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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

LENGTH CONTRACTION , A High Speed EFFECT, and understanding it's basic concepts.

Today we are going to talk about a very interesting concept of relativistic physics ie. THE LENGTH CONTRACTION, This concept is firstly postulated by George Fitzgerald and Hendrick Antoon Lorentz to explain the negative outcome of Michelson - Morley experiment and rescue the hypothesis of stationary aether.
But when Albert Einstein put his the special theory of relativity in September 1905.
Length contraction become a clear topic , because this contraction can be easily explained by using the special theory of relativity.
The second postulate in the special theory of relativity says that the speed of light in the  vaccum is constant for all observers, regardless the motion of light source an observer, but you have to remember that any observable mass can't travel with the speed of light.
but what would happened to the object which is moving with the speed of light. If a object is travelling with c then some physical dimensions of the object changes.
The physical dimensions which goes into change, is it's length. It is observed that when does a object travel with a very high speed or with the speed of light, then the length of the object decreases.
Here a illustration is given to understand the length contraction phenomenon with different speed. The first pic have normal speed, and second pic have 80% of speed of light, and third pic is 99% of speed of light.
You can clearly see phenomenon of length contraction.
Length contraction is the phenomenon in which the the original length of the object decreases when they are traveling very fast.
This phenomenon is also known as Lorentz contraction or Lorentz Fitzgerald contraction. This contraction always occurs in the direction of propagation of objects.
This effect is negligible at daily basis speeds but, This effect become more significant when they are travelling with the speed of light.
If length contraction occurred due to the increasement in the object velocity in the direction of the motion.  Then anyone can freely ask that why does length contraction phenomenon occurs? Why does object length decreases if it is travelling with very high speed? We all know that length contraction is true event not a illusion but many of us think that it is a work of illusion. If it is not a illusion,then how can we explain it.
Undoubtedly it's explaination is somehow complicated if we try to explain it theoretically without any use of special theory of relativity, so here today we are going to explain it with the help special relativity. Let's begin...
Let's consider a two frame of reference S and S' , having coordinates (xyz) and (x'y'z')
S' frame is moving with constant speed of velocity of v with respect to frame S along x axis. A metal rod of length L0 which is its proper length, put on the frame S'. If frame is moving with v velocity then this rod is also moving with v velocity along x axis.

Let's marked the two ends point of rod is A and B. And if the distance of point of A and B with respect to S frame is x1 and x2. Then their proper length can be given as L0=x2-x1
And the distances of point A and B wrt to S' frame is x1' and x2'. And we know object is moving with v which is very high then it suffer with length contraction. And the contracted length is given as L. Which is given as L = x2'-x1'.
Now we have to use Lorentz Transformation equation to find the relation between x1 to x1' and x2 to x2'.
The general equation of relation is given as below.
     x = (x'+ vt')/√[1-(v^2/c^2)]
Obtain the two relations by putting x1 and x2 in the above equation.
         x1 = (x1'+ vt')/√[1-(v^2/c^2)] and
         x2 = (x2'+ vt')/√[1-(v^2/c^2)]
Now subtract x1 from x2 to find the proper length of the rod.
L0 = x2-x1 =(x2'+ vt')/√[1-(v^2/c^2)]-(x1'+ vt')/√[1-(v^2/c^2)]
 If we solve it then vt' term get cancelled. And new equation will be.
L0 = ( x2' - x1')/√[1-(v^2/c^2)]
And we know that x2'-x1' is equal to L which is contracted length. Then we get
     L0 = L/√[1-(v^2/c^2)] if we find for L then it becomes L =L0×√[1-(v^2/c^2)] and here we clearly see that L is smaller than L0. This is value of contracted length if it is travelling with very high speed. If we put v = c in the above formula then we find that L become 0. Means objects having the speed of light then it's length contracted to infinitly very small , which is somehow equal to zero, according to the equation.
So this is all about THE LENGTH CONTRACTION.



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…