### 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).…

# HYDROSTATIC : FLUIDS AT REST

## PRESSURE DUE TO LIQUID

*. Pressure is thrust applied by the liquids at rest per unit surface area of the objects when it is in contact with the liquid.
If F is the force applied by the liquid on the small surface area of ∆A then Pressure is given in the form of limit as follows :

*. In CGS system unit of pressure is dyne/cm^2 and in SI system it is N/m^2. A pressure of one
N/m^2 is called a Pascal.

### PASCAL LAW

Pascal law states that pressure applied by a enclosed liquid is transmitted equally in all directions , to every position of the liquid and wall of the container.

### HYDROSTATIC PRESSURE OF A LIQUID COLUMN

*. Pressure is given as = force / area = ρgh
Where ρ is the liquid density and h is height of the liquid column.

*. All hydraulic press and brakes are based on Pascal law.

*. Unit of pressure is Pascal and it denoted as Pa.

*. 1 Bar = 10^5 Pa and 1 torr = 1 mm of Hg.

### DENSITY AND RELATIVE DENSITY

*. Density is given by = mass /volume
For water it is = 10^3 kg / m^3
1 litre = 1000 cc = 1000 cm^3 = =1000×(10^-2m)^3 = 10^-3 m^3

*. Relative density = density of substance/ density of water at 4 ° C
= Weight of substance in air/loss of weight in water.

*. Density of any mixture = m1+m2/v1+v2
= (m1+m2)ρ1ρ2/(m1ρ2 + m2ρ1)
If m1 = m2 = m then ρ = 2ρ1ρ2/ρ1+ρ2
Density of mixture is the harmonic mean of the densities of the two densities.
*. But if,  v1= v2 = v , then ρ = m1+m2/v1+v2
= ρ1v + ρ2v/v+v = ρ1+ρ2/2
Density of mixture of two liquid is the arithmetic mean of both densities.

*. The variation of liquid density with pressure is ρ = ρ0[1+ ∆P/K] , where ∆P is the change in Pressure and K is the bulk modulus of elasticity of the liquid.

*. Relative density is called specific gravity and has no units and dimensions.

## LAWS OF FLOATATION

Laws of floatation is based on the Archimedes principle .
Weight of floating body = weight of the liquid displaced

*. Volume of body immersed = volume of fluid displaced.
*. It is found that when any object is immersed fully or partially into the water it looses some of its weight, and the loosen weight is equal to the weight of the displaced water by the portion of the object which is immersed.
*. Apparent weight = original weight - weight of the displaced water.
*. W = Mg - mg = aρgh - aσgh = agh(ρ-σ)

## SURFACE TENSION

*. It is property of the liquid due to which the free surface of the liquid tends to attain a minimum surface area and behave like a stretched membrane is called surface tension.
*. Surface tension of the liquid is the measure of the force per unit length on the either side of any imaginary line drawn tangentially over the liquid surface.
Mathematically it is given as-
S = F/l , here F is the force acting either side of the imaginary line , and l is the length of the imaginary line.
*. It's SI unit is N/m
*. Dimensional formula is [MT^-2]

### FACTOR AFFECTING SURFACE TENSION

#### TEMPERATURE

Surface tension decreases with rise in temperature.

#### IMPURITIES

If impurities is highly soluble then it increases the surface tension but if it is sparingly soluble then it can decrease the surface tension.

#### APPLICATION OF SURFACE TENSION

*. Lead balls are spherical in shape.
*. Rain drops and mercury globules when places on the plate it become spherical in shape.
*. Hairs of shaving brush when dipped in the water it spread out but when it is taken out it sticks together.
*. A greased needle float on the surface of the liquid.
*. Insect like mosquito can stand on the surface of the water.
*. Bits of the camphor gum when placed on the surface of liquid moved irregularly .

#### EXCESS PRESSURE INSIDE THE DROPS AND BUBBLES

*. Excess pressure inside a liquid drops.
∆P = 2S/R , or P-P0 = 2S/R

*. Excess pressure inside the soap bubbles.
∆P = 4S/R , or P-P0 = 4S/R

*. Excess pressure of a air bubbles inside the liquid.
∆P = 2S/R

## CAPILLARITY

The rise and fall of liquid in the capillary tube is called capillarity.

#### ANGLE OF CONTACT

It is the angle between the tangent to the liquid surface at point of contact and the solid surface inside the liquid.
It is denoted as θ

#### DEPENDENCY OF THE ANGLE OF CONTACT

*. It depends on the nature of solid and liquid in contact.
*. Cleanliness of the surface in contact.
*. Medium above the free surface.
*. Temperature of the liquid.

#### CAPILLARY RISE

Here angle of angle of contact is acute angle and meniscus of liquid inside the tube is concave as shown in the above diagram.
The pressure difference between the two side of the meniscus is given as-
Pa - Pi = 2S/r = 2S/r.secθ = 2Scosθ/r
Pressure difference between the two meniscus is also given as = ρgh
ρgh = 2Scosθ/r , h = 2Scosθ/rρg

### 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…