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Discrete Mathem...

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  • Question 1
    2 / -0.33

    What is the solution of the recurrence relation?

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

  • Question 2
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    The following propositional statement is

    [(p → r) ∧ (q → r)] → [(p ∨ q) → r]

  • Question 3
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    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?

  • Question 4
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    If \(f\left( z \right) = \frac{1}{{{{\left( {1 - z} \right)}^2}}}\) then the coefficient of z13 is _____

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

  • Question 6
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    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

  • Question 7
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    Consider a 4-ary tree T consisting of 17 vertices. What is the sum of the degree of T?

  • Question 8
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    What is the contrapositive of the following assertion?

    If your GATE score is 80+ in CS, then you’ll get a single digit rank.

  • Question 9
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    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?

  • Question 10
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    The number of edges in a regular graph of degree d and n vertices is

  • Question 11
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    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?

  • Question 12
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    Which of the following statement for the connected graph is/are CORRECT?

  • Question 13
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     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)

  • Question 14
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    The following is the incomplete operation Cayley table of a 4- element group in which e is the identity element of group.

    *

    p

    q

    e

    s

    p

    q

    r

    p

    e

    q

     

     

     

     

    e

    p

    q

    e

    s

    s

     

     

     

     


    The last row of the table is 

  • Question 15
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    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?

  • Question 16
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    The statement A → B is logically equivalent to which of the following below?

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

  • Question 17
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    Find the generating function for the sequence given recursively by

    an - 2an-1 - 4an-2 = 0 with a0 = 2 and a1 = 5?

  • Question 18
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    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 = _____.

  • Question 19
    2 / -0.33

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

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