QUIZLE - Who Wants To Be An Quizmaster ?

Sunday, October 25, 2009

GATE EC PRACTICE TEST : COMMUNICATIONS

New practice test added on 'communications' topic in examzone section of iQuizzle. this will surely examine your preparation in communications topic. This is very important and interesting part as far as GATE examination is considered.Figure below, analyzes topic wise weightage in previous GATE papers. You will find how important communications is from GATE point of view.
Click on image to zoom.

CLICK HERE--> ONLINE PRACTICE TEST : GATE EC : COMMUNICATIONS

Wednesday, October 21, 2009

GATE STUDY MATERIAL : LECTURES BY IIT PROFESSORS :- CIRCUIT THEORY & DIFFERENTIATION(Maths) : DIRECT DOWNLOAD LINKS

Here ,I am posting direct download links of all the lectures by IIT professors on CIRCUIT THEORY and Differentiation(Mathematics) topic. Please visit this page to see them

GATE EC Study Material IIT LECTURES : CIRCUIT THEORY & Diffrentiation(Mathematics)

Wednesday, October 14, 2009

GATE MATHEMATICS : CALCULUS

ONLINE TEST : GATE MATHS :- CALCULUS

Chain Rule :

Let w = f(x,y,z) be continuous and have continuous first partial derivative in a domain D in xyz-space. Let x = x(u,v), y = y(u,v), z = z(u,v) be functions that are continuous and have first partial derivatives in a domain B in the uv-plane, where B is such that for every point (u,v) in B, the corresponding point [x(u,v), y(u,v), z(u,v)] lies in D. Then the function

w = f(x(u,v), y(u,v), z(u,v))

is defined in B, has partial derivatives w.r.t. u and v in B,

$\bg_white \frac{\partial w}{\partial u} = \frac{\partial w}{\partial x}\frac{\partial x}{\partial u} + \frac{\partial w}{\partial y}\frac{\partial y}{\partial u} + \frac{\partial w}{\partial z}\frac{\partial z}{\partial u}$

$\bg_white \frac{\partial w}{\partial v} = \frac{\partial w}{\partial x}\frac{\partial x}{\partial v} + \frac{\partial w}{\partial y}\frac{\partial y}{\partial v} + \frac{\partial w}{\partial z}\frac{\partial z}{\partial v}$

Mean Value Theorem :

Let f(x,y,z) be continuous and have continuous first partial derivative in a domain D in xyz space. Let P₀ :(x₀,y₀,z₀) and P : (x₀ + h,y₀ + k,z₀ + l) be points in D such that the straight line segment P₀P joining these points lies entirely in D. Then

$\bg_white f(x_0 + h, y_0 + k, z_0 + l) - f(x_0,y_0,z_0) = h\frac{\partial f}{\partial x} + l\frac{\partial f}{\partial y} + l\frac{\partial f}{\partial z}$

Indefinite Integrals :

If f(x) and F(x) are two functions of x such that
d/dx{f(x)} = F(x), then integral of F(x) is

$\bg_white \int F(x) dx = f(x) + c$
where c is any constant. Due to the addition of 'c' it is an indefinite integral.

Definite Integrals

If f(x) is a continuous functions of x in [a,b] and ψ(x) is another function of x such that

$\bg_white \frac{d}{dx}{[\psi (x)]} = f(x)$
then
$\bg_white \int_{a}^{b}f(x)dx = \psi (b) - \psi (a)$

Theorem of Integral Calculus :

$\bg_white \int_{a}^{b}f(x)dx = \lim_{h\rightarrow 0} h[f(a) + f(a + h) + f(a + 2h) + . . . + f(a + (n - 1)h]\\\\ where n = \infty, h = 0, nh = b - a$

Gamma Function :

$\bg_white \Gamma{n} = \int_{0}^{\infty} e^{-x} x^{n-1}dx,\\\\ where\\ n\ is\ a\ positive\ integer.$

Beta Function :

$\bg_white \Gamma{n} = \int_{0}^{\infty} e^{-x} x^{n-1}dx,\\\\ where\\ n\ is\ a\ positive\ integer.$

Euler's Theorem on Homogeneous Function:

If z is homogeneous function of x, y of order n, then

Taylor's Series of Two Variables :

If f(x, y) and all its partial derivatives up to nth order are finite and continuous for all points (s, y),
where a ≤ x ≤ a + h, a ≤ y ≤ a + k
Then

$\bg_white f(a+h, b+k ) = f(a,b) + (h\frac{\partial}{\partial x} + k\frac{\partial}{\partial y})f\\ + \frac{1}{2!}(h\frac{\partial}{\partial x} + k\frac{\partial}{\partial y})^{2}f + \frac{1}{3!}(h\frac{\partial}{\partial x} + k\frac{\partial}{\partial y})^{3}f = ...$

Maximum Value Theorem:

A function of x,y will be the maximum at x = a, y = b.

if f(a, b) > f(a+h, b+k)
or
if f(a+h, b+k) - f(a,b) < 0, then f(a,b) is maximum.

Minimum Value Theorem

A function of x,y will be the minimum at x = a, y = b.

if f(a, b) < f(a+h, b+k) or if f(a+h, b+k) - f(a,b) > 0, then f(a,b) is minimum.

Line Integral :

If $\bg_white \overrightarrow F (x, y, z)$ is a vector function.
Then Line Integral of $\bg_white \overrightarrow F$ along any given curve DC will be
$\bg_white \int_{c}\left [F . \frac{d\overrightarrow r}{ds} \right ]ds$

where $\bg_white \int_{c}^{}\left [F . \frac{d\overrightarrow r}{ds} \right ]ds$ is a unit vector along tangent of curve PQ

$\bg_white \int_{c} \left [F . \frac{d\overrightarrow r}{ds} \right ]ds$

Surface Integral :

Surface integral of $\bg_white \overrightarrow F$ over S is given surface

$\iint_{s} \left (\overrightarrow F . \hat n \right) ds$
where
$\bg_white \hat {n} = \frac{grad\ f}{|grad\ f|}.dS = \frac{dx . dy}{\left((\hat n . k)\right)}$

Volume Integral :

Volume integral of over the volume V enclosed by a closed surface.

$\bg_white \ =\ \int \iint_{V} \overrightarrow F . dV$

Green's Theorem :

$\bg_white \oint _{C} (\phi dx + \psi dy) = \iint_{R}\left (\frac{\partial \psi}{\partial x} - \frac{\partial \phi}{\partial y}\right )dxdy$
where
$\bg_white \phi (x,y), \psi (x,y), \frac{\partial \phi}{\partial y},\frac{\partial \psi}{\partial x}$
are continuous function over a region R bounded by simple closed curve C in x-y plane.

Stroke's Theorem :

$\bg_white \oint \overrightarrow F . d\overrightarrow r = \iint_{S}\left (\bigtriangledown X \overrightarrow F\right ).\overrightarrow n dS \\\\ =\iint_{S}\left (\bigtriangledown X \overrightarrow F\right ).dS \\\\\\ where\\ \hat n = cos \alpha\ \hat i + cos \beta\ \hat j + + cos \gamma\ \hat k\\$

is unit external normal to any surface dS.

Gauss's Theorem of Divergence :

The surface integral of the normal component of a vector function $\bg_white \overrightarrow F$ taken around a closed surface S is equal to the integral of the divergence of $\bg_white \overrightarrow F$ taken over the volume V enclosed by the surface S.
$\bg_white \iint_{S}\overrightarrow F.\hat n .dS = \int \iint_{V} div \overrightarroe F dV$

Monday, October 5, 2009

GATE Mathematics : Linear Algebra

ONLINE TEST : GATE MATHS :- LINEAR ALGEBRA

Important Types Of Matrices :

1) Null/ Zero matrix : all elements are zero

2) Diagonal Matrix : square matrix whose all non-diagonal elements are zero.

3) Scalar matrix : diagonal matrix whose all diagonal elements are
equal to zero.

4) Symmetric matrix : In a Square matrix for all i and j , a_ij = a_ji

5) Skew Symmetric Matrix : A square matrix is called skew symmetric matrix if
i)for all i and j , a_ij = - a_ji
ii) All diagonal elements are zero.

6) Upper Triangular Matrix : A triangular matrix whose elements below the leading diagonal are zero .

7) Orthogonal Matrix : AA^T = I

8) Matrix A^θ : = (conjugate of A)^T

9) Unitary Matrix : A^θA = I

10) Hermitian Matrix : i) a_ij = conjugate of a_ji
ii) A = A^θ

11) Idempotent Matrix : A² = A

12) Periodic matrix : A^k+1 = A

13) Nilpotent Matrix : A^k = 0,k>0

14) Involuntary Matrix : A² = I

15) Adjoint of A Matrix : adj. A is the transpose of the matrix of co-factors of any matrix A.

16) Inverse Matrix : A^-1 = 1/|A| adj. A

** Rank of Matrix :

The rank of matrix is 'r' if

a) It has at least one non-zero minor of order 'r'.

b) every minor of 'A' of order higher than 'r' is zero.

i.e. Rank = No. of non-zero rows in upper triangular matrix.

Rank of augmented matrix A^ defining any given set of linear equations and coefficient matrix C decides type of solution:

1) Consistent Equations : Rank A^ = Rank C

i) Unique solution : Rank A^ = Rank C = n, n => No. of unknowns

ii) Infinite Solution : Rank A^ Rank C = m, m < n 2) Inconsistent Equations : Rank A^ != Rank C No Solution Possible.

Rank of Matrix and Matrix Dependency :

Vectors A1, A2, ..An are said to be dependent if :

1) all vectors are of same order

2) n scalars a1,a2, ..an (at least one non-zero) exist as

a1.A1 + a2.A2 + ...+an.An = 0

Otherwise they are linearly independent.

**Rank of matrix A is maximum no. of linearly independent row vectors of A or no. of linearly independent column vectors of A
Hence A and A^T has same rank..

** m vectors with n components each are linearly independent if if the matrix with these vectors as row vectors has rank m, but they are linearly dependent if that rank is less than m.

TERMS YOU SHOULD ALSO KNOW :

LINEAR SYSTEM, HOMOGENEOUS AND NON-HOMOGENEOUS SYSTEMS, STOCHASTIC MATRIX, TRIVIAL SOLUTION, GAUSS ELIMINATION, ROW EQUIVALENT SYSTEMS, ECHELON FORM, VECTOR SPACE, ROW SPACE, COLUMN SPACE, CRAMER'S RULE, MINORS AND CO-FACTORS, GAUSS-JORDAN ELIMINATION.

Tuesday, September 22, 2009

GATE ELECTRONICS AND COMMUNICATION SOLVED QUESTION PAPER 2006 SECTION 1

GATE electronics and communication solved question paper 2006 section 1.

Please Visit AllAboutGate.Tk

Tuesday, September 8, 2009

GATE ELECTRONICS AND COMMUNICATION SOLVED QUESTION PAPER 2009

Here it comes!
GATE EC - 2009 ,solved question paper. Second in this series. Don't forget to reply ! Coming soon - GATE EC - 2008 !

GATE ELECTRONICS AND COMMUNICATION SOLVED QUESTION PAPER 2009

Thursday, September 3, 2009

GATE ELECTRONICS AND COMMUNICATION SOLVED QUESTION PAPER 2007

Hi Friends

I am starting new section -AllAboutGate.Tk Section. This new website is all about GATE !Here you will find previous years GATE question papers-fully solved. There won't be any plain question papers but interactive GATE exam ..So solving paper is more of a fun than boring monotonous tests available on net.When your answer is wrong ,you will find explanation for correct answer on results page. Do comment on main site if you find any bugs. Right now I have started this section with GATE EC -2007 question paper..but I will add more papers soon....GATE 2009 paper is coming soon ..!

Sunday, October 25, 2009

Wednesday, October 21, 2009

Wednesday, October 14, 2009

Chain Rule :

Mean Value Theorem :

Indefinite Integrals :

Definite Integrals

Theorem of Integral Calculus :

Gamma Function :

Beta Function :

Euler's Theorem on Homogeneous Function:

Taylor's Series of Two Variables :

Maximum Value Theorem:

Minimum Value Theorem

Line Integral :

Surface Integral :

Volume Integral :

Green's Theorem :

Stroke's Theorem :

Gauss's Theorem of Divergence :

Monday, October 5, 2009

Important Types Of Matrices :

** Rank of Matrix :

Rank of Matrix and Matrix Dependency :

**TERMS YOU SHOULD ALSO KNOW : **

Tuesday, September 22, 2009

Tuesday, September 8, 2009

Thursday, September 3, 2009

TERMS YOU SHOULD ALSO KNOW :