Discrete Mathem...

What is the solution of the recurrence relation?

\({a_n} = 8{a_n}_{ - 1} - 16{a_n}_{ - 2}\) ? 

The following propositional statement is

Let f: Z -> N be defined by 

\(f\left( x \right) = \;\left\{ {\begin{array}{*{20}{c}} {4x - 1,\;\;if\;x > 0} \\ { - 4x,\;if\;x \leqslant 0} \end{array}} \right.\)

Which of the following is true?

If \(f\left( z \right) = \frac{1}{{{{\left( {1 - z} \right)}^2}}}\) then the coefficient of z13 is _____

Which of the following statement is false about the given set G = {1, 3, 5, 7} with respect to ⊗₈ (Multiplication modulo 8)?

If f(x) = \(\frac{{3{\rm{x\;}} + {\rm{\;}}2}}{{4{\rm{x\;}}-{\rm{\;}}1}}\) and g(x) = \(\frac{{{\rm{x\;}} + {\rm{\;}}2}}{{4{\rm{x}} - {\rm{\;}}3}}\) then

I. fog(x) = 2x

II. gof(x) = x

Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?

What is the contrapositive of the following assertion?

The minimum number of edges and vertices required to form 12 faces whose minimum degree is 4, in a simple connected planar graph are x and y. Find x + y?

The number of edges in a regular graph of degree d and n vertices is

Find the total number of relations which is neither reflexive nor irreflexive on a set A where A = {a, b, c, d} and 1K = 1024?

Which of the following statement for the connected graph is/are CORRECT?

 Let A and B denote the sets containing 3 and 25 distinct objects respectively and G denote the set of all possible functions defined from set A to set B. Let g be randomly selected function from G. What is the probability of g being one-to-one is _____. (answer upto 2 decimal places)

The following is the incomplete operation Cayley table of a 4- element group in which e is the identity element of group.

The last row of the table is 

Consider graph H(V, E) where v ϵ vertices and e ϵ edges. H is a complete undirected graph on 7 vertices where each vertices of H are labeled. What is the number of distinct cycles of length 4 in H?

The statement A → B is logically equivalent to which of the following below?

Assume NOT is having higher precedence then ∨ and ∧ operator.

Find the generating function for the sequence given recursively by

Let G be a graph with 100! vertices, with each vertex labelled by a distinct permutation of the numbers 1, 2, … , 100. There is an edge between vertices 𝑢 and 𝑣 if and only if the label of 𝑢 can be obtained by swapping two adjacent numbers in the label of 𝑣. Let 𝑦 denote the degree of a vertex in G, and 𝑧 denote the number of connected components in G.

Then, 𝑦 + 10𝑧 = _____.

 Which of the below-given statements is/are false?