Engineering Mathematics · Combinatorics
Official IIT answer key · IIT Kharagpur · Audited Aug 2026
GATE CSE 2014 Set 1 Q49 · NAT · 2 marks
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Topic notes
GATE evaluates Generating Functions by testing the candidate's ability to find closed-form representations of ordinary generating functions (OGFs) for piecewise or parity-dependent sequences. Questions require decomposing sequences linearly and applying operations like substitution (e.g., x2) and differentiation to handle polynomial coefficients. These items test analytical fluency with infinite series and discrete mathematics manipulations.
Full Combinatorics guide →A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-pennants is \(1)\, the set of all possible 2-pennants is \(2), (1,1)\and the set of all 3-pennants is \(2,1), (1,1,1), (1,2)\. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10-pennants is …
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