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Recent questions tagged go2025-dm-2

4 votes
1 answer
2
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 2
Consider a set $A$ with $6$ elements. Let $N_1$ denote the number of bijective functions from $A$ to $A$ and let $N_2$ denote the number of onto (surjective) functions from $A$ to $A.$ $N_2 - N_1 = \_\_\_\_\_.$
Consider a set $A$ with $6$ elements. Let $N_1$ denote the number of bijective functions from $A$ to $A$ and let $N_2$ denote the number of onto (surjective) functions fr...
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7 votes
1 answer
5
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
6
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
7
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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2 votes
2 answers
8
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 8
How many bit strings of length $7$ contain more $0$’s than $1$’s? $93$ $84$ $64$ none of these
How many bit strings of length $7$ contain more $0$’s than $1$’s?$93$$84$$64$none of these
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3 votes
1 answer
10
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
14
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$$\begin{array}{|cl|cl|} \hline A. & 0,1,2,3,4,5,6,7,\ldots & P. & \frac{x(1+x)}...
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5 votes
1 answer
16
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 16
A board is formed by combining $100$ squares of same size, $10$ in each direction. The total number of squares (of all sizes) that can be formed from the resultant board is $\_\_\_\_$
A board is formed by combining $100$ squares of same size, $10$ in each direction. The total number of squares (of all sizes) that can be formed from the resultant board ...
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2 votes
2 answers
18
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 18
The number of positive integers less than $1000$ which are divisible by exactly one of $7$ or $11$ is $\_\_\_\_$
The number of positive integers less than $1000$ which are divisible by exactly one of $7$ or $11$ is $\_\_\_\_$
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1 votes
1 answer
22
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 22
The number of ways in which we can choose $3$ numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8,9\}$ so that more odd numbers are chosen than even is $\_\_\_\_\_$
The number of ways in which we can choose $3$ numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8,9\}$ so that more odd numbers are chosen than even is $\_\_\_\_\_$
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5 votes
2 answers
23
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 23
Which of the following is the generating function corresponding to the sequence $0,1,0,0,2,0,0,3,0,0,4,0,0,5, \dots $. $\frac{x^3}{(1-x)}$ $\frac{x}{(1-x)^2}$ $\frac{x}{(1-x^3)^2}$ $\frac{x}{1-x^3}$
Which of the following is the generating function corresponding to the sequence $0,1,0,0,2,0,0,3,0,0,4,0,0,5, \dots $.$\frac{x^3}{(1-x)}$$\frac{x}{(1-x)^2}$$\frac{x}{(1-x...
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7 votes
1 answer
25
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 25
The closed form solution for the $n^{th}$ term $(n > 1)$ of the sequence with generating function $\frac{9x}{1-2x}+ \frac{x}{1-x}$ is given by $1.2^n+1$ $2.9^{n-1} + 1$ $9.2^n + 1$ none of these
The closed form solution for the $n^{th}$ term $(n 1)$ of the sequence with generating function $\frac{9x}{1-2x}+ \frac{x}{1-x}$ is given by$1.2^n+1$$2.9^{n-1} + 1$$9.2^...
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8 votes
1 answer
28
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
29
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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6 votes
1 answer
30
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 30
Number of triangles that can be formed with vertices on a $3 \times 3$ grid of points is $\_\_\_\_$
Number of triangles that can be formed with vertices on a $3 \times 3$ grid of points is $\_\_\_\_$
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