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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).…

Hydrodynamics : fluid at motion , study notes for IIT JEE | concept booster, chapter highlights |

HYDRODYNAMICS : FLUID IN MOTION

FLUID MOTION

STREAMLINE FLOW

It is the type of flow in which the path taken by the fluid particles under a steady flow is streamline in the direction of the fluid velocity at that point.

LAMINAR FLOW

In this type of flow, fluid flows in steady state and moves in the form of layers of different velocities and never intermix while flowing.

TURBULENT FLOW

It is also a type of the fluid motion in which velocity of the particles is greater than its critical velocity and particles become irregular during motion.

CRITICAL VELOCITY

It is the maximum velocity of the fluid up to which the flow is streamline and above which it become turbulent is called critical velocity.

Mathematically ;
Vc = kη/ρr , where η is viscosity of liquid, ρ  is the density of the liquid, r is the radius of the tube.

REYNOLDS NUMBER

It is the number scale which determines the nature of the motion of the liquid through the pipe.
Reynolds number is given as-
= (Inertial force per unit area/viscous force per unit area)
Mathematically;
N = ρvr/η
where v is the velocity of the liquid, r is the radius of the tube and ρ is the density of the liquid.
On the basis of Reynolds number, we have -
0<N<2000  , is streamline flow
2000<N<3000 , streamline to turbulent
3000<N is purely turbulent.

EQUATION OF CONTINUITY

Equation of continuity says that if an incompressible and non viscous fluid flowing through a pipe of non uniform cross sectional area then the product of the velocity of the fluid and cross sectional area at every point inside the pipe remains the same.
Mathematically;
A1v1 = A2v2  , or Av = constant
This equation is known as equation of continuity.

BERNOULLI'S PRINCIPLE

This principle states that, for a incompressible, non viscous fluid in a streamlined irrotational flow , the sum of the pressure energy, kinetic energy and potential energy at per unit volume remains constant at every cross sectional area throughout the liquid flow.

Mathematically it is given as ; 
P + 1/2ρv^2 + ρgh = constant
Or P/ρg + h + v^2/2.g = new constant

*. If the fluid is flowing through a horizontal tube, the both ends at the same level, then the potential energy becomes zero because height is zero,(h=0)

P/ρg + v^2/2g = constant

*. If fluid is in rest inside the tube then velocity is zero everywhere in the pipe, in this case -

P1 + ρgh1 = P2 + ρgh2 
P1 - P2 = ρg(h2 - h1)

APPLICATIONS OF BERNOULLI'S PRINCIPLE

SPEED OF EFFLUX

It is the speed of the liquid which flow through the small orifice (narrow hole) is equal to that which a freely falling body would acquire in falling through a vertical distance equal to the depth of the orifice below the free surface of the liquid.
Speed of efflux is given by v = √2gh

*. HORIZONTAL RANGE - when liquid flows out from a narrow hole which is at depth h below the free surface of the liquid of a fully filled tank of height H. Then it covers some horizontal distance from the foot of the tank and this horizontal distance called the range of the efflux.
Range of the efflux is given as -
R = velocity of efflux × time taken by the liquid to reach the ground.
Time taken by the liquid to reach the ground level is, T = √2(H-h)/g
R = √2gh × √2(H-h)/g = 2√h(H-h)

VENTURI-METER 

It is a device used to measure the flow speed of incompressible , non viscous fluid using a U shaped manometer attached to it, with one arm at narrow end and one arm at broader end.
After applying Bernoulli's principle -

v = √{2(ρm)gh/ρ}.[(a1^2/a2^2) - 1]^-1/2

where , ρ is the density of the fluid
ρm is the density of fluid in manometer
a1 and a2 are area of cross section

DYNAMIC LIFT OF A BALL DUE TO MAGNUS EFFECT

When a spinning ball is thrown in air, then it somehow deviate from its original path. This deviations arise due to the pressure difference between the upper and lower faces of the spinning ball , due to this Pressure difference ball experienced a upward lift by the net force acting upon it , is called Magnus effect.

Lift of an aircraft wings and blown off the roof without damaging the house are some examples where Magnus effect can be seen.

VISCOSITY

*. It is the tendency of the fluids to opposes the relative motion of its layer is called viscosity of the liquid.
*. Backward dragging force are also called viscous drag or viscous force.

*. According to Newton, viscous force ( F) between the two layers is given as -
F = -ηA(dv/dx) , where η is the cofficient of viscosity of the liquid.
A is the area of each layer and dv/dx is velocity gradient.
Here negative sign shows that viscous force act in opposite direction of the flow of the liquid.

COFFICIENT OF VISCOSITY

It is defined as the ratio of shearing stress to the strain rate.
η = (F/A)/(v/l) = Fl/vA

*. Dimensional formula is [ML^-1T^-1]
*. SI unit is poiseuille (Pl) or Pa.s or N/m^2 .s
*. In CGS system it unit is dyne/cm^2 called poise. 1 Pl = 10 poise.
*. For ideal fluid value of viscosity is zero.
*. Viscosity is due to transport of momentum.
*. Relative viscosity is = η/(ηwater)

STOKES LAW

Stokes law states that , if a sphere of radius r moves with velocity v through the liquid of viscosity η , then the drag force experienced by the sphere is given as -
               F = 6πηrv

TERMINAL VELOCITY

It is the maximum velocity acquired by a body while falling through a viscous liquid called terminal velocity.
The constant terminal velocity attained by the sphere of radius r of density ρ while falling in the fluid of viscosity η and density σ is -
V(t) = 2r^2.(ρ-σ)g/9η

POISEUILLE FORMULA

It is the rate of volume of fluid coming out of the tube. 
Mathematically it is given as-
V/t = πPr^4/8ηl ,
 where P is pressure difference, η is cofficient of viscosity of fluid , l is the length of the tube and r the radius of the tube.

*. Series combination ( V1 = V2)

V/t = P/[(8ηl1/πr1^4) + (8ηl2/πr2^4)]
Here, P = P1 + P2
P1 and P2 is pressure difference between first and second tube.

*. Parallel combination ( P1 = P2)

V/t = P[(πr1^4/8ηl1) + (πr2^4/8ηl2)]
Here, V = V1 + V2

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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…

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…

A detailed unit conversion table in Hindi.

UNITS CONVERSION TABLE
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…