Tuesday 25 February 2020

Central Excise Day celebrated on 24th February across India


Central Excise Day is celebrated every year on February 24 across India. The day is being celebrated to honour the service of Central Board of Excise and Custom (CBEC) to the country. The day is celebrated to honour the officers associated with CBEC and their services. This is done to encourage the officers to carry out their duties with utmost sincerity. The officers, every year perform checking of corruption in goods from manufacturing sector. The day is celebrated to commemorate the legislation of Central Excise and Salt act in 24 February, 1944.
About Central Board of Indirect Taxes and Customs
The Central Board of Indirect Taxes and Customs is formerly known as the Central Board of Excise and Customs. The Customs and Central Excise/ Central GST department was established to administer customs laws. Now the department is under the Department of Revenue, Ministry of Finance which deals with the policy formulation concerning levy and collection of Customs, Central Excise duties, Central Goods & Services Tax and IGST, prevention of smuggling and administration of matters relating to Customs, Central Excise, Central Goods & Services Tax, IGST and Narcotics to the extent under CBIC’s purview.
The Board is the administrative authority for its subordinate organizations, including Custom Houses, Central Excise and Central GST Commissionerates and the Central Revenues Control Laboratory.
Important takeaways for all competitive exams:
  • Chairman of Central Board of Excise and Custom: M. Ajit Kumar.
  • Headquarters of Central Board of Excise and Custom: New Delhi.

Thursday 23 January 2020

Daily Vocabulary



1. NIMBLY (Adjective) तीव्रता से अदल
Meaning: having or showing quickness of mind
Synonym: alert, brainy, bright, brilliant, clever
Antonym:  dim-witted, doltish, dopey (also dopy), dorky [slang], dull,
Usage: Her nimble fingers make knitting look so easy

2. ENFEEBLEMENT (Noun) दुर्बलीकरण
Meaning: a gradual sinking and wasting away of mind or body
Synonym:  decaying, declension, decline, degeneration, descent, deterioration
Antonym: comeback, improvement, rally, recovery, recuperation, rehabilitation
Usage: Daily exercise can help to halt some of the enfeeblement that comes with advanced years.

3. INVIGORATE (Verb) सबल बनाना
Meaning: to give life, vigor, or spirit to
Synonym: amp (up), animate, brace, energize, enliven, fillip, fire
Antonym: damp, dampen, deaden, dull, kill
Usage: The fresh air and sunshine invigorated the children after a long winter indoors.
4. DISENFRANCHISE (Verb) नागरिकता से वंचित करना
Meaning: Deprive of the right to vote.
Synonym: Opress, shackle, coerce
Antonym: Liberate, release, permit
Usage: Government should disenfranchise the people having the voting identity of two cities/states
5. SCAPEGOAT (Noun) बलि का बकरा
Meaning: A person who is blamed for the wrongdoings of others
Synonym: Whipping boy, victim
Antonym: Armed man, cocked sparrow
Usage: Rajesh always finds a scapegoat to blame whenever he encountered a problem.
6. COY(Adjective) संकोची 
Meaning: intentionally keeping something secret
Synonyms: bashful, timid
Antonyms: forward, unshy
Usage: She gave me a coy look from under her schoolgirl’s fringe.7. INCUR (verb) झेलना
Meaning: become subject to (something unwelcome or unpleasant) as a result of one’s own behavior or actions.
Synonyms: provoke, earn, arouse, induce.
Antonyms: avoid, shun, elude, evade.
Usage: The surgery wasn’t what scared the sick man, it was all of the medical bills he would incur from the procedure.
8. PANDER (verb) बढ़ावा देना
Meaning: gratify or indulge (an immoral or distasteful desire or taste or a person with such a desire or taste)
Synonyms: indulge, gratify, satisfy, yield.
Antonyms: dissatisfy, deny, refuse, disturb.
Usage: She tries to hold on to as much genuine stuff as she can while pandering to fancier tastes.
9. BRACE (verb) सहारा देना
Meaning: prepare (someone) for something difficult or unpleasant.
Synonyms: nerve, gird, strengthen, fortify.
Antonyms: dampen, deaden, drain, debilitate.
Usage: Along with most of my neighbors in the Washington, D.C. metropolitan area, I was braced for the presidential transition.
10. SMUG (adjective): आत्मसंतुष्ट
Meaning: having or showing an excessive pride in oneself or one’s achievements.
Synonyms: bighead, complacency, egotism, vainglory.
Antonyms: diffidence, bashfulness, demureness, shyness.
Usage: Because Rocky had a smug attitude during his meeting with the principal, he projected the image he was proud of his misdeeds.

Monday 20 January 2020

Time And Work  (Notes)

Time= Work done/Efficiency
  • When work is same.
 Time∝1/Efficiency
  • If A can do a piece of work in n days.
                                               Then, per day working efficiency of A = 1/n
  • If working efficiency of A & B is → x : y.
Then, the time taken by A & B to finish the work is in the ratio → y : x
                e.g. If A does three times faster work than ‘B’, then ratio of work done by A and B is 3 : 1.
                Then
                   Ratio of time taken by A & B = 1 : 3
  • If A can do a piece of work is x days and B can do a piece of work in y days, then both of them working together will do the same work in
xy/(x+y)  days
Explanation 
⇒ A’s 1 day’s work = 1/x
B’s 1 day’s work = 1/y
(A + B)’s 1 day work = 1/x+1/y =(x + y)/xy
A + B will complete the work in = xy/(x + y)
Q. A can finish a piece of work by working alone in 6 days and B, while working alone, can finish the same work in 12 days. If both of them work together, then in how many days, the work will be finished? 
Sol.  x = 6, y = 12
Working together A + B will complete the work in = xy/(x + y)=(6 × 8)/18
= 4 days


  • If A, B & C will working alone, can complete a work in x, y and z days, respectively, then they will together complete the work in
xyz/(xy+yz+zx)
Explanation
⇒ A’s 1 day work = 1/x
B’s 1 day work = 1/y
C’s 1 day work = 1/z
(A + B + C)’s 1 day work = 1/x+1/y+1/z  =(yz+xz+xy)/xyz
(A + B + C) will complete the work in
=xyz/(yz+xz+xy)

Q. A, B, and C can complete a piece of work in 10, 15 and 18 days, respectively. In how many days would all of them complete the same work working together?
Sol. x = 10 days, y = 15 days & z = 18 days
The work will be completed in
=(10×15×18)/(10×15+15×18+18×10)
=2700/600=4½  days
  • Two persons A & B, working together, can complete a piece of work in x days. If A, working alone, can complete the work in y days, then B, working alone, will complete the work in
⇒xy/(y-x)
Explanation 
⇒ A + B’s 1 day work = 1/x
A’s 1-day work = 1/y
B’s 1 day work = 1/x-1/y
=(y-x)/yx
B will complete the work = yx/(y – x)

Q. A and B working together take 15 days to complete a piece of work. If A alone can do this work in 20 days, how long would B take to complete the same work?
Sol. x = 15, y = 20
B will complete the work in = (15 × 20)/5
= 60 days

Click Here to Attempt More Questions From Quantitative Aptitude For SSC CGL 

  • If A & B working together, can finish a piece of work is x days, B & C in y days, C & A in z days. Then, A + B + C working together will finish the job is
⇒2xyz/(xy+yz+zx)
Explanation
⇒ A + B’s 1 day work = 1/x
B + C’s 1 day work = 1/y
C + A’s 1 day work = 1/z
[(A + B) + (B + C) + (C + A)]’s 1 day’s work
=1/x+1/y+1/z
=(yz+xz+xy)/xyz
2 (A + B + C)’s 1 day work = (xy + yz + xz)/xyz
A + B + C’s 1 day work = (xy + yz + xz)/2xyz
A + B + C working together will complete the work in
=2xyz/(xy+yz+xz)

Q. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How long would they take to complete the full work together?
Sol. x = 12 days, y = 15 days, z = 20 days
A+B+C=(2×12×15×20)/(180+300+240)
=7200/720=10 days
  • If A can finish a work in x days and B is k times efficient than A, then the time taken by both A and B, working together to complete the work is
x/(1+k)
Explanation
⇒ Ratio of working efficiency, A & B = 1 : k
Ratio of Time taken = k : 1
k → x days
1r → x/k days
A → x days
B → x/k days
1 day work of A = 1/x
1 day work of B = k/x days
(A + B)’s 1 day work = 1/x+k/x=(k + 1)/x
(A + B) will complete the work is = x/(k+1)

Q. Harbans Lal can do a piece of work in 24 days. If Bansi Lal works twice as fast as Harbans Lal, how long would they take to finish the work working together?
Sol. x = 24, k = 2
Working together they will complete the work in = 24/(1 + 2)
=24/3=8 days

WAVES NOTES- 11TH PHYSICS


WHAT IS A WAVE
wave is a disturbance that travels or propagates and transports energy and momentum without the transport of matter. The ripples on a pond, the sound we hear, visible light, radio and TV signals are a few examples of waves. Sound, light and radio waves provide us with an effective means of transmitting and receiving energy and information.
Waves are of two types : mechanical and electromagnetic.
Mechanical waves require material medium for their propagation. Elasticity and density of the medium play an important role in propagation of mechanical waves. That is why the mechanical waves sometimes are referred to as elastic waves.
Electromagnetic waves require absolutely no material medium for their propagation. They can travel through vacuum. Light, TV signals, radio waves, X-rays, etc. are examples of non mechanical waves. These are electromagnetic in nature. In an electromagnetic wave, energy travels in the form of electric and magnetic fields.
Classification of Waves
There are three ways of classifying mechanical waves.
1. Based on Direction of Motion of Particles
Waves differ from one another in the manner the particles of medium oscillate (or vibrate) with reference to the direction of propagation.
(i) Transverse Waves : In such waves, the oscillatory motion of the particles of the medium is transverse to the direction of propagation. Consider the wave travelling along a rope.
https://i0.wp.com/www.dronstudy.com/wp-content/uploads/2016/11/img_582bf83000670.png?w=1170&ssl=1The direction of propagation of the wave is along the rope, but the individual particles of the rope vibrate up and down. The electromagnetic wave (light, radio waves, X-rays, etc.) through not mechanical, are said to be transverse, as the electric and magnetic field vibrate in direction perpendicular to the direction of propagation.
(ii) Longitudinal Waves : In these waves, the direction of vibration of the particles of the medium is parallel to the direction of propagation.
https://i0.wp.com/www.dronstudy.com/wp-content/uploads/2016/11/img_582bf97293488.png?w=1170&ssl=1
The figure shows a long and elastic spring. When we repeatedly push and pull on end of the spring, the compression and rarefaction of the spring travel along the spring. A particle on the spring moves back and forth, parallel and anti-parallel to the direction of the wave velocity.
Sound waves in air are also longitudinal. Some waves (for example,ripples on the surface of a pond) are neither transverse nor longitudinal but a combination of the two. The particles of the medium vibrate up and down, and back and forth simultaneously describing ellipses in a vertical plane.
In strings, mechanical waves are always transverse, when the string is under a tension.
In gases  and liquids, mechanical waves are always longitudinal, e.g., sound waves in air or water. This is because fluids cannot sustain shear. They do not posses rigidity. They posses volume elasticity, because of which the variations of pressure (i.e., compression and rarefaction) can travel through them. For this reason, the longitudinal waves are also called pressure waves.
The waves on the surface of water are of two kinds: Capillary waves and gravity waves. Capillary waves are ripples of fairly short wavelength  - no more than a few centimeters. The restoring force that produces these waves is the surface tension of water.
Gravity waves have wavelength of several meter and restoring force is the pull of gravity.
In solids, mechanical waves (may be sound) can be either transverse or longitudinal depending on the mode of excitation. The speeds of the two waves in the same solid are different (longitudinal waves travel faster than transverse waves).
2. Based on Dimensionality of Propagation
One-dimensional wave travels along a straight line, e.g., waves produced on a string.
Two-dimensional wave propagates over a surface, e.g, water ripples, vibration of the surface of a drum.
Three-dimensional wave propagates in all directions, e.g., sound waves.
3. Based on Particle Behaviour in Time
These can be two types of waves – wave pulse and wave train.
(i) Wave pulse: In this case, the motion of a particle of the medium has following time sequence. First the particle is in equilibrium (no motion) state. It then gets some type of motion or disturbance, and finally it returns to it equilibrium position. We can generate a transverse wave pulse on a string by once displacing one end of the string up and down.
https://i0.wp.com/www.dronstudy.com/wp-content/uploads/2016/11/img_582bfe1fe829f.png?w=1170&ssl=1
As the displacement pulse travels along the string each particle in the string begins at rest, experiences a displacement as the pulse passes through it, and then returns to the equilibrium.
(ii) Wave Train : In a wave train all the particles of the medium undergo a continuous periodic motion. Any continuous succession of pulses constitution a wave train. Specially, if the periodic motion of the particles is simple harmonic motion, the wave is called sinusoidal wave train.
Wave Function
The disturbance created by a wave is represented by wave function. For a string, the wave function is a (Vector) displacement; whereas for sound waves, it is (scalar) pressure or density fluctuation. In the case of light or radio waves, the wave function is either an electric or magnetic field vector.
Mathematical Representation of Wave Function
Consider a disturbance or a pulse travelling along x-direction with a velocity v. Let us look at this pulse from two different frames of reference. The xy-frame is stationary, whereas the other frame x'y' is moving with velocity v along x-axis, as shown in the figure. We assume that the origins of the two frames concede at t = 0.
https://i0.wp.com/www.dronstudy.com/wp-content/uploads/2016/11/img_582c02c6ccb0f.png?resize=309%2C161&ssl=1
In the moving frame, the pulse appears to be at rest, since both the pulse and the x'y'- frame are moving with the same velocity v. Therefore, at any time the vertical displacement y' at position x' is given by some function f(x'that describes the shape of the pulse;
y=f(x)          ........(i)
In the stationary frame, the pulse has the same shape but it is moving with a velocity v. It means that the displacement y is a function of both x and t.
The coordinates of any point on the pulse as measured in the two frame are related as
y=y
x=xvt
Thus, Eq. (i) may be modified as
y=f(xvt)        ..........(ii)
This equation represents a wave motion along +ve x-direction.
Any given feature (phase) of the pulse, for example, its peak, has a fixed value of x'. It means that
x=xvt=constant ....(iii)
The quantity xvt is called the phase of the wave function.
Differentiating  Eq. (iii) w.r.t. time, we get
dxdt=v
where v is the wave velocity or phase velocity. It is the velocity at which a particular phase f the disturbance travels through space. If the wave is travelling along the negative x-axis, the wave function is given by Eq. (ii) modified as
y=f(x+vt)
In general, the wave motion in one dimension is given by
y=f(x±vt)
The Wave Equation
A travelling wave satisfies a differential equation, called the linear wave equation,
2yx2=1v22ydt2
Any function of space and time which satisfies above differential equation is a wave.
Functions such as y = A sin wt   or   y = A sin kx do not satisfy above equation, hence do not represent waves. On the other hand; functions such as
Asin(kxwt)
Asinkxsinwt
[Asin(kxwt)+Bcos(kx+wt)]
(axbt)−−−−−−−
(axbt)2
AeB(xvt)2
or Acos2(kxwt) satisfy the wave equation, and hence these are wave functions.
Note that for a function to be wave function, the three quantities xt and v must appear in the combinations (xvt) or (x+vt). Thus, (xvt)2 is acceptable but (x2v2t2) is not.
Negative sign between t and x implies that the wave is travelling along positive x-axis and vice-versa.
Example 1
The wave function of a pulse is given by y=32+(x−4t)2, where y is in metres and t is seconds.
Determine the wave velocity of the pulse and indicate the direction of propagation of the wave.
Solution
On comparing the given expression with
y=f(xvt)
we get the velocity of the wave as
v=4m/s
Since these occurs negative sign between x and t in the given expression, the wave propagates along the +ve x-axis.
Harmonic Wave Train
If the source of the wave is a simple harmonic oscillator, the function f(x±vt) is sinusoidal and it represents a harmonic wave train or simply, a plane progressive wave. When such a wave passes through a given region, the particles of the medium execute simple harmonic motion.
A 1-D (one dimensional) plane progressive wave in its most general form is given by
y=Asin(kxwt+ϕ0)
Clearly a set of four parameters Aϕ0w and k completely describes a plane progressive wave.
(1) Amplitude (A)
It represents the maximum value of the wave function from its equilibrium value.
(2) Phase Constant (ϕ0)
The phase constant or initial phase ϕ0 enables us to find the position from where time is considered. If all t = 0, x = 0 and y is also zero, then ϕ0 will be zero which is usually the case with a wave. Henceforth, we shall assume ϕ0 = 0 and the wave is travelling along positive x-axis unless stated otherwise.
(3) Angular Frequency (w)
At a given position, the wave function at time t' is given as
y,=Asin(kxwt,)
The wave will repeat itself, if y' = y or t=t+(2πw) [as sin(0+2π)=sinθ]
The time after which a wave repeats itself is called time period  (T), given by 
T=tt=2πw
It is exactly the same time that it takes for one wavelength to pass the point.
Further, the rate at which the wave repeats itself is called its frequency (f),
f=1T=w2π
The SI unit of f is Hz (hertz).
It is same as the number of complete vibrations of a point that occur in one second.
The angular frequency (w) is related to the frequency as
w=2πf
w is measured in rad/s.
Note that w, f or T are the characteristics of the source producing the wave and are independent of the nature of the medium in which the wave propagates.
(4) Wave Number (k)
The wave number or propagation constant (k) of a wave train is defined as

k=2πλ
where λ is the wavelength. The wavelength (λ) is the distance between two consecutive points vibrating with the same phase (for example, two creasts).
The constant k or wavelength λ depends on the nature of the medium.
Example 2
The equation of a transverse wave is a stretched string is given as
y=2sin2π{x30t0.01}
where y and x are cm and t is in s. Find
(a)  the amplitude                                   (b)  the frequency
(c)  the wavelength, and                         (d)  the wave velocity
Solution
Comparing the given equation with the standard equation,
y=Asin(kxwt)=Asin{2πλx2πTt} =Asin2π{tT}
we get,
(a) amplitude, A = 2 cm
(b)  frequency, f  = 100 Hz
(c)  wave length, 
λ = 30 cm
(d) wave velocity,  
v==100×30=3000 cm/s = 30 m/s
Example 3
Calculate the velocity of sound in a gas, in which the difference in frequencies of two waves of wavelength 1.0 m and 1.01 m is 4 Hz.
Solution
Let the frequencies of the two waves be f1 and f2. Then
f1f2=4
Since, v=, we can write
12=4
or v(1λ11λ2)=4 or v(11.011.01)=4
v=4×1.010.01=404ms−1
Phase Difference and Path Difference
The argument of the harmonic function,
y=Asin(kxwt+ϕ0)
is called phase of the wave, ϕ. Thus,
ϕ=kxwt+ϕ0              .................(i)
The phase ϕ changes both with distance x and time t.
The change in phase Δϕ with change in time Δt for fixed value of x is found by partially differentiating. Eqn (i) w.r.t. t, as
Δϕ=wΔt=2πTΔt
Δφ=2πTΔt     .................(ii)
Similarly, the change in phase Δf with change in distance Δx for fixed value of time t is given as
Δφ=kΔx=2πλΔx
Δφ=2πλΔx  .......................(iii)
The change in x is also called path difference. If Δx=λ = l, we get Δϕ=2π. That is, a path difference λ corresponds to a phase difference of 2π rad.
Example 4
A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60° out of phase ?

Solution
We know that for a wave v=.
λ=vf=360500=0.73m
Given,
Δφ=60=π180×60=π3rad
We know that
phase difference,Δφ=2πλ (path diffrence,Δx)
Δx=λ2πΔφ=0.722π×π3 = 0.12m