Register

Web Page

Syllabus: Combinatorics: Counting, Recurrence relations, Generating functions.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&1&0&0&2&1&0&0&1&0&0&0.6&2
\\\hline\textbf{2 Marks Count} & 2 &0&1&1&0&1&0&1&2&1&0&0.9&2
\\\hline\textbf{Total Marks} & 5 &1&2&2&2&3&0&2&5&2&0&2.4&5\\\hline
\end{array}}}$$

Filter

Most answered questions in Combinatory

1 votes
3 answers
92
Generating Function
What will be solution of this function for coefficient of $x^{100}$? $\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$
What will be solution of this function for coefficient of $x^{100}$?$$\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$$
User Avatar
0 votes
3 answers
94
Combinatorics
A company hires 11 new employees, each of whom is to be assigned to one of 4 subdivisions. Each subdivision will get at least one new employee. In how many ways can these assignments be made?
A company hires 11 new employees, each of whom is to be assigned to one of 4 subdivisions. Each subdivision will get at least one new employee.In how many ways can these ...
User Avatar
0 votes
3 answers
95
Self Doubt
How to evaluate this quickly? $\large\sum^{20}_{r=0}(-1)^r\binom{r+2}{r}\\OR\\\large\sum^{20}_{r=0}(-1)^r(r+2)(r+1)$
How to evaluate this quickly?$\large\sum^{20}_{r=0}(-1)^r\binom{r+2}{r}\\OR\\\large\sum^{20}_{r=0}(-1)^r(r+2)(r+1)$
User Avatar
1 votes
3 answers
96
ISI2018-MMA-5
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is$3$$33$$63$$93$
User Avatar
1 votes
3 answers
98
Kenneth Rosen Edition 6th Exercise 5.5 Example 10 (Page No. 377)
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
User Avatar
0 votes
3 answers
99
Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
User Avatar
3 votes
3 answers
101
KENETH ROSEN
How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and the same right neighbor? ANSWER IS 6 OR 3 .????
How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and ...
User Avatar
0 votes
3 answers
102
Permutations and combinations
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
User Avatar
1 votes
3 answers
104
Discrete maths
Number of ways to distribute 6 distinct balls into 3 distinct boxes,such that each box contains at least 1 ball?
Number of ways to distribute 6 distinct balls into 3 distinct boxes,such that each box contains at least 1 ball?
User Avatar
0 votes
3 answers
105
NET nov-17 paper-2 Q8
Let P and Q be two propositions , ~(P<->Q) is equivalent to : a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P
Let P and Q be two propositions , ~(P<->Q) is equivalent to :a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P
User Avatar
2 votes
3 answers
106
P and C doubt
Given a 4 *4 grid points , how many Triangles with vertices on the grid can be formed?
Given a 4 *4 grid points , how many Triangles with vertices on the grid can be formed?
User Avatar
1 votes
3 answers
107
UPSC prelim test
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking atleast one ball of each colour? a) 15 b) 16 c) 17 d)18
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without repla...
User Avatar
2 votes
3 answers
108
Permutations
How many different words of 3 length can be formed from a,e,i,o,u containing a,e ?
How many different words of 3 length can be formed from a,e,i,o,u containing a,e ?
User Avatar
Page: