Declaration of Result of AIPMT 2012 (Pre)


The result of All India Pre-Medical/Pre-Dental Entrance Preliminary Examination, 2012 held on 1st April, 2012 (Sunday) has been declared. Out of 275742 registered candidates, 257960 candidates appeared in the Preliminary Stage Examination. 30788 Candidates have qualified for appearing in the Final Stage Examination to be held on 13th May, 2012 (Sunday).
The candidates can access the result on CBSE’s website www.aipmt.nic.in and www.cbseresults.nic.in

Admit cards for AIEEE-2012

The 11′th All India Engineering/Architecture Entrance Examination, 2012 for admission to B.E./B.Tech and B.Arch./B.Planning in various national level institutes will be held on 29′th April, 2012 (Offline) and 7′th, 12′th, 19′th and 26th May, 2012 (Online) all over India and abroad. The admission cards for candidates appearing in the Examination have been dispatched. In case a candidate does not receive his/her admit card through post, he/she may download the same from the AIEEE Website i.e. www.aieee.nic.in .
For obtaining the duplicate admit card, candidates may required to remit Rs. 80/- (Rupees Eighty Only) through Demand Draft in favour of the Secretary, CBSE, payable at Delhi/New Delhi. The candidates are advised to check their particulars on AIEEE website after entering their Registration number of AIEEE 2012.

CSIR-NET Physics and GATE physics: Fourier Series

CSIR-NET Physics and GATE physics: Fourier Series: Fourier series is an expansion of a periodic function of period $2\pi$ which is representation of a function in a series of sine or cosine...

Mathematics revision sheet for class 11 and class 12 physics


Differentiation
We have two quantities x and y such that y=f(x) where f(x) is some function of x.We may be interested in finding followings things
1. \frac{dy}{dx}
2. Maximum and Minimum values of y.It can be find with the method of Maxima and Minima
\frac{dy}{dx} is the called the derivative of y w.r.t to x
It is defined as
\frac{dy}{dx}=\lim_{\Delta x \to 0}\left ( \frac{\Delta y}{\Delta x} \right )
Some commonly known functions and their derivatives are:-
y=x^n\frac{dy}{dx}=nx^{n-1}
y=sinx\frac{dy}{dx}=cosx
y=cosx\frac{dy}{dx}=-sinx
y=tanx\frac{dy}{dx}=sec^{2}
y=cotx\frac{dy}{dx}=-cosec^{2}
y=secx\frac{dy}{dx}=secx tanx
y=ln x\frac{dy}{dx}=\frac{1}{x}
y=e^{x}\frac{dy}{dx}=e^{x}
Some important and useful rules for finding derivatives of composite functions
1. \frac{d}{dx}(cy)=c\frac{dy}{dx} where c is constant
2. \frac{d}{dx}(a+b)=\frac{da}{dx} + \frac{da}{dx} where a and b are function of x
3. \frac{d}{dx}(ab)=a\frac{db}{dx}+b\frac{da}{dx}
4. \frac{d}{dx}(\frac{a}{b})=\frac{[b\frac{da}{dx}-a\frac{db}{dx}]}{b^{2}}
5. \frac{dy}{dx}=(\frac{dy}{da})(\frac{da}{dx})
6.\frac{d^{2}y}{dx^{2}}=(\frac{d}{dx})(\frac{dy}{dx})
Maximum and Minimum values of y
Step 1:
fine the derivative of y w.r.t x
(\frac{dy}{dx})
Step2:
Equate
\frac{dy}{dx}=0
Solve the equation to find out the values of x
Step3:
find the second derivative of y w.r.t x and calculate the values of
\frac{d^{2}y}{dx^{2}}
for the values of x from step2
if \frac{d^{2}y}{dx^{2}}>0 then the value of x corresponds to mimina of y then y_{min} can be find out by putting this value of x
if \frac{d^{2}y}{dx^{2}}<0 then the value of x corresponds to maxima of y then y_{max} can be find out by putting this value of x
Integration
I=\int_{a}^{b}f(x)dx
It reads as integration of function f(x) w.r.t. x within the limits from x=a to x=b.
Integration of some important functions are
\int sinx dx=-cosx
\int cosx dx=sinx
\int sec^{x}dx=tanx
\int cosec^{x}dx=-cotx
\int \frac{1}{x}dx=lnx
\int x^{n}dx=\frac{x^{n+1}}{n+1}
\int e^x dx=e^x
Useful rules for integration are
\int cf(x)dx=c\int f(x)dx
\int[f(x)+h(x)]=\int f(x)dx+\int h(x)dx
\int f(x)g(x)dx=f(x)\int g(x)dx -\int\left ( f'(x)\int g(x)dx \right ) dx
Trigonometry
Properties of trigonometric functions
1. Pythagorean identity
sin^2 A +cos^2 A=1
1+tan^ A=sec^2 A
1+cot^2 A=cosec^2 A
2. Periodic function
sin(A+2\pi)=sinA
cos(A+2\pi)=cosA
3.Even-Odd Identities
cos(-A)=cos(A)
sin(-A)=-sin(A)
tan(-A)=-tan(A)
cosec(-A)=-cosec(A)
sec(-A)=sec(A)
cot(-A)=-cot(A)
4. Quotient identities
tan(A)=\frac {sin A}{cos A}
cot(A)=\frac{cos A}{sin A}

5. Co-function identities

sin\left ( \frac{\pi}{2}-A \right )=cos(A)
cos\left ( \frac{\pi}{2}-A \right )=sin(A)
tan \left ( \frac{\pi}{2}-A \right )=cot(A)
cosec \left( \frac{\pi}{2}-A \right )=sec(A)
sec\left ( \frac{\pi}{2}-A \right )=cosec(A)
cot\left ( \frac{\pi}{2}-A \right )=tan(A)

6. Sum difference formulas

sin(A\pm B)=sin(A)cos(B) \pm sin(B)cos(A)
cos(A \pm B)=cos(A)cos(B) \mp sin(A)sin(B)
tan(A \pm B)=\frac {tan(A) \pm tan(B)}{1 \mp tan(A) tan (B)}


7. Double angle formulas

cos(2A)=cos^2(A)-sin^2(A)=2cos^2 (A)-1=1-2sin^2(A)
sin(2A)=2sin(A)cos(A)
tan(2A)=\frac{2tan(A)}{1-tan^2(A)}

8. Product to sum formulas
sin(A)cos(B)=\frac {1}{2}[cos(A-B)-cos[A+B]
cos(A)cos(B)=\frac {1}{2}[cos(A-B)+cos[A+B]
sin(A)cos(B)=\frac {1}{2}[sin(A+B)+sin[A-B]
cos(A)sin(B)=\frac {1}{2}[sin(A+B)-sin[A-B]

9. Power reducing formulas

sin^2 A=\frac{1-cos(2A)}{2}
cos^2 A=\frac{1+cos(2A)}{2}
tan^2 A=\frac{1-cos(2A)}{1+cos(2A)}

10. reciprocal identities
Sin(A)=\frac{1}{cosec(A)}
cos(A)=\frac{1}{sec(A)}
tan(A)=\frac{1}{cot(A)}
 cosec(A)=\frac{1}{sin(A)}
Sec(A)=\frac{1}{cos(A)}
cot(A)=\frac{1}{tan(A)}
Binomial Theorem
(a+b)^n=C_{0}^{n}a^{n}+C_{1}^{n}a^{n-1}b+C_{2}^{n}a^{n-2}b^2+.........+C_{n}^{n}b^{n}
From the binomial formula, if we let a = 1 and b = x, we can also obtain the binomial series which is valid for any real number n if |x| < 1.
(1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+………..
Geometric Series
a,aq,aq^2,aq^3,aq^4...........aq^{n-1} where q is not equal to 0, q is the common ratio and a is a scale factor.Formula for the sum of the first n numbers of geometric progression
S_{n}=\frac{a(1-q^n)}{(1-q)}
Infinite geometric series where |q| < 1
If |q| < 1 then a_{n} \to 0, when n -> infinity So the sum S of such a infinite geometric progression is:
S=\frac{1}{(1-x)} which is valid only for |x|
Arithmetic Progression
a,a+d,a+2d,a+3d..........a+(n-1)d
The sum S of the first n values of a finite sequence is given by the formula:
S=\frac{n}{2}[(2a + d(n-1)]
Quadratic Formula
ax^2+bx+c=0
then
x=-\frac{b\pm?(b2-4ac)}{2a}

Download this post as pdf

Popular Posts