GATE EC PRACTICE TEST : ANALOG CIRCUITS : PART III :- BJT/FET

Hola !!!
This is the third test in 'analog circuits' practice tests series. All MCQs are BJT/FET numerical based with figures and elaborate explanation. Main point covered is FET and BJT small signal analysis.Hope you like this one. Now remaining last test in this series will be based on Linear circuits and power amplifiers.As it is not possible to include each and every point in the syllabus,I have taken only important points for tests. In the last post on this topic I will highlight the points which I missed out during this test series.






--->>>---C-L-C-K-H-E-R-E--->>>---GATE EC PRACTICE TEST : ANALOG CIRCUITS : PART - III - BJT/FET --->>>--->>>

GATE EC PRACTICE TEST : ANALOG CIRCUITS PART - II

The second in this series. I have tried to include some figure based numerical problems and common data or linked answer type questions. I'll add one more test on this topic containing linear circuits based questions. But still I think BJT and FET part is not covered completely by any of the tests so will add one more test solely belonging to these three terminal devices.

Go Here To Give Online Test :


-->>>-C-L-I-C-K->>>-H-E-R-E->>> GATE EC PRACTICE TEST : ANALOG CIRCUITS - PART - II

GATE EC PRACTICE TEST : ANALOG CIRCUITS - PART - I

Analog Circuits is the most important topic as far as GATE scoring is considered. It is the core of electronics engineering field . Most of the numerical questions and linked answer questions in GATE EC paper come from this subject and the questions on frequency responses of amplifiers, cut-off frequencies, FET parameters, transistor biasing are most common. I am starting series of tests on this topic. First test consists only simple theoretical concepts and few direct formula based numericals.


Please do comment here if you like/dislike. Your feedback is appreciated and is valuable. I will try my best to post tests on daily basis,so check blog frequently if you haven't subscribed.







GATE EC PRACTICE TEST : ANALOG CIRCUITS - I

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

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)

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,

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

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


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


then

Theorem of Integral Calculus :

Gamma Function :

Beta Function :

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

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 is a vector function.
Then Line Integral of along any given curve DC will be



where is a unit vector along tangent of curve PQ

Surface Integral :

Surface integral of over S is given surface



where

Volume Integral :

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

Green's Theorem :

where

are continuous function over a region R bounded by simple closed curve C in x-y plane.

Stroke's Theorem :

is unit external normal to any surface dS.

Gauss's Theorem of Divergence :

The surface integral of the normal component of a vector function taken around a closed surface S is equal to the integral of the divergence of taken over the volume V enclosed by the surface S.

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.