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

TRUE DISCOUNT AND BANKER'S DISCOUNT TRICKS IN HINDI

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
4).…

GALILEANS & LORENTZ TRANSFORMATIONS | The basic mathematical operations for the special theory of relativity.

Today we are going to talk about a very important concepts that is the GALILEANS & LORENTZ TRANSFORMATIONS. And this concept of transformation is very important for the mathematical explaination of relativistic physics. When Einstein put his special theory of relativity in September 1905. Then various new concept get born out of this theory, that is the time dilatation, length contraction , mass energy equivalence, relativistic mass. And all this new concept can only be explained by using mathematics. So today we are going to take a look on this foundation mathematics of special theory of relativity, without which special theory of relativity is somehow incomplete.
So Let's starts our talk with galilean transformation.

GALILEAN TRANSFORMATION

GALILEANS & LORENTZ TRANSFORMATIONS | The basic mathematical operations for the special theory of relativity.
Consider the two frame of reference S and S' having the coordinates of any point P is (x,y,z) and (x',y',z') , initially both frame of reference are at same position ie. concide to each other, where t is zero for both reference when they are at initial stage. Then if second frame S' starts moving in the direction of x - axis with some constant velocity v with respect to first frame of reference S. ( First frame is a fixed frame of reference).

Here you have to remember that this velocity is very very very small in comparison to speed of light. This is a day to day life velocity. Galilean Transformation is applicable only for small moving frame velocities.
If second frame is moving away from the fixed frame S with v velocity then the time elapsed for any observer which is present at fixed frame S will be t , but for observer which is in the moving frame will be t'.


And we know from above data that distance of point P from first frame S is x, and from second frame S' is x'. Then the distance travelled by the second frame S' wrt first frame S is given by the product of velocity v and time t ie. vt. ( Here v and t both are respect to S).
Then the distance between the point P and second frame S' is given as difference of total distance from S ie. x and travelled distance ie.  vt ,.     x' = x - vt.   if second frame S' starts moving towards the fixed frame S, then total distance x is given as
                            x = x' + vt'
And if S' is moving along x axis only then y and z coordinates of point P is not changing, only x undergoes in changes because frame is moving along x axis. It means y' = y and
z' =z , and if velocity is very small then t and t' will also same and there will be no difference in time.
Then the elements of fixed frame S is related to the elements of moving frame S' is as follows.
           x' = x - vt , y' = y , z' = z , and t' = t
This relationship is is called Transformation, and this Transformation is given by Galileo so it is called galilean transformation.
Now let's talk about Lorentz Transformation

LORENTZ TRANSFORMATION


We have talked about the galilean transformation above , which is applicable only for small velocity. In which S' is moving with small velocity v wrt fixed frame S.
But what would happen if second frame S' starts moving with the approx of speed of light.
If it is moving with speed of light then difference between the t for fixed frame and t' for moving frame is significant , because time becomes very very slow for moving frame wrt to fixed rest frame , which is called time dilation.

Now let's talk about the Lorentz Transformation.
Consider the two frame of reference S and S' having the coordinates of any point P is (x,y,z,t) and (x',y',z',t') , initially both frame of reference are at same position ie. concide to each other, where t is zero for both reference when they are at initial stage. Then if second frame S' starts moving in the direction of x - axis with some constant velocity v with respect to first frame of reference S. And this velocity v is approximately equal to the speed of light,.    ( First frame is a fixed frame of reference).

 Now think that from a light source , a beam of light is to be focused on the point P from the origin of the fixed frame of reference S. And the same light beam is also focused on the point P from the origin of the moving frame of reference S'.
And we know from above data that distance of point P from first frame S is x, and from second frame S' is x'.
GALILEANS & LORENTZ TRANSFORMATIONS | The basic mathematical operations for the special theory of relativity.
Then these distances can also be expressed as :    x = ct , from the first frame of reference S, and x' = ct' , from the second frame of reference S', which is moving.
                     x = ct
                     x' = ct'
from the galilean transformation we know that ,.  x' = x - vt , and  x = x' + vt'
But in Lorentz Transformation this relation is written as :
       x' = k(x-vt)      and     x = k(x'+vt')
Where k is some constant.
Multiplying these two  equations we get,
     xx' = k^2(x-vt)(x'+vt').   Putting the value of x and x' in the multiplication, we get,
    c^2tt' = k^2(ct-vt)(ct'+vt')
    c^2tt' = k^2(c^2tt' + cvtt' -cvtt' -v^2tt')
     c^2tt' = k^2(c^2tt'-v^2tt')
 Then , k^2 = 1/[1- (v^2/c^2)]
   And finally we get
        k = 1/√[1- (v^2/c^2)] and this value of constant k is called Lorentz factor which is denoted by γ.
And  So ,.      γ = 1/√[1- (v^2/c^2)]
This is very important result , because it is very helpful to deriving the expression for time dilation , relativistic mass, length contraction. So this is all about THE GALILEAN & LORENTZ TRANSFORMATION.

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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

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.

THREE DIMENSIONAL GEOMETRY

ORIGIN
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.
COORDINATE AXES 
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.
COORDINATE PLANES 
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.
SIGN CONVENTI…

A detailed unit conversion table in Hindi.

UNITS CONVERSION TABLE
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…