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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 SPECIAL THEORY OF RELATIVITY | understanding the basic concepts.

Today we are going to talk about a very interesting concept of classical mechanics,
And which topic we are going to talk about today, is always being a subject of discussion so far. Most of the people can't understand this concept after reading once, but today we are going to talk about this with a simplified explanation... If you want to understand then read it till end.
THE SPECIAL THEORY OF RELATIVITY | A theory that changed the world.
We are talking about , THE SPECIAL THEORY OF RELATIVITY. Which are originally proposed by the genius Albert Einstein in 26 September 1905 with the title of  " ON THE ELECTRODYNAMICS OF MOVING BODY". And it is generally accepted and experimentally confirmed physical theory.
After coming this theory , the way of watching the universe has been changed completely.
If we want to understand this theoretical concept. Then we have to start it from starting point. Then let's start...
Going further in the article , we have to take a look at the basic idea behind this theory , which is termed as the postulate of special theory of relativity. There are two postulate regarding to this theory. Which is as follows.

1). The laws of physics are invariant ( identical) in all inertial frame of reference.(ie. non accelerating frame of reference).

2). Second is , the speed of light in vaccum is same for all observers , regardless of the motion of the observers or light source.
In other word we say that any observable mass can't travel with the speed of light or more than it, the speed of light is considered constant in all type of frame of reference.

These are two basic idea on which the special theory of relativity are proposed by the Albert Einstein.
This theory is widely accepted by the people and give rises the brand new concept like - time dilation , space contraction , mass energy equivalence , relativistic mass , constancy of speed of light, relative of simultaneity. Now we are going to take dive in the postulate of this theory, to understand this.


In the inertial frame of reference , in which any particle moves with the constant velocity. Then in this type of situation laws of physics are invariant,  means it does not change. In inertial frame of reference Newton's laws of motion are applied good.
Let's take it differently,

Take a ball and drop it from a finite height towards the ground, in this event you can apply simply laws of motion to find speed , time interval , acceleration and displacement of the ball. Because this event has occurred in inertial frame of reference.
Now think for a plane, which is moving with a constant velocity with respect to its airport. If it moving with a constant velocity wrt it's airport , then it is the example of inertial frame of reference, now take that same ball and drop it from a finite height inside the rocket , then you will find that laws of physics are also applicable here , same as on the ground. And here you can also find velocity , displacement, acceleration , time interval by applying Newton's laws of motion.

Einstein shows that motion , speed and time all are relative.
 Take a look and find out how is it relative.


THE SPECIAL THEORY OF RELATIVITY | A theory that changed the world.
Have you wondered that when are you sitting in the moving train, then you must have noticed that when a train which is moving in opposite direction of your train passes your train very fastly, and we think that how slow our train is moving. And a another thing you also must have been noticed that , when two train are moving with same speed in same direction then we see that train are at rest and seems as they are not moving.
Here the concept of relativity of speed applied.
If there are two train having speed u m/s and v m/s and if they are moving in the opposite direction then the relative speed of train for a person , sitting in any train is given by =(u + v) m/s and this is the speed of the other train which is moving opposite to our train.

And if they are moving in same direction then relative speed is given as =(v - u) m/s and this is the speed of other train which is moving parallel in same direction of our train. This gives the feel of rest if the velocity of each train is same.


Einstein shows that motion is relative phenomenon, let's take a example to understand it.
THE SPECIAL THEORY OF RELATIVITY | A theory that changed the world.
Think of a train which is moving with u km/h , and you are outside the train. You are watching that your friend sat on the roof of the moving train. He has a ball in his hand, the velocity of the ball and your friend is same as the velocity of the train. Here your are watching the train so you are a observer, and from your reference train is moving in some direction. But do you know what your friend feel, when he sees at you , he saw that you are moving with same velocity as train in the opposite direction that of train, for your friend reference of seeing is changed, your friend velocity wrt train is zero, and u km/h wrt ground and you in the direction of motion of train. So he saw that you are moving in opposite direction that of the train. So we can say that nature of motion changes if reference point changes.


In the era of sir Isaac Newton , Newton strongly believe that time is a absolute, he always says that if 3 hrs for me then 3 hrs for every objects in the universe. But Albert Einstein did not agree with him , Einstein think that time is a relative quantity and it is also true so far. Einstein says that time is effected with the velocity, if anyone who is travelling with a very high speed, then time passes slowly for him, in comparison with person who is at rest.
THE SPECIAL THEORY OF RELATIVITY | A theory that changed the world.
In the verification of this statement , scientists performs various experiment, one of the experiment is -
Scientists take two atomic clocks , they synchronised their time reading, after synchronization one clock is sent for the tour around earth with high velocity, while another clock keep at rest in the laboratory.
After coming back from the tour, their time reading is noticed and scientists found the difference in time reading in both clock.
This shows that time is relative, and it is found that time also slows near the high masses objects such as black hole , neutron stars , etc. Great Pyramids of Giza also slows the time for little bit.
A interesting phenomenon with relatively of time is that , if you go for a journey by a probe which can travels at the speed of light, for one year, when you come back from your journey then you saw that your age is changed only by two years ( one year in going and one year is coming) but on the earth many years has been passed, this gives a new concept of TIME TRAVEL. How it happened, Is time travel possible? we will talk about it in another post.
Now you understand that time is a relative quantity. Look at the following formula.
                T = D/S.   If speed is very large then time become very small and vice versa.

Now let's talk about the second postulate.


We have all read that second postulate says that speed of light is constant in all type of point of reference or constancy of speed of light.
For understanding this statement let's take an example.
Consider a train which is moving with u km/h and a your friend is sitting in the roof of the train and he takes a ball in his hand.
And you are an observer and stands on the ground outside of the train. Train in moving with velocity u km/h and suddenly your throw the ball with v km/h in the direction of the train motion, then you saw that the velocity of ball is faster than the speed of the train by (u+v) km/h , but what happened if your friend throw the ball with the speed of light, and what will you see. Do you see the speed of the ball is (c+u) km/h , ( where c is the speed of light in km/h). You as an observer sees that the speed of ball is only the speed of the light, because nothing in the stellar space whose speed is greater than the speed of light, means speed of light is maximum constant speed ever found. (Speed of light is maximum as per our researches, calculation and discovery, may be some objects have speed larger then the speed of light, and yet to be discovered).
THE SPECIAL THEORY OF RELATIVITY | A theory that changed the world.
the concepts which is come into existence after coming the special theory of relativity are TIME DILATION, SPACE CONTRACTION, RELATIVISTIC MASS , SPACE TIME AND MASS ENERGY EQUIVALENCE. we are not going to talk about these topic today.
We will discuss these topic in detail in coming articles.
Now let's talk about why special theory of relativity is special.
This theory is "special" because this theory is applicable only in special case, where the space time is flat, ie. The curvature of space time should be 2D , and if space time is 2D or flat then it is described by the energy - momentum tensors , where gravitational effect is negligible. This make this theory special.
But Einstein developed a new theory to describe the effect of gravity in space time and that theory is THE GENERAL THEORY OF RELATIVITY. which is published in 1915.
And we will discuss about this theory in coming articles.
So this is all about THE SPECIAL THEORY OF RELATIVITY. Also read  General 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=…

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…