Discrete mathematics PYQ GATE QUIZ (original) (raw)

Which of the following graphs is isomorphic to

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

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

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

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

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

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 ________ .

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

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

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

There are 206 questions to complete.

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