### 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).…

### ALTERNATING CURRENT fast revision notes for IIT JEE | quick concept booster | Laws of nature.

ALTERNATING CURRENT
*. It is the current which varies in magnitude continuously and changes its direction alternatively and periodically.
It is represented as , I = I0sinωt , where I0 is the maximum value of AC current called as peak current. I is called the instantaneous value of alternating current. ω is called angular frequency of alternating current. Which is given as-
ω  = 2π/T = 2πυ, T is time period of A.C and υ is frequency of A.C.

*. It is the type of sinusoidal waves , which are represented by sine and cosine angle.

*. Alternating voltage or EMF can be represented as. E = E0sinωt , where E is instantaneous value of alternating voltage , E0 is the peak voltage.

MEAN VALUE OF A.C

*. It is the value of alternating current , which send same amount of electric charge through the circuit in half cycle as it sent by steady current in the same time. It is denoted by Im. Derivations for mean value of alternating current over half cycle is as below.

*.  Mean value ofAlternating current over a complete cycle is zero.
*. Similarly Alternating EMF is given as-
Em = 2E0/π = 0.637E0

ROOT MEAN SQUARE VALUE OF AC.

*. It is the value of alternating current over a complete cycle which would generate same amount of heat energy in the circuit , as it is generated by steady current in the same circuit.
It is denoted as I.rms , I.eff or Iv.
Derivations for RMS current is as follow:
E.rms = E0/√2 = 0.707E0 = 70.7% of E0.

*. Form factor is given as = I.rms/I.m = 1.11

AC THROUGH RESISTOR
*. Instantaneous EMF is E = E0sinωt
Then I = E/R = E0sinωt/R = I0sinωt
*. When AC flow through the resistor then voltage and current are in same phase.

AC THROUGH INDUCTOR
*. The instantaneous voltage across the inductor is E = E0sinωt and I = I0sin(ωt- π/2)
Where I0 is given as = E0/ωL

*.  In the inductor current lags behind the voltage by π/2 , and voltage lead the current by π/2.

*. INDUCTIVE REACTANCE -  In electrical circuits inductor plays the role of resistor , when Alternating current passes through the inductor it opposes the flow of Alternating current , this resistance by the inductor is called the inductive reactance. It is denoted as XL.
*. Inductive reactance XL = ωL = 2πυL

AC THROUGH CAPACITOR
*. Instantaneous voltage across the capacitor is
E = E0sinωt and I = I0sin(ωt+π/2)
Where I0 is equal to ωCE0.

*. Current leads the voltage by the angle π/2 and voltage lags behind the current by the angle π/2.

*. CAPACITIVE REACTANCE - In the electrical circuits capacitor also plays the role of resistor. When AC passes through it , it opposes the flow of Alternating current , so resistance through the capacitor is called capacitive reactance.
It is denoted as Xc.
*. Capacitive reactance is given as , Xc = 1/ωC
= 1/2πυC

AC THROUGH R-L CIRCUIT
*. If AC source is  E = E0sinωt and the instantaneous current in the circuit is
I = I0sin(ωt - φ) , where I0 is = E0/Z , where Z is the impedance of the L-R circuit.
Z = √(R^2+XL^2)

*. In this circuit voltage leads current from 0 to π/2.
*. Tanφ = XL/R and cosφ = R/Z
*. Resultant voltage is given as V= √(VL^2+VR^2)
[Here VL is voltage across inductor and VR is voltage across resistor]

A.C THROUGH R-C CIRCUIT
*. If AC source is E = E0sinωt and the instantaneous current in the circuit is
I = I0sin(ωt - φ) , where I0 is = E0/Z , where Z is the impedance of the L-R circuit.
Z = √(R^2+Xc^2)

*. In this circuit voltage lags current from -π/2 to 0.
*. Tanφ = Xc/R and cosφ = R/Z
*. Resultant voltage in the circuit is -
V= √(Vc^2+VR^2)
[Here Vc is voltage across capacitor and VR is voltage across resistor]

AC THROUGH L-C CIRCUIT
*. If AC source is E = E0sinωt and the instantaneous current in the circuit is
I = I0sin(ωt - φ) , where I0 is = E0/Z , where Z is the impedance of the L-C circuit.
Z = |XL - Xc|
*. If xL is greater than Xc then voltage leads current by +π/2. But if Xc is greater than xL then voltage lags by -π/2
*. Resultant voltage in the circuit is-
V = vL- Vc  , if vL > Vc
V = Vc - vL , if Vc > vL

AC THROUGH L-C-R CIRCUIT
*. If AC source is E = E0sinωt and the instantaneous current in the circuit is
I = I0sin(ωt - φ) , where I0 is = E0/Z , where Z is the impedance of the L-C-R circuit.
Z = √[R^2+ (xL - Xc)^2] = √[R^2+ (ωL - 1/ωC)^2]

*. In this circuit Alternating current lags behind the voltage by phase φ.
Tanφ = (xL - Xc)/R and cosφ = R/Z

*. vL = I0.xL , Vc = I0.Xc , vR = I0.R
*. If xL = Xc , then tanφ = 0 and Z = R and voltage and current are in same phase. The AC circuit is resistive.
If xL > Xc, then tanφ is positive and voltage leads the current by phase angle Φ.
And circuit is called inductive dominant
If xL < Xc , then tanφ is negative and voltage lags behind the current by phase angle φ.
And circuit is called capacitance dominant.

IMPEDANCE TRIANGLE
Impedance triangle is right angled triangle whose base is ohmic resistance (R) and it's altitude is resultant reactance (xL - Xc) and it's hypotenuse represent the impedance (Z).
Impedance Z = √[R^2+ (xL - Xc)^2]
= √[R^2+ (ωL - 1/ωC)^2]

ADMITTANCE -  It is the reciprocal of the impedance of a AC circuit. It is denoted as Y.
Y = 1/Z = 1/√[R^2+ (xL - Xc)^2]
Unit of admittance is per ohm or Siemens.

SUSCEPTANCE - It is the reciprocal of the reactance of the AC circuit , and it is denoted by S.
✓ susceptance = 1/reactance
It unit is same as admittance as per ohm or Siemens.
*. Reciprocal of inductive reactance is called inductive susceptance.
sL = 1/ωL
Reciprocal of the capacitive reactance is called the capacitive susceptance.
*.  Capacitive susceptance = 1/capacitive reactance
Sc = ωC

RESONANCE IN L-C-R CIRCUIT
*. An AC circuit is said to be resonant circuit, when the natural frequency of the circuit become equal to the frequency of the applied voltage.
*. At resonance
xL = Xc , vL = Vc
φ become zero [ V and I is in the same phase.]
Z(min) = R, because xL- Xc = 0.
I(max) = V/R

*. Resonant frequency
When xL = Xc then ωL = 1/ωC , ω = 1√LC
Or resonant frequency υR = 1/2π√LC

*. Bandwidth ∆υ = υ2 - υ1

*. QUALITY FACTOR (Q) - It gives the idea about the stored energy as well as lost energy. It measures the sharpness of the resonance of the L-C-R circuit.
Q = 2π×max energy stored per cycle/max energy lost per cycle.
*. Q = xL(r)/R = Xc(r)/R = 2π(υr)L/R = 1/2π(υr)CR
= √(L/C.R^2) = υr/bandwidth = υr/(υ2 - υ1).

*. Q- factor denotes the sharpness of the tuning.
- High Q factor means lower rate of energy loss.
- Higher value of Q- factor means          sharper peak current.

ASSOCIATION OF POWER IN AC CIRCUIT

*. If AC source is  E = E0sinωt and the instantaneous current in the circuit is
I = I0sin(ωt - φ) then instantaneous power in the circuit is -
P = E0sinωt.I0sin(ωt - φ)
= E0.I0sinωt.(sinωt.cosφ - cosωt.sinφ)
*. AVERAGE POWER (Pav)
ZI(max)^2 = V0.I0^2/I0 = V0.I0 , so it can be written as , V0.I0.cosφ/2
*.Root mean square power P(rms)= E(rms).I(rms)
*. Power factor cosφ = average power/rms power
Cosφ = R/Z
*. Maximum power dissipated in resistive circuit or L-C-R resonant circuit.
*. No power dissipated in purely inductive and Purley capacitive circuit. So current flowing through these circuit is called wattless current.

CHOKE COIL

*. It is the coil of high inductance and negligible resistance.

*. It is used to control the current in the AC circuit at minimum power loss. that is;
cosφ =r/Z = r/√(r^2 + xL^2) = (r/ωL)~0

*. Ideal choke coil has zero resistance.
*. Choke coil is the work of series L-R circuit. It choke coil have small resistance r then current is given by I = V/Z , Z = √[(R+r)^2 + (ωL)^2]

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LC OSCILLATION
*. It is the oscillation of energy between capacitor and inductor. Capacitor produce electric field energy and inductor produce magnetic field energy.

*. The frequency of oscillation is υ = 1/2π√LC.
*. In the LC oscillation , according to Kirchhoff's loop rule :
q/C - LdI/dt = 0 , but I = -dq/dt = - d^2q/dt^2
Then on solving we get-
d^2q/dt^2 + q/LC = 0 , comparing it with equation of simple harmonic motion
d^2x/dt^2 + ω^2x=0 , we get, ω^2=1/LC
Or ;  ω = 1/√LC

*. Electrical energy stored in capacitor is
Uc = q^2/2C
*. Magnetic energy stored in inductor is
uL = LI0^2/2 , where I0 max. current

*. In the LC oscillation
U = q^2/2C =LI0^2/2

TRANSFORMER
*. It is a Device which is used to increase or decrease the Alternating current. Which is based on the phenomenon of mutual induction.

*. If transformer is ideal means there is no loss of energy in the transformer then input power is equal to output power.
P = V×I , Vp×Ip = Vs×Is

*. Constructing a ideal transformer is impossible, always some energy is escaped in the form of heat.  95% or more efficient transformer is regarded as best and we'll designed transformer.

*. In any transformer
*. If Ns > Np , then voltage is stepped up , this type of arrangement in transformer is called step up transformer.

*. If Ns < Np , then voltage is stepped down , this type of arrangement in transformer is called stepped down transformer.

### 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…