Thursday, 1 February 2018

Normal Forms

GATE NOTES
Normal Forms in DBMS

Steps to find Normal Forms-

  1. Find Candidates key
  2. Find Prime attributes and Non prime attributes
  3. Check for Normal Forms, from starting from 1NF to higher order.
1NF- Relational DBMS does not allow multi-valued or composite attribute.
2NF- Relational DBMS does not allow partial dependency.
3NF- Either LHS of an FD should be super key or RHS should be prime attribute.

Partial Dependency - Partial dependency means that a non-prime attribute is functionally dependent on part of a candidate key.
Prime attribute - All candidate keys.
Non prime attribute - All non candidate keys.

Tuesday, 30 January 2018

L-HOSPITAL RULE





GATE NOTES,
L-Hospital Rule



Monday, 29 January 2018

Static Single Assignment

GATE NOTES
Static Single Assignment

According to Static Single Assignment

  • A variable cannot be used more than once in the LHS
  • A variable should be initialised atmost once.

Sunday, 28 January 2018





GATE NOTES
PROPOSITIONAL LOGIC

Saturday, 27 January 2018

Birthday Attack

GATE NOTES
BIRTHDAY ATTACK
  • Birthday attack work only with random messages and not with chosen messages.

Tuesday, 23 January 2018

GATE Notes,
Probability Formulas

Probability Range
0 ≤ P(A) ≤ 1

Rule of Complementary Events
P(Ac) + P(A) = 1

Rule of Addition
P(AB) = P(A) + P(B) - P(AB)

Disjoint Events
Events A and B are disjoint iff
P(AB) = 0

Independent Events
Events A and B are independent iff
P(AB) = P(A) P(B)

Conditional Probability

P(A | B) = P(AB) / P(B)

Friday, 12 January 2018

CS GATE 2014
If the matrix A is such that 
then the determinant of A is equal to

(A) 0 
(B) 1 
(C) 2
(D) 3

Sol.

Thursday, 11 January 2018

GATE 2018 SYLLABI
LU Decomposition ?

[A] = [L][U]






L- Lower triangular matrix.
U- Upper triangular matrix.

For example-

GATE 2018 SYLLABI
Unique, Infinite, Many, Consistent, Inconsistent Solutions ?

1) a₁x + b₁y = c₁
2) a₂x + b₂y = c₂


If
a₁/a₂ ≠ b₁/b₂ 
Than, its called unique solution.it means intercepting lines.Its also called consistent solution.

If
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Than its called no solution. It means parallel lines. Its also called inconsistent solution.

If
a₁/a₂ = b₁/b₂ = c₁/c₂
Than, its called infinite many soluiton. It means coincident lines.Its also called consistent solution.

For example-


Wednesday, 10 January 2018

GATE 2005
What are the eigenvalues of the following 2 × 2 matrix? 
SOL.



Matrix multiplication?






Determinant calculation ?


Eigen Values and Characteristics roots ?

To find Eigen values use, | A - λI | = 0
For characteristics roots, ( A - λI )X = 0
When represents characteristics roots in matrix they called Eigen vectors.

If A is an n × n matrix, then the sum of the n eigenvalues of A is the trace of A and the product of the n eigenvalues is the determinant of A.

Eigenvalues of a Matrix and its Transpose are same.

Monday, 20 November 2017

GATE 02

GATE 2016, SET I, 1 Mark

A processor can support a maximum of 4GB, where the memory is word-addressable (a word consists of two bytes). The size of address bus of the processor is at least _________bits.

Sol.
First we will convert 4GB in to Bytes
4GB = 230 X 4 = 230 X 22 = 232 Bytes
Given in problem, a word consist 2 Bytes,
So, no of words = 232 / 2 = 231
The size of address bus of the processor is at least 31 bits.

GATE 01

GATE 2013

R (ABCDEFGH)
CH → G
A → BC
B → CFH
E → A
F → EG

Find the number of candidate keys?

Sol. Which one is not at right side.
That is D.
so,
[D]+ →  D
Its not candidate key., because not all keys determined in it.
[DA]+ →  DABCFHEG
Its candidate key because all keys are determined in it.
[DB]+ →  ABCFHEGA
Its candidate key because all keys are determined in it.
[DC]+ →  DC
Its not candidate key., because not all keys determined in it.
[DE]+ →  DEABCFHG
Its candidate key because all keys are determined in it.
[DF]+ → DFEGABCH   
Its candidate key because all keys are determined in it.
[DCH]+ →  DCHG
Its not candidate key., because not all keys determined in it.

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