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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

GRAVITATIONAL LENSING, understanding the basic concepts.

Today in "Laws Of Nature" we are going to talk about a new concept ie. Gravitational lensing. Have you heard this term ever before, if not then, then you are at right place. Here you can understand everything about gravitational lensing, Such as -

what is Gravitational lensing?, how can Gravitational field form lens ? , How is this lens is different from the lens , which we have read in ray optics. (ie. Convex and concave lens), which type of lens is formed by Gravitational field? Does it is convex or concave.?
So let's explore what is Gravitational lensing?
 Before going further in the article let's take a historical look on this concept.  The concept of Gravitational lensing was first introduced by the physicist Orest Chvolson (1924) and Frantisek link (1936), these two mens are credited for first to discuss on this effect in print. But this effect is commonly associated with the Albert Einstein, who has published an article on this subject in 1936.

We know that our universe is composed of a large network of electromagnetic radiation, which carries energy from one place to another with the speed of light.
And also our universe is composed of uncountable planets, galaxies, stars, asteroids , black holes , and many more. And we also know that some objects are small but some objects are very massive, which is beyond our thinking. And all these objects are distributed randomly in the universe and controlled by the laws of nature.
And one of the laws which we are going to talk today is Gravitational lensing, which seems us as an effect.
Let's think for a situation in which you are a observer and a light source is present several light years distant from you. And a light beam is coming towards you with the speed of light. Then suddenly a very massive objects comes between the light source and you , then what would happen , what do you see, in this situation? In astrophysics this phenomenon is termed as Gravitational lensing.
So Gravitational lensing is a phenomenon in which very massive objects such as cluster of galaxies , or any other massive objects lies in between the distant light source and the observer and this massive objects are capable of bending the direction of light as it travels from the source to the observer.
And distribution of this massive objects between the light source and observer is called Gravitational lens.

And amount of bending of light can be predicted by Einstein's general theory of relativity. Classical physics are also predicts the amount of bending of light but it is half as predicted by Einstein's GTR.
Fritz Zwicky says in 1937 that this effect allows the galaxies to act as Gravitational lens.
This Gravitational lens is very large, which is formed due to the distortion of the space time, and amount of this distortion of space time is depends on the massiveness of the objects. Large mass , large distortion and larger Gravitational lens. And the bending of the light beam depends on the distance of light beam from the centre of the distortion.
If beam is passing closely to the centre of  distortion then a large deflection of light can be seen, if it is passing furthest from the centre , then minimum deflection would be seen.
Gravitational lens has no any single focal point ,but is has a focal line. The term 'lens'
is first given by the Physicist O.J Lodge , in the context of the Gravitational light deflection. If the light source, massive lensing object and the observer lie in the straight line then the original light source will appear as a ring to the observer around the massive lensing object. If there is misalignment then the observer will see an arc of light, instead. This phenomenon is first mentioned by the Physicist Orest Chvolson of st. Petersburg.  in 1924. And quantified by the Albert Einstein in 1936 by his general theory of relativity. So this ring is named as the Einstein ring.
Sometimes the lensing masses such as cluster of galaxies, does not cause a spherical distortion in space time. If this happen then the source will appear partial arcs scattered around the lens.  Then observer may see multiple distorted images of source, and the numbers and shape of distorted images will depend on the relative position between the source , lens and observer.
There are three types of Gravitational lensing.


 In the strong lensing , anyone can easily see the complete distorted image of the source in the form of ring ( Einstein ring), arcs, and multiple images.
This type of lensing has formed when distortion of space time is spherical. This strong lensing produce the images which is separated by several arcminutes. A galaxy which has mass of 100 billions solar masses creates multiple images which is separated by few arcminutes. For strong lensing source, lens and observer must be closing aligned. If they are not properly aligned then observer only see an arc. For having strong Gravitational lensing a very massive objects must be present in between the source and observer. Strong lensing can also be observed in X-rays and radio waves.


In weak gravitational lensing, the distortion of image of background source is much smaller, so anyone can't see the multiple images and a complete distorted circular shaped image, called Einstein ring. This weak lensing arise due to random distribution of massive objects such as cluster of galaxies and this cluster of galaxies have not a fixed centre of mass, every galaxy has its own centre of mass, due to various space time distortion are present. so when light passes from the source through this cluster towards the observer then it suffer various convergence and divergence and finally observer get a very small distorted images of the background source. But how he get? this much smaller distorted image can only be detected by analysing the large number of sources in statistical way, this lensing, statistically shows the stretching of the background object perpendicular in the direction to the centre of the lens. This effect is used to study the cosmic background and galaxy surveys.


 In microlensing , observer can not see any distortion in the image of the source, it means there is no any distortion in the shape of image, the mass of the lens objects is very small, that it is not able to distort the source image. In microlensing the lens object may be a planet or any other object such as stars in the milky way galaxy. And the background source star may be present in the very distant or remote galaxy. Due to microlensing source appears very bright to the observer. But this brightness keeps changing with time due to the motion of stars and planets, during the motion of the lens object, first brightness increases and reached at the peak and then starts decreasing. It can be occur in our solar system. So when stars and it's orbiting planets when aligned in a line to the observer , then gravity increases the brightness of the stars. This method can be used find that object which do not emit light.
So this is Gravitational lensing...



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…

CORONA VIRUS, history of origin , discovery , infection mechanism, symptoms and treatment.

Today we are going to talk about a virus , which is spreading very fastly all over the world. The virus which we are going to talk about is the CORONA VIRUS. So today we will talk about everything of this virus. So let's starts ...

According to the biological study , Coronavirus is a cluster of viruses that causes diseases in birds and mammals. Therefore humans are also mammals then in human being this viruses cause respiratory infections , and one of the respiratory infections is mild common cold. Coronavirus can lead to diarrhea in cows and pigs but in chicken they can cause upper respiratory infections. Currently there is no vaccine or antiviral drugs for the treatment of diseases caused by Coronavirus.
The family of Coronavirus is coronaviridae, and it's subfamily is Orthocoronavirinae and order is Nidovirales, Coronavirus is a member of Orthocoronavirinae subfamily. All Coronavirus is coated with positive sense single …

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.

Speed , Distance and Time problems tricks in Hindi | fast track arithmetic formulae for problem solving.

1). दूरी = चाल × समय
2). समय = दूरी/चाल
3). चाल = दूरी/समय
4). किलोमीटर को मील बनाने के लिए गुना किया जाता है =       5/8 से
5). मील को किलोमीटर बनाने के लिए गुना किया जाता है =       8/5 से
6). फुट - सेकंड को मील - घंटा बनाने के लिए गुना किया जाता है = 15/22 से
7). मील - घंटा को फुट - सेकंड बनाने के लिए गुना किया जाता है = 22/15 से
8). मी - सेकंड को किमी - घंटा बनाने के लिए गुना किया जाता है = 18/5 से
9). किमी - घंटा को मी - सेकंड बनाने के लिए गुना किया जाता है = 5/18 से
10). यदि एक व्यक्ति दो निश्चित स्थानों के बीच की दूरी a किमी/घंटा की चाल से खत्म करता है, तो t1 घंटे देर से पहुंचता है, तथा जब b किमी/घंटा की चाल से तय करता है, तब वह t2 घण्टे पहले पहुंचता है, तो दोनो स्थानों के बीच की दूरी =     ab(t1+t2)/(b-a) km
11). यदि कोई व्यक्ति a km/h की चाल से चलता है, तो वह अपनी मंजिल पर t1 घंटे लेट पहुंचता है, अगली बार वह अपनी चाल में b km/h की वृद्धि करता है, तो वह t2 घंटे लेट पहुंचता है, तब उसके द्वारा तय की गई दूरी = a(a+b)(t1-t2)/b
12). दो व्यक्ति X …