GATE Engineering Mathematics: Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) – Previous Year Questions
15 GATE previous year questions on Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) (Engineering Mathematics, Computer Science) with answers and explanations, from every paper.
- GATE 2017 CS Q57 – The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is .
- GATE 2016 CS Q12 – Let a n be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for a n?
- GATE 2016 CS Q36 – The coefficient of x12 in (x3 + x4 + x5 + x6 + )3 is .
- GATE 2016 CS Q37 – Consider the recurrence relation a 1 = 8, a n = 6n2 + 2n + a n-1. Let a 99 = K 104. The value of K is .
- GATE 2015 CS Q45 – Let a n represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a n?
- GATE 2018 CS Q11 – Which one of the following is a closed form expression for the generating function of the sequence \a n\, where a n=2n+3 for all n=0,1,2,?
- GATE 2019 CS Q15 – Let U=\1,2,,n\. Let A=\(x,X) x X,\ X U\. Consider the following two statements on A . I. A =n2n-1 II. A = k=1nk nk Which of the above statements…
- GATE 2026 CS (CS1) Q57 – Let G be an undirected graph, which is a path on 8 vertices. The number of matchings in G is . (answer in integer)
- GATE 2025 CS (CS1) Q30 – Let S be the set of all ternary strings defined over the alphabet \a,b,c\. Consider all strings in S that contain at least one occurrence of two…
- GATE 2023 CS Q15 – The Lucas sequence L n is defined by the recurrence relation: L n = L n-1 + L n-2, for n 3, with L 1 = 1 and L 2 = 3. Which one of the options given…
- GATE 2023 CS Q48 – Let U = \1, 2, , n\, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with A =…
- GATE 2022 CS Q32 – The number of arrangements of six identical balls in three identical bins is .
- GATE 2022 CS Q36 – Which one of the following is the closed form for the generating function of the sequence \a n\ n0 defined below? a n=casesn+1, & n is odd\\ 1, &…
- GATE 2021 CS Q29 – There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that: - The…
- GATE 2020 CS Q52 – 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…