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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

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.
THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.
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 lensing, gravitational redshifts of light, and most importantly, that why planets and stars rotates?

So let's talk about


Before starting the general theory of relativity, we have to understand that what is space time?, it is very important.
 According to Albert Einstein , space and time can't be isolated, means without space time has no meaning, and without time , space has no meaning. You can understand this statement by following example:

Imagine you are going to date your girlfriend. And you thought for a place for meeting both ie. Taj Mahal palace at 4 "O" clock evening.
But you message your girlfriend only that lets meet at TAJ MAHAL PALACE. What do you think , will she come.... No, she will not come , because she has no idea about time that when she has to come there?
But again you message that lets meet at 4 "O" clock at evening, again she will not come , because she has no idea about space , she will not understand that where has to come.
So by this example we can conclude that space and time are interrelated to each other. If we remove anyone then there was no meaning of other. Space and time is not different terms, this is a single term that is spacetime. And for occuring any event, space and time both are required.
By his general theory of relativity , Einstein says that space time is interrelated or interwoven such that it's behave like a 2D flat curvature, and it is directly related to energy and momentum , whatever matter and radiation present. This relationship is described by Einstein field equation, which is system of differential equations.

According to the Einstein's theory of general relativity, space time are interwoven such that it makes a net and this net has the elastic property due to this property it behaves like a infinitly stretched membrane like a trampoline. Which is shown as below:
THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.
(Here you have to remembered that general theory of relativity is applicable only when space time is taken as 2D flat curvature).

All the celestial bodies such as galaxies , stars , planets , asteroids , black holes or everything which are present in the universe are lie in this infinitly stretched membrane of spacetime. And in the trampoline like membrane, we know that higher masses objects create more slope and get fixed at the centre. And if we put small objects in the slope, then they all roll towards the higher mass. And we have all must seen this phenomenon somewhere in our daily life events. Which can be seen below.
THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.
Exactly same phenomenon has also occurs in the universe. The objects which have higher mass then they distort the space time more and create more slope, and objects which have small masses then they distort the space time less and create small slope.
And if the small objects get stuck in the slope of higher masses objects, then they start free falling with rolling motion towards the higher mass objects , and this free falling of objects in the slope or by the slope is coined as gravity. And every free falling body has some acceleration and this acceleration is called acceleration due to gravity. But why gravity create then you can say simply that space time slope is the cause of creation of gravity, but why this slope created , they again you can say that slope is created because depression of space time due to large mass objects.
THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.
In our solar system sun has very large mass , and because it has large mass then it depressed the space time more and create more slope. And all the small objects such as mercury , Venus , earth, mars, Jupiter and all planets with asteroids , and other small objects get stuck into the slope of sun , and due to this all the planets and small objects are in free falling towards the sun with rolling motion. This rolling motion gives the rotation to the planets and object such as asteroids. And same as, Our natural satellite the moon is also get stuck in the slope of the earth , and continuously free falling towards the earth . But anyone can ask question that why do they not collide?
In the answer of this question , we can say that , everything in the universe has been moving. And moon is free falling in the slope of earth because earth has greater mass than moon, and same , earth is free falling in the slope of sun, and sun is free falling in the space time slope of our galaxy the milky way, and our milky way is free falling in the slope of the black hole, which is in the centre of our galaxy. And may be this black hole is free falling in the slope of other black hole. Everything in this universe is moving due to distortion in the space time curvature because of mass.
THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.
Then we can say that higher mass  gives higher depression and higher depression gives higher space time slope and higher space time slope gives higher gravity.

If we talk about the Newton's laws of Gravitation, then we can find that Newton only measure the magnitude of force, and which type of force it is. Newton has no idea about the space time distortion due to mass and creation of slope,he has no idea that planets are free falling in the slope of space time.
He think that somewhere a force exist which attracts the planets and any other objects , and give a acceleration , and he says this acceleration as acceleration due to gravity. Then he derived a formula for this attraction or force named force of gravity or gravitational force in terms of mass and distance between them. Which is as follows:
                       F= GMm/r^2
 But he did not know ,why mass shows the property of gravity? In reality mass have no property of gravity , we have to understand the term gravity, gravity is a effect which is created due distortion in the space time curvature due to mass. This distortion this slope of space time create the effect of gravity.
THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.
And Newton only measure the magnitude of gravity as force, but Einstein shows that why gravity exist and how is it create?
This all explaination is only given by the general theory of relativity. Also read Special theory of relativity



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=…