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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 speed of EFFLUX and THE TORRICELLI'S LAW , Understanding the basic concepts and it's derivations.

So , today we are going to talk about the concept of TORRICELLI 'S LAW and speed of EFFLUX. This concept is the application of Bernoulli principle. This is a very interesting phenomenon of hydrodynamics, this law is given by a Italian scientist  Evanglista Torricelli's in 1643. He calculate the velocity of fluid which are flowing as jet from a hole of a tank.
The speed of EFFLUX and THE TORRICELLI'S LAW , Explained???
Going further in the Article , we have to understand the meaning of efflux first.
Then , what is efflux?
If we talk about the efflux then efflux is nothing ,  but it is a simple flowing of fluid just like a jet from a very tiny hole ie. Orifice , and it is necessary that the cross sectional area of the orifice is very small as compared to the cross sectional area of the tank.

Many of us must have seen , the flowing of fluid through a hole of a tank like as a jet , and we have seen that this flowing fluid falls to the ground at some distance from the base o the tank. This distance from the base of the tank is called range of fluid jet.
Now we are going to talk about the Torricelli law.


If we talk about the Torricelli law then Torricelli law only tells us about the speed of efflux. And says that if a tank is filled with the fluid to the height h , above the orifice, then the speed of efflux is equal to the speed of free fall of a drop of fluid from the free surface of the fluid to the orifice.
This velocity of efflux can be find by equating the kinetic energy gained to the potential energy lost during free fall of drop of fluid.
Now we are going to deriving the formula for speed of efflux.


Let's take a tank , in which fluid is filled to the height Y and the height of the orifice from the base of the tank is y.
Then the height of the fluid above the orifice is h = Y - y
And the elements at the free surface of fluid of the tank is , A2, v2 , p2 , and at the orifice is , A1 , v1 , p1, and ρ is the density of the fluid.
If tank is open at the top then p2 = p(atm) and p1 = p(atm) because orifice is always open to the atmosphere.

Then applying equation of continuity , we get;
                    A1v1 = A2v2
                    v2 = A1v1/A2. 
Here A1v1 is small because orifice is very small , and A2 is large then on solving we get v2 is very very small and seems us negligible , so we take v2  as zero.

Now applying the concept of Bernoulli principle;

p1 + ρgy + (1/2)ρv1^2 = p2 + ρgY
Here (1/2)ρv2^2 is zero because v2 seems us zero.
So then,
  (1/2)ρv1^2 = p2 - p1 + ρg(Y -y)
And we know that, Y - y = h
 So, (1/2)ρv1^2 = (p2 -p1) + ρgh
     v1^2 = 2gh + 2(p2 - p1)/ρ
Then velocity of efflux is :
       v1 = √(2gh + 2(p2 - p1)/ρ.    [ p1 = p(atm)
This formula is applicable when tank is closed.
If tank is open then p2 became p(atm).
And formula became:
           v1 = √2gh.   [ p2-p1 = 0 , because both are atmospheric pressure.]
In kinematics this formula is the velocity of free falling objects.


If fluid is flowing like a jet then it must be some horizontal distance, that is called range.
Then this range can be simply calculated by multiplying the velocity of efflux and time taken by it to striking the ground. If y is the height of orifice and Y is the height of fluid column, then-
Then time taken by it to coming the ground is given as:
   Applying second equation of motion, we get.
               y = ut + (1/2)gt^2
                   y = (1/2)gt^2.        [ ut = 0 ]
  Then ,.  t = √2y/g
Then range R = v1×t = √2gh×√y/g
                 R = √4yh = 2√yh
 Then maximum range is given as follows:
   R = 2√yh = 2√y(Y - y) 
Differentiate Range wrt to y , we get;
        R'(y) = 2 [1/{2√y(Y - y)} ×(Y-2y)]
 Equating R'(y) equal to 0
          (Y -2y)/√y(Y-y) = 0
 We get ,.    Y - 2y =0 
 Then double differentiation of Y-2y wrt to y , then we get (-2) which is less than 0 , so it is Maxima.
                    Y = 2y , y = Y/2 is point of Maxima.
Putting value of y= Y/2 in the formula of range, then we get,
                     R = 2√Y(Y -(Y/2))/2
                   R = 2√Y^2/4 = Y
It means it's maximum range is equal to the height of the fluid column in the tank .


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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

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…