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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).…

THE DOPPLER EFFECT | the Doppler effect explaination | Doppler effect for IIT JEE | why does Doppler effect occurs?.

Today we are going to talk about THE DOPPLER EFFECT , it is a very important concept of acoustic physics. Doppler effect is also known as Doppler shift , which is named after the Austrian Physicist Christian Doppler, who described this phenomenon in 1842.

* DOPPLER EFFECT

When there is a relative motion between source of the sounds waves/light waves and the observer along the line joining them , then the frequency observed by the observer is different from the actual frequency of the sound source.
This phenomenon is called Doppler effect (or Doppler shift).
THE DOPPLER EFFECT | the Doppler effect explaination | Doppler effect for IIT JEE | why does Doppler effect occurs?.
If the observer and the source are moving towards each other then the observed frequency is greater than the actual frequency of the source. And if they are moving away from each other then the observed frequency is smaller than the actual frequency of the source.
Before going further take a look on this relative notation.
v = velocity of the sound waves w.r.t ground.
Vo = velocity of the observer.
Vs = velocity of the source.

* IF SOUND SOURCE IS MOVING AND OBSERVER IS STATIONARY

Tap the play button, and see the demonstration of Doppler effect.
 If the sound source is emitting the sound waves of frequency f and moving with the velocity Vs towards the observer , then the ratio of the observed frequency to the actual frequency is-
      f'/f = (v/v-Vs) , 
Observed frequency is f' =  (v/v-Vs).f
Apparent wavelength is  λ' = (v-Vs/v).λ

In this expression , the positive direction is taken along the velocity of the sound that is , from source to the observer. 
Vs is positive if the sound source is travelling towards the observer and Vs is negative if sound source is travelling away from the observer.
THE DOPPLER EFFECT | the Doppler effect explaination | Doppler effect for IIT JEE | why does Doppler effect occurs?.
* IF SOUND SOURCE IS STATIONARY AND OBSERVER IS MOVING WITH VELOCITY Vo.

If the sound source (rest) is emitting the sound waves of frequency f and observer is moving with the velocity Vo , away from the source, then the ratio of the observed frequency to the actual frequency is-
       f'/f = (v-Vo/v)
Observed frequency is f' = (v-Vo/v).f
Apparent wavelength is λ' = (v/v-Vo).λ

In this expression , the positive direction is taken along the velocity of the sound that is , from source to the observer. 
Vo is positive if the observer is travelling away from the source and Vo is negative if observer is travelling towards the sound source.

* IF SOURCE AND THE OBSERVER BOTH ARE MOVING WITH VELOCITIES Vs AND Vo.

If both source and the observer are moving with the velocities Vs and Vo , then the ratio of the observed frequency to the actual frequency is-

WHEN THEY ARE MOVING AWAY FROM EACH OTHER

When they are moving away from each other then, the ratio of the observed frequency to the actual frequency is-
       f '/f = [v-Vo/v-(-Vs)]
Observed frequency f' is = [v-Vo/v-(-Vs)].f
Apparent wavelength is λ' = [v-(-Vs)/v-Vo].λ

In this expression , the positive direction is taken along the velocity of the sound that is , from source to the observer. 
In this situation , when both source and observer are moving away from each other, then we saw that sound source is moving in opposite direction that of the sound waves , it means Vs is negative.
But observer is moving in the direction of the sound waves, it means Vo is positive. See below..
THE DOPPLER EFFECT | the Doppler effect explaination | Doppler effect for IIT JEE | why does Doppler effect occurs?.
WHEN THEY ARE MOVING TOWARDS EACH OTHER

When they are moving towards each other then, the ratio of the observed frequency to the actual frequency is-
       f '/f = [v-(-Vo)/v-Vs]
Observed frequency f' is = [v-(-Vo)/v-Vs).f
Apparent wavelength is λ' = [v-Vs/v-(-Vo)].λ

In this expression , the positive direction is taken along the velocity of the sound waves that is , from source to the observer. 
In this situation , when both source and observer are moving towards from each other, then we saw that sound source is moving in the direction of the sound waves , it means Vs is positive.
But observer is moving in the opposite direction that of the sound waves, it means Vo is negative. 

WHY DOES DOPPLER EFFECT OCCURS

If we want to understand that why does Doppler effect occurs ,then first of all , we have to understand the some basic features of the sound waves.
We know that sound waves is the type of longitudinal waves , in which particles of the medium oscillates (to and fro motion) in the direction or opposite direction of the propagation of the waves in the form of compression or rarefaction.
All waves usually propagate in the form of wave front, Sound waves have spherical wave fronts but when we see it from side it seems us circular.
When sound source is stationary and it emits waves of wavelength λ and frequency f, then this waves propagate uniformly in all directions (3-dimensionally) at the same rate , having same wavelength , frequency and pitch at any instant.

But when this sound source starts moving away or towards the observer, the produced waves didn't propagate uniformly in all the direction at the same rate.
If sound source is moving towards the observer then the wave fronts gets compressed , in the direction of the motion of the sound source.
Due to this wavelength gets shorten and frequency ( no of waves per second) gets increased, and then waves takes short time to reach the observer's ears. and observer hears the Sound of high frequency or high pitch.
THE DOPPLER EFFECT | the Doppler effect explaination | Doppler effect for IIT JEE | why does Doppler effect occurs?.
But when sound source is moving away from the observer then the wave fronts gets stretched in the opposite direction of the motion of the sound source. Due to this wavelength gets increased and frequency gets decreased, and then waves takes slightly more time to reach the observer's ears, and observer hears the sound of low frequency or low pitch.
REMEMBER : The change in wavelength and frequency, which is experienced by the observer is apparent. The actual frequency and wavelength of the source didn't change.

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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…

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 ...

OVERVIEW OF CORONAVIRUS
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.
BIOLOGICAL INTRODUCTION OF coV
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.

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…

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

SPEED , DISTANCE AND TIME PROBLEMS TRICKS IN HINDI
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 …