Matrices
  • Idempotent Matrix : For a matrix A , if we get A2 = A , then it is an idempotent matrix.
  • Nilpotent Matrix : For a matrix A, if at some m we get Am = 0, then it is called nilpotent matrix, and smallest value of m at which this condition is satisfied is called order of matrix.
  • Involutory Matrix : For a matrix A , if we get A2 = I , then it is called involutory matrix.
  • Singular Matrix : For a matrix A, if det(A) is zero, then it is called singular matrix.
  • Non- Singular Matrix: For a matrix A , if det(A) is non-zero , then it is called non - singular matrix.
  • Symmetric matrix : For a matrix , if AT = A , then it is symmetric matrix.
  • Skew- Symmetric matrix : For a matrix , if AT = -A , then it is skew - symmetric matrix.
  • Sum of Symmetric and skew symmetric matrix is twice the matrix.

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Petersan Graph
  • Petersan graph is a graph with 10 vertices and 15 edges.
  • It is a non-planar graph.
  • It has got hamiltonian path but not hamiltonain cycle.
  • It has got chromatic number 3.

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set2018 @setgate 29 Aug 2017 06:01 pm

@shivani 

pls explain point 3 .what are the condition for checking hamilton path

Akshay Saxena @akshay0612 30 Aug 2017 10:22 am

start from a vertex and you can trace each vertex exactly once without repeating vertices but you cant reach to the starting vertex without repeating try it.

Habib Mohammad Khan @habibkhan 29 Aug 2017 07:40 pm

One more point that can be added is this graph contains K5 and its isomorphic image as well..

Mathematical Logic : Rules of Inference
  • Precedence of logical operators is as follows:
    ¬  > ∧  >  ∨   > →  >  ↔
    where, ¬  , ∧  ,  ∨  is left associative and → ,  ↔ is right associative.
    Example: P →Q →R can be wriiten as  (P →(Q →R))
  • Following are the rules of inference:
  1. Modus Ponens: 
    P
    P
    ________
    Q
    ________
  2. Modus Tollens:
    ¬Q
    P->Q
    ________
    ¬P
    ________
  3. Disjunctive Syllolgism:
    P∨Q
    ¬P
    ________
    Q
    ________
  4. Constructive Dilemma:
    (PQ ) ∧ (RS )
    (P∨R )
    ________
    Q∨S
    ________
  5. Destructive Dilemma:
    (PQ ) ∧ (RS )
    (¬Q∨¬S)
    ________
    ¬P∨¬R
    ________
  6. Disjunctive Syllolgism:
    P∨Q
    ¬P
    ________
    Q
    ________

Example:
If child studies , mom will not scould
Mom scoulded
Inference: Child did not study.
Ans. p =  child studies
q = Mom scould
p->~q
q
_____
~p          ///using Modus Tollens
_____
~p means child did not study.
Thus , given inference is true.

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Mathematics

Following are the topics to be covered in the mathematics section:

  • Linear Algebra
  • Calculus
  • Combinatory
  • Probability
  • Numerical Methods
  • Graph Theory
  • Set Theory & Algebra
  • Mathematical Logic

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