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

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

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Most answered questions in Combinatory

2 votes
1 answer
451
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 4
Let $G(x)= \frac{1}{(1-x)} =\sum_{0}^{\infty}f(i)x^i$ where $|x|< 1$. $f(i)$ is $1$ $i$ $2i$ $i+1$
Let $G(x)= \frac{1}{(1-x)} =\sum_{0}^{\infty}f(i)x^i$ where $|x|< 1$. $f(i)$ is$1$$i$$2i$$i+1$
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7 votes
1 answer
452
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 5
The number of bit strings of length $6$ that do not contain “$1111$” as a substring is $\_\_\_\_$
The number of bit strings of length $6$ that do not contain “$1111$” as a substring is $\_\_\_\_$
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4 votes
1 answer
453
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 6
The number of positive integers less than $1000$ which are divisible by $7$ but not by $11$ is $\_\_\_\_$
The number of positive integers less than $1000$ which are divisible by $7$ but not by $11$ is $\_\_\_\_$
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4 votes
1 answer
454
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 7
How many $10$ digit numbers greater than $1987654321$ have no two digits same? $8 \times 9!$ $9 \times 9!$ $7 \times 9!$ None of the above
How many $10$ digit numbers greater than $1987654321$ have no two digits same?$8 \times 9!$$9 \times 9!$$7 \times 9!$None of the above
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3 votes
1 answer
456
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 10
Let $S_1 = \{1,2,3,\ldots,100\}$ and $S_2 = \{a,b,c,\ldots,z\}.$ Number of one-one (injective) functions from $S_2 \to S_1$ when $f(m) = 13$ is $\_\_\_$ $^{100}P_{25}$ $^{99}C_{25}$ $^{99}P_{25}$ $1$
Let $S_1 = \{1,2,3,\ldots,100\}$ and $S_2 = \{a,b,c,\ldots,z\}.$ Number of one-one (injective) functions from $S_2 \to S_1$ when $f(m) = 13$ is $\_\_\_$$^{100}P_{25}$$^{9...
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3 votes
1 answer
460
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 14
Match the sequences on the left with their corresponding generating functions on the right ... $A-P,B-Q,C-R,D-S$ $A-P,B-R,C-S,D-Q$ $A-Q,B-R,C-S,D-P$ None of the above
Match the sequences on the left with their corresponding generating functions on the right$$\begin{array}{|cl|cl|} \hline A. & 0,1,2,3,4,5,6,7,\ldots & P. & \frac{x(1+x)}...
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5 votes
1 answer
461
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 16
A board is formed by combining $100$ squares of same size, $10$ in each direction. The total number of squares (of all sizes) that can be formed from the resultant board is $\_\_\_\_$
A board is formed by combining $100$ squares of same size, $10$ in each direction. The total number of squares (of all sizes) that can be formed from the resultant board ...
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1 votes
1 answer
464
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 22
The number of ways in which we can choose $3$ numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8,9\}$ so that more odd numbers are chosen than even is $\_\_\_\_\_$
The number of ways in which we can choose $3$ numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8,9\}$ so that more odd numbers are chosen than even is $\_\_\_\_\_$
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7 votes
1 answer
466
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 25
The closed form solution for the $n^{th}$ term $(n > 1)$ of the sequence with generating function $\frac{9x}{1-2x}+ \frac{x}{1-x}$ is given by $1.2^n+1$ $2.9^{n-1} + 1$ $9.2^n + 1$ none of these
The closed form solution for the $n^{th}$ term $(n 1)$ of the sequence with generating function $\frac{9x}{1-2x}+ \frac{x}{1-x}$ is given by$1.2^n+1$$2.9^{n-1} + 1$$9.2^...
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2 votes
1 answer
467
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 26
In a college $10$ Servers are bought and they are to be distributed among $4$ laboratories such that each laboratory gets at least one server. The total number of ways in which this can be done is $\_\_\_$
In a college $10$ Servers are bought and they are to be distributed among $4$ laboratories such that each laboratory gets at least one server. The total number of ways in...
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3 votes
1 answer
468
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 27
What is the middle term in the expansion of $\left(\frac{y\sqrt{x}}{2} - \frac{2}{x\sqrt{y}}\right)^{12}$. $924\left(\frac{y}{x}\right)^6$ $924\left(\frac{y}{x}\right)^3$ $2^{10}\left(\frac{y}{x}\right)^6$ None of the above
What is the middle term in the expansion of $$\left(\frac{y\sqrt{x}}{2} - \frac{2}{x\sqrt{y}}\right)^{12}$$.$924\left(\frac{y}{x}\right)^6$$924\left(\frac{y}{x}\right)^3$...
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8 votes
1 answer
469
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 28
The $n^{th}$ term of the sequence generated by the function $\frac{2}{(1-x)^2} \cdot \frac{x}{1-x-x^2}$ is represented as $a_n$. The value of $a_6$ is$\_\_\_\_\_\_$.
The $n^{th}$ term of the sequence generated by the function $\frac{2}{(1-x)^2} \cdot \frac{x}{1-x-x^2}$ is represented as $a_n$. The value of $a_6$ is$\_\_\_\_\_\_$.
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10 votes
1 answer
470
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 29
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., 3689 is one). The total number of $6$ digit increasing numbers is _______
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., 3689 is one). The total number of $6$ digit increasing numbers is ______...
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