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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

Mass - Energy Equivalence, (E = mc^2), understanding the basic concepts and it's derivation

Today we are going to talk about a famous formula , which has changed the thinking of the world and who give the underlying concept of time travel. We are talking about the mass - energy equivalence ie. E = mc^2 ,
This formula is given by Albert Einstein in 21 November 1905 , in the paper "Does inertia of a body depends upon its energy content"   mass energy equivalence is a product of the special theory of relativity and physicist Henry Poincaré described it as a paradox.
Mass - Energy Equivalence,  (E = mc^2) and it's derivation
Mass energy equivalence is a very important principle of relativistic physics , which give a relation between mass and energy. This principle tell us that anything which have mass has an equivalent amount of energy and vice versa, vice versa means if mass contain energy then energy contain mass. And this fundamental quantities are related to each other by Einstein's famous formula ie. E = mc^2. Where c is speed of light ( c = ~3×10^8 m/s). According to this formula, if anyone wants to calculate the energy of a body having mass m then he has to multiply it with the squared of speed of light ie. c^2. It means if anyone is travelling with the squared of the speed of light then , then he has been converted into energy. Then from this we can say that mass can't be exist without energy , and energy can't be exist without mass. If energy is exist then somewhere mass will also exist , and if mass is present then energy will also present , because we know that energy can't be exist without mass.
        E = mc^2 , then m = E/c^2
Energy content of any body is directly proportional to it's mass, if mass is large then energy corresponding to it is also large.
And we have seen in special theory of relativity that mass is a relativistic quantity, mass of the body increases if it's velocity is increasing. And here conversation of mass into energy is occurring at speed of light, it's means the mass of the body is approximately infinite. Every body has its two mass, one when it is in rest and one when it is in motion.
Mass - Energy Equivalence,  (E = mc^2) and it's derivation
When it is in rest , then mass corresponding to it is called rest mass or invariant mass. This mass is invariant to all frame of reference. But when body is in motion then it's mass changes , and the variation of mass due to motion ( relativity of mass ) and mass corresponding to this motion is called relativistic mass. Which is given as:
           m = m0/√[1-(v^2/c^2)]
When a body is in motion then it's total energy is greater than its rest energy.
Now we are going to derive the formula for                        E = mc^2


Mass - Energy Equivalence,  (E = mc^2) and it's derivation

Consider the relation
 m = m0/√[1-(v^2/c^2)]  , squaring both sides we get, m^2 = m0^2/[1-(v^2/c^2)] , taking denominator to LHS.
m^2(c^2 -v^2)/c^2 = m0^2 ,, on solving we get
  m^2c^2 - m^2v^2 = m0^2c^2
Now differentiate it, then we get
 2mc^2dm - ( 2mv^2dm + 2vm^2dv) = 0
     2mc^2dm = 2mv^2dm + 2vm^2dv
Cancelling 2m , we get;
   c^2dm = v^2dm + mvdv
Now take a small kinetic energy dk for small velocity. Then
                  dk = dw = fds
     dk = fds = (dp/dt)ds
   dp/dt = d(mv)/dt = vdm/dt + mdv/dt
Putting the value of dp/dt into (dp/dt)ds ,, we get;
 dk = (vdm/dt)ds + (mdv/dt)ds
And can written as ;
dk = (vds/dt)dm + (mds/dt)dv
  dk = v^2dm + mvdv
And v^2dm + mvdv it is equal to c^2dm
Then dk = c^2dm ,, so now integrate it
    Int(dk) = int( c^2dm )
We get
      K = mc^2 = E ,, and we can write Purley
                            E = mc^2
This is the derivation for the mass energy equivalence.



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…