Discrete mathematics PYQ GATE QUIZ

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Question 1

Which of the following graphs is isomorphic to 

graphThoery2012

  • A

  • B

  • C

  • D

Question 2

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” 

 

  • A

  • B

  • C

  • D

Question 3

Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

  • 360
     

  • 45
     

  • 30
     

  • 15
     

Question 4

How many onto (or surjective) functions are there from an n-element (n >= 2) set to a 2-element set?
 

  • 2(2n - 2)
     

  • 2n - 2
     

  • 2n - 1
     

  • 2n
     

Question 5

The bisection method is applied to compute a zero of the function f(x) = x4 – x3 – x2 – 4 in the 
interval [1,9]. The method converges to a solution after ––––– iterations
 

  • 7
     

  • 5
     

  • 3
     

  • 1
     

Question 6

Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

  • 6
     

  • 5
     

  • 4
     

  • 3
     

Question 7

The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ________ .

  • 12

  • 10

  • 8

  • 15

Question 8

Let an represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for an?

  • an–2 + an–1 + 2n–2

  • an–2 + 2an–1 + 2n–2

  • 2an–2 + an–1 + 2n–2

  • 2an–2 + 2an–1 + 2n–2

Question 9

Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G = (V,E) with V divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?

  • Both DHAM3 and SHAM3 are NP-hard

  • SHAM3 is NP-hard, but DHAM3 is not

  • DHAM3 is NP-hard, but SHAM3 is not

  • Neither DHAM3 nor SHAM3 is NP-hard

Question 10

Consider the following two problems on undirected graphs 

α : Given G(V, E), does G have an independent set of size | V | - 4?
β : Given G(V, E), does G have an independent set of size 5?

Which one of the following is TRUE?

  • α is in P and β is NP-complete

  • α is NP-complete and β is in P

  • Both α and β are NP-complete

  • Both α and β are in P

There are 206 questions to complete.

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