### 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).…

### ELECTROMAGNETIC INDUCTION notes for IIT JEE/ NEET , AIIMS | chapters on your finger tips | laws of nature.

ELECTROMAGNETIC INDUCTION
Electromagnetic induction is a very important phenomenon of electromagnetism. It is a phenomenon in which EMF is produced in the coil, whenever magnetic flux linked with the coil changes. The produced EMF is called induced EMF and current so produced due to induced EMF is called induced current.

MAGNETIC FLUX (Φ)
*.It is the total no. of magnetic field lines passing perpendicularly through the surface , when it is placed in the magnetic field(B).
Φ = B.A = BAcosθ
B is the magnetic field , A is the surface area and θ is the angle between the direction of the magnetic field and the normal vector of the surface area.

*. The SI units of magnetic flux(φ) is weber (Wb).

*. Any one can change the magnetic flux by-
-  changing the intensity of magnetic field.
-  changing the coil orientation wrt to magnetic field.
- changing the surface area.

FARADAY'S FIRST LAW - whenever magnetic flux linked with the coil or loop of wire or any closed circuit changes, then there will always produce an EMF called induced EMF. This induced EMF will remains untill and unless magnetic flux keeps changing.

FARADAY'S SECOND LAWS - Second laws gives the magnitude of induced EMF. The induced EMF is directly proportional to the rate of change of magnetic flux. Mathematically it is given as-
Induced EMF = ε = -(dφ/dt) = -(φ2 - φ1)/t

LENZ'S LAW

*. According to lenz's law the direction of the flow of induced current in the circuit is such a way that it opposes the change in magnetic flux that produce it.
*. It is used to find the direction of current.
*. It follows the rule of energy conservation.

APPLICATIONS OF LENZ'S LAW

*. When south pole of a bar magnet is used to move towards the coil , then the current induced in the coil is in clockwise direction.
*. When south pole of a bar magnet is used to move away from the coil then the direction of the induced current in the coil is anticlockwise.
*. When any current carrying coil is moved towards a stationary coil then the direction of the induced current is as follows:
*. When any current carrying coil is moved away from a stationary coil then the direction of the induced current is as follows:
*. When any current flowing through the straight wire changes then then the induced current in the nearby coil is in anticlockwise direction , as shown below:
FLEMING RIGHT HAND RULE

It is a rule which helps us to find the direction of induced current and EMF in a conductor. Which are in the effect of changing magnetic field.

HOW TO APPLY THIS RULE: Stretch the fingers of your right hand in such a way that the fore finger , central finger and the thumb are in the position of mutually perpendicular direction ,and the thumb are allign in the direction of the magnetic force or in the direction of the motion of the conductor.
Fore finger are in the direction of magnetic field , and the central finger are in the direction of induced current or EMF.

MOTIONAL EMF
*. If a conducting rod of length l is moving with velocity v on the two conducting parallel rails in uniform magnetic field (B)  , as shown above.
x is the distance travelled by the rod of length l in time t.
Then magnetic flux is given as  Φ = B.A
Where area A = xl= vtl ,.  Φ = B.vlt

*. Induced EMF is given as , |ε|= (dφ/dt) = Blv
*. Induced current is I = ε/R = Blv/R
*. Magnetic force is F = lIB = l.(Blv/R).B=B²l²v/R
*. Power used in moving the conductor =
P = dW/dt = F×v = (B²l²v/R)×v = B²l²v²/R
*. Electrical power used =
P(thermal) =dH/dt =l²R =(Blv/R)^2.R = B²l²v²/R

*.  If the rod is moving in vertical plane - then it achieve a maximum constant velocity v and it's magnetic force F = mg.
F = mg =B²l²v/R , v = mgR/B²l²

*. If conducting rod performing rotational motion then motional EMF induced across the end is -
ε = (1/2)Bωl² =Bl²πυ = Bl²π/T

EDDY CURRENTS
*. It is the current induced in the bulk pieces of conductors , when magnetic flux linked with it changes is called eddy currents.
*. Eddy currents so produced is always perpendicular to the direction of the magnetic field.
*. It shows both heating and magnetic effect.
*. Magnitude of eddy currents is i = e/R.
*. It's direction can be given by the lenz's law or Fleming right hand rule.

APPLICATION OF EDDY CURRENT

*. It is used in electromagnetic damping.
*. Induction furnace
*. Electric power metre
*. Magnetic braking in electronic trains.

INDUCTANCE

*. It is a sacalr quantity and play the same role in electrical circuit as inertia played in mechanics.
*. It is the measure of the ratio of the total magnetic flux linkage to the current.ie.
L = N(φB)/I.   Where φB is magnetic flux.
*. It's dimensional formula is ML^2T^-2A^-2 and it's unit is Henry denoted as H.

SELF INDUCTION
*. Self induction is the property of a coil by virtue of which it opposes any change in the strength of the current by inducing a EMF called back EMF.
*. When the current in the coil is switched ON , then the self induction opposes the growth of current. And when current in the coil is switched OFF , then self induction opposes the decrease in the current.
*. It is also called inertia of electricity.
*. The self induced EMF in the coil is e = -L(dI/dt)
*. The coefficient of self induction or self induction L is = N(φB)/I = NBA/I
*. Self induction of the long solenoid having cross sectional area A , length l and no. of turns N is = L = μ0N²A/l.
*. Self induction of the long solenoid having core of any other magnetic material μ is =
L = μ0μrN²A/l = μ0μrn²Al = μ0μrn²V
*. Self induction of the planar coil of radius R is =
μ0N²πR/2

MUTUAL INDUCTION
*. It is phenomenon of inducing a opposing EMF in secondary coil by changing the current or magnetic flux linked with the primary coil.
M₁₂ = N₁φ₁/I₂ , M₂₁ = N₂φ₂/I₁
*. The mutual induction of the two coil depends upon -
- geometry of the two coil ie. shape, size , numbers of turns , nature of materials on which two coils are bound.
- distance between the two coils.
- relative placement of the two coils ie. Orientation of the two coils.
*. Mutual induction of the two long coaxial solenoid is = M₁₂ = μ0n₁n₂Al,..M₂₁= μ0n₁n₂Al
*. Mutual induction can be given as:
M₁₂=M₂₁=M = μ0N₁N₂A/l
*. Mutual induction of two concentric and coplanar coil M(c1c2) = N₂B₁A₂/I₁
=  μ0N₁N₂πr₂²/2r₁
*. Magnetic energy per unit volume can be given as: = uB = UB/V = B²/2μ0,. [UB is magnetic energy]

*. COMBINATION OF INDUCTANCE

SERIES COMBINATION:

*  Ls = L₁ + L₂ , if M = 0 , if M is not equal to 0 then,
Ls = L₁ + L₂ +-2M , + sign occurs when bindings are in same sense and - sign are used when bindings are in opposite sense.

*. PARALLEL COMBINATION
1/Lp = 1/L₁ + 1/L₂ if M = 0 , 1/Lp =L₁L₂ /L₁ + L₂
if M is not equal to 0 then,
1/Lp =L₁L₂- M^2/L₁ + L₂+-M

ENERGY STORED IN THE INDUCTOR

*.Magnetic energy stored in the inductor having I current is U = (1/2)LI^2.
*. Power consumed by the inductor = iL(di/dt)
*. Energy consumed in dt time = iL(di/dt)dt

GROWTH OF CURRENT IN SERIES L-R CIRCUIT

*. Equation of EMF in the circuit is=
e = lR + L(dI/dt)
*. When key is closed the current in the circuit increases exponentially with respect to the time.
The current in the circuit at any instant of time t is I = e(1-e^[-Rt/L])/R
*. The quantity L/R is called the time constant of the circuit and it is denoted as τ.
*. At one time constant , the current in the circuit is 63% of the final current.
*. If there is any change in the circuit containing inductor then there is no instantaneous effect in the flux of the inductor.
L1I1 = L2I2

CURRENT DECAY IN L-R CIRCUIT

*. EMF equation is given as :
lR + L(dI/dt) = 0
*. Current at any instant in the circuit is =
I = I0e^[-Rt/L]
*. Current in the circuit after one time constant
I = I0e^-1 = 0.37% of initial current.

AC GENERATOR
*. It is a device which is used to obtain the AC current or EMF  by rotating the coil in the magnetic field with some external force.
*. Due to rotation of the coil flux linkage with coil continuously gets changing.
*. Due to change in magnetic flux EMF generated is |e| = dφ/dt = d(NBAcosωt)/dt= NBAωsinωt
*. e = NBAωsinωt = e0sinωt , e0 is the peak voltage.
*. Alternating current generated is :
I = e/R = (NBAω/R)sinωt= I0sinωt

### 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…