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GATE CSE

Combinatorics

Discrete Mathematics

Previous Years Questions

Marks 1

More
The number of arrangements of six identical balls in three identical bins is ___________.
GATE CSE 2022
The number of $$4$$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using ...
GATE CSE 2015 Set 3
The recurrence relation capturing the optional execution time of the Towers of Hanoi problem with $$n$$ discs is
GATE CSE 2012
In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures ...
GATE CSE 2004
$$m$$ identical balls are to be placed in $$n$$ distinct bags. You are given that $$m \ge kn$$, where $$k$$ is a natural...
GATE CSE 2003
$$n$$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, ...
GATE CSE 2003
Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. How many distinct pairs of sequence, $$B$$...
GATE CSE 2003
The minimum number of colors required to color the vertices of a cycle with $$n$$ nodes in such a way that no two adjace...
GATE CSE 2002
The solution to the recurrence equation $$T\left( {{2^k}} \right)$$ $$ = 3T\left( {{2^{k - 1}}} \right) + 1$$, $$T\lef...
GATE CSE 2000
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are ...
GATE CSE 2000
The number of binary strings of $$n$$ zeros and $$k$$ ones such that no two ones are adjacent is:
GATE CSE 1999

Marks 2

More
There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned ...
GATE CSE 2021 Set 1
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two ...
GATE CSE 2020
The coefficient of $${x^{12}}$$ in $${\left( {{x^3} + {x^4} + {x^5} + {x^6} + ...} \right)^3}\,\,\,\,\,\,$$ is _________...
GATE CSE 2016 Set 1
The number of distinct positive integral factors of 2014 is _______ .
GATE CSE 2014 Set 2
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....
GATE CSE 2014 Set 1
There are 5 bags labeled 1 to 5. All the coins in given bag have the same weight. Some bags have coins of weight 10 gm, ...
GATE CSE 2014 Set 1
When $$n = {2^{2k}}$$ for some $$k \ge 0$$, the recurrence relation $$$T\left( n \right) = \sqrt 2 T\left( {n/2} \right...
GATE CSE 2008
In how many ways can $$b$$ blue balls and $$r$$ red balls be distributed in $$n$$ distinct boxes?
GATE CSE 2008
The exponent of $$11$$ in the prime factorization of $$300!$$ is
GATE CSE 2008
Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$. Which of the foll...
GATE CSE 2008
Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$. The value of $${x_...
GATE CSE 2008
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit...
GATE CSE 2007
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit...
GATE CSE 2007
What is the cardinality of the set of integers $$X$$ defined below? $$X = $$ {$$n\left| {1 \le n \le 123,\,\,\,\,\,n} \r...
GATE CSE 2006
For each elements in a set of size $$2n$$, an unbiased coin in tossed. The $$2n$$ coin tosses are independent. An elemen...
GATE CSE 2006
Consider the polynomial $$P\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3},$$ where $${a_i} \ne 0,\forall i...
GATE CSE 2006
Let $$n = {p^2}q,$$ where $$p$$ and $$q$$ are distinct prime numbers. How many numbers $$m$$ satisfy $$1 \le m \le n$$ a...
GATE CSE 2005
Let $$G\left( x \right) = 1/\left( {1 - x} \right)2 = \sum\limits_{i = 0}^\infty {g\left( i \right)\,{x^1}} \,\,\,,$$ ...
GATE CSE 2005
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two p...
GATE CSE 2005
The recurrence equation $$\,\,\,\,\,\,\,T\left( 1 \right) = 1$$ $$\,\,\,\,\,\,T\left( n \right) = 2T\left( {n - 1} \rig...
GATE CSE 2004
In how many ways can we distribute 5 distinct balls, $${B_1},{B_2},......,{B_5}$$ in 5 distinct cells, $${C_1},{C_2},......
GATE CSE 2004
Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints wi...
GATE CSE 2004
How many 4 digit even numbers have all 4 digits distinct?
GATE CSE 2001
Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers a...
GATE CSE 1999
Solve the following recurrence relation $$\,\,\,\,\,\,\,{x_n} = 2{x_{n - 1}} - 1\,\,n > 1$$ $$\,\,\,\,\,\,\,{x_1} = ...
GATE CSE 1998
In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak...
GATE CSE 1998
The recurrence relation $$\,\,\,\,\,$$ $$T\left( 1 \right) = 2$$ $$T\left( n \right) = 3T\left( {{n \over 4}} \right)...
GATE CSE 1996
The number of substrings (of all length inclusive) that can be formed from a character string of length $$n$$ is
GATE CSE 1994
How many sub strings can be formed from a character string of length $$n$$?
GATE CSE 1989
Solve the recurrence equations: $$\,\,\,\,\,\,\,\,\,\,T\left( n \right) = \left( {{n \over 2}} \right) + 1$$ $$\,\,\,\,...
GATE CSE 1988
(a) Solve the recurrence equations $$\,\,\,\,\,\,\,\,\,T\left( n \right) = T\left( {n - 1} \right) + n$$ $$\,\,\,\,\,\,...
GATE CSE 1987

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