism and Gandhism, leaning heavily towards Gandhian Socialism."

This term was added after 42 Amendment, 1976 but it was previously existent in Constitution through certain directive principles of State Policy.

SECULAR- The term "Secular " in Preamble refers to absence or elimination of religion based differences in social matrix of India. Being a secular state, India provides to all its citizens "Right to Freedom of Religion" and equal support and protection to all religious communities.

The term was added after 42 Amendment,1976 but it was intrinsically present in Constitution of India in form of Article 25 to 28 i.e. Fundamental Right to Freedom of Religion.

DEMOCRATIC- The term "Democratic " in Preamble captures a deeper meaning embracing social, political and economic democracy. Based on the doctrine of Popular Sovereignty, the Preamble to the Constitution defines India as democratic state where supreme power lies with the people of country.

Universal adult franchise, periodic elections, rule of law, independence of judiciary and absence of discrimination are the manifestation of Indian democratic polity.

REPUBLIC- The term "Republic " in Indian Preamble indicates that India has an elected head of state i.e. President for fixed period of 5 years. In Republic, the head of state is elected directly or indirectly by the people for a fixed time length.

Through its democratic composition, Indian Constitution seeks secure to all its citizens JUSTICE, LIBERTY, EQUALITY, FRATERNITY. Let's understand the meanings of these terms in order to have clear view of Indian Preamble and Constitution.

JUSTICE- The term "Justice " refers to three distinct forms- social, economic, and political justice provided to citizens through various provision of Fundamental Rights and Directive Principles.
Social justice denotes the equality of all citizens at social level and the absence of social discrimination based on caste, color, race, religion, sex and so on.
Economic justice denotes the equality of all citizens irrespective of their wealth, income and economic status. A combination of social and economic justice is called "distributive justice."
Political Justice denotes equal treatment of all citizens in political processes, equal access to all political powers and equal rights to all people without discrimination.

The ideals of justice: social, economic, political had been adopted from the Russian Revolution (1917).

LIBERTY- The term "Liberty " refers to the freedom of speech and expression within the constitutional limits. The Constitution provides to all its citizens liberty of thought, expression, belief, faith and worship through various Fundamental Rights which is enforceable in the court of law in case of violation.

EQUALITY - The term "Equality " implies the absence of any special privileges extended to any section of society i.e. equal treatment of all citizens irrespective of their social, political and economic status. The Preamble to the Constitution secures to all citizens of India equality of status and opportunity. The Fundamental Rights ensuring civic equality are-
ARTICLE 14- Equality before the law.
ARTICLE 15- Prohibition of discrimination on grounds of religion, race, caste, sex and place of birth.
ARTICLE 16- Equality of opportunity in matters of public employment.
ARTICLE 17- Abolition of untouchability.

FRATERNITY- The term "Fraternity " refers to sense of brotherhood and belongingness with nation. Our constitution seeks to promote and establish fraternity through single citizenship. Also, the fundamental duties( Article 51A) say that it shall be the duty of every citizen of common brotherhood amongst all people of India transcending religious, linguistic, regional and sectional diversities.
In this sense, our constitution opposes communalism, casteism etc. that hampers the unity and integrity of nation.

Is Preamble an integral part of Constitution?

In Berubari Union Case, Supreme Court stated that Preamble can't be considered as an integral part of Indian Constitution due to its limited applicability. It also outlined that Preamble will not be considered valid if the language of provisions in constitution is clear. But in Keshavananda Bharati Case 1973, SC over-ruled earlier decision and regarded Preamble as an important instrument for interpreting the constitution.
Eventually, in 1995 case of Union Government vs LIC of India, the Supreme Court regarded Preamble as an integral part of the Constitution.


After the enactment of the constitution, there had been deliberate discussions about "whether Preamble is a part of the Constitution or not?" In Keshavananda Bharati Case1973, according to Supreme Court verdict, Preamble is regarded as part of Constitution and subject to amendment provided that the basic features of the Constitution can't be destroyed. Under this verdict, the certain basic features described are-
• Supremacy of Law
• Federalism and Secularism
Our Preamble had been amended only once during Emergency Period, 1976. Under the 42 Constitutional Amendment, the three terms- SOCIALIST, SECULAR and INTEGRITY were added in Preamble which were inherently existing in the Constitution.

From the above analysis, it's significant to encapsulate that our Indian Preamble broadly reflects the nature of the political system and the strengthening principles that the Constitution seeks to ascertain and promote. In Preamble, the people of India are determined to constitute India into SOVEREIGN i.e. independent state, SOCIALIST i.e democratic socialist state (where both private and govt. sectors can co-exist), SECULAR i.e. state without religion-based differences, DEMOCRATIC i.e. state where supreme power lies in hands of people and REPUBLIC i.e. state is considered as public matter rather than private property of the monarch. The Preamble strives to propagate JUSTICE, LIBERTY, EQUALITY, FRATERNITY irrespective of one's social, political, economic and financial backgrounds to bring a sense of oneness.



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Boat and stream short-tricks in Hindi | Fast track arithmetic formulae for competitive examination.

BOAT AND STREAM (नाव एवं धारा)
1). यदि शांत जल में नाव या तैराक की चाल x किमी/घंटा व धारा की चाल y किमी/घंटा है, तो धारा के अनुकूल नाव अथवा तैराक की चाल = (x+y) किमी/घंटा
2). धारा के प्रतिकूल नाव अथवा तैराक की चाल = (x-y) किमी /घंटा
3). नाव की चाल = (अनुप्रवाह चाल + उद्धर्वप्रवाह चाल)/2
4). धारा की चाल =  (अनुप्रवाह चाल - उद्धर्वप्रवाह चाल)/2
5). यदि धारा की चाल a किमी/घंटा है, तथा किसी नाव अथवा तैराक को उद्धर्वप्रवाह जाने में अनुप्रवाह जाने के समय का n गुना समय लगता है,(समान दूरी के लिए), तो शांत जल में नाव की चाल = a(n+1)/(n-1) किमी/घंटा
6). शांत जल में किसी नाव की चाल x किमी/घंटा व धारा की चाल y किमी/घंटा है, यदि नाव द्वारा एक स्थान से दूसरे स्थान तक आने व जाने में T समय लगता है, तो दोनो स्थानों के बीच की दूरी = T(x^2 - y^2)/2x km
7). कोई नाव अनुप्रवाह में कोई दूरी a घंटे में तय करती है, तथा वापस आने में b घंटे लेती है, यदि नाव कि चाल c किमी/घंटा है, तो शांत जल में नाव की चाल = c(a+b)/(b-a) km/h
8). यदि शांत जल में नाव की चाल a किमी/घंटा है, तथा वह b किमी/घंटा की चाल से बहती हुई नदी में गत…

Emergence of British East India Company as an Imperialist Political Power in India

Dynamically changing India during early eighteenth century had a substantially growing economy under the authority of Mughal emperor Aurangzeb. But after his demise in 1707, several Mughal governors established their control over many regional kingdoms by exerting their authority. By the second half of eighteen century, British East India Company emerged as a political power in India after deposing regional powers and dominating over Mughal rulers. The present article attempts to analyze the reasons for emergence of British East India Company as an imperial political power in India and their diplomatic policies of territorial expansion. In addition to this, I briefly highlighted the Charter Acts (1773, 1793, 1813, 1833 and 1853) to trace its impact on the working process of Company.Establishment of East India Company in India

In 1600, British East India Company received royal charter or exclusive license…

Three dimensional geometry (part-1) | study material for IIT JEE | concept booster , chapter highlights.


In the following diagram X'OX , Y'OY and Z'OZ are three mutually perpendicular lines , which intersect at point O. Then the point O is called origin.
In the above diagram X'OX is called the X axes, Y'OY is called the Y axes and Z'OZ is called the Z axes.
1). XOY is called the XY plane. 2). YOZ is called the YZ plane. 3). ZOX is called the ZX plane.
If all these three are taken together then it is called the coordinate planes. These coordinates planes divides the space into 8 parts and these parts are called octants.
COORDINATES  Let's take a any point P in the space. Draw PL , PM and PN perpendicularly to the XY, YZ and ZX planes, then
1). LP is called the X - coordinate of point P. 2). MP is called the Y - coordinate of point P. 3). NP is called the Z - coordinate of the point P.
When these three coordinates are taken together, then it is called coordinates of the point P.

A detailed unit conversion table in Hindi.

CENTIMETRE GRAM SECOND SYSTEM (CGS)1). MEASUREMENT OF LENGTH (लंबाई के माप) 10 millimeter = 1 centimetres10 centimetre = 1 decimetres  10 decimetre = 1 metres 10 metre = 1 decametres 10 decametres = 1 hectometres 10 hectometres = 1 kilometres 10 kilometres = 1 miriametresMEASUREMENTS OF AREAS ( क्षेत्रफल की माप )  100 millimetre sq. = 1 centimetre sq.
 100 centimetre sq. = 1 decimetres sq. 100 decimetres sq. = 1 metre sq. 100 metre sq. = 1 decametres sq  100 decametres sq. = 1 hectometres sq. 100 hectometres sq. = 1 kilometres sq. 100 kilometres sq. = 1 miriametres sq.
MEASUREMENTS OF VOLUME ( आयतन की माप) 1000 millimetre cube. = 1 centimetre cube.
 1000 centimetre cube. = 1 decimetres cube. 1000 decimetres cube. = 1 metre cube. 1000 metre cube. = 1 decametres cube. 1000 decametres cube. = 1 hectometres cube. 1000 hectometres cube. = 1 kilometres cube. 1000 kilometres cube. = 1 miriametres cube.
MEASUREMENTS OF VOLUME OF LIQUIDS  (द्रव्य के आयतन का माप) 10 millilitre=…

THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.

Today we are going to talk about a very important and revolutionary concept that is THE GENERAL THEORY OF RELATIVITY.
This theory came into existence after 10 years of special theory of relativity (1905), and published by Albert Einstein in 1915.
This theory generalise the special theory of relativity and refines the Newton's laws of universal gravitation.
After coming this theory people's perspective about space and time has been changed completely. And this theory give a new vision to understand the spacetime geometry.
This theory gives a unified description of gravity as a geometrical properties of space and time.
This theory helps us to explain some cosmological phenomenon that is ,

* why small planets revolve around the big stars?
* Why everything in this universe is keep moving?
* Why mostly planets and stars are spherical in shape?
* Why does gravity create?
* Why does time become slow near the higher gravitating mass. Ie. Gravitational time dilation.
And gravitational…