Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

1 votes

1 answer

5961

What are the values of the sum?
$\sum_{j \in S} 1$ where S = {1, 3, 5, 7}. if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?

$\sum_{j \in S} 1$ where S = {1, 3, 5, 7}.if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?

SomnathKayal

663 views

SomnathKayal asked Mar 28, 2016

3 votes

2 answers

5962

if R1 is irreflexive and R2 is irreflexive then can R1 union R2 be reflexive ? true or false
if R1 is irreflexive and R2 is irreflexive then can R1$\cup$ R2 be reflexive ? true or false

if R1 is irreflexive and R2 is irreflexive then can R1$\cup$ R2 be reflexive ? true or false

saket nandan

3.1k views

saket nandan asked Mar 22, 2016

1 votes

1 answer

5963

No. of ways in which 2n white and 2n black balls can be arranged such that no consecutive n white balls are together

The number of ways in which $2n$ white and $2n$ black balls can be arranged such that no consecutive $n$ white balls are together, is${}^{2n+1}C_2 + {}^{4n}C_{2n}$${}^{2n...

sampad

2.9k views

sampad asked Mar 21, 2016

1 votes

2 answers

5964

In how many ways can 2n seats in a congress be divided among 3 parties ?
Problem: In how many ways can 2n seats in a congress be divided among 3 parties so that the coalition of any 2 parties will ensure them of majority? Answer: Total number of ways in which the seats can be ... add 3 with the final expression. This question is similar to this except the problem considering even number of seats.

Problem: In how many ways can 2n seats in a congress be divided among 3 parties so that the coalition of any 2 parties will ensure them of majority?Answer: Total number o...

SomnathKayal

654 views

SomnathKayal asked Mar 18, 2016

2 votes

0 answers

5965

Find the coefficient of x7 in expansion of (1+3x-2x3)10.
Find the coefficient of x7 in expansion of (1+3x-2x3)10. How to apply multinomial theorem to solve this types of problems?

Find the coefficient of x7 in expansion of (1+3x-2x3)10. How to apply multinomial theorem to solve this types of problems?

sampad

3.9k views

sampad asked Mar 15, 2016

0 votes

2 answers

5966

set of all equivalence class of set A of cardinality C

lokesh singh mahar

1.6k views

lokesh singh mahar asked Mar 9, 2016

1 votes

1 answer

5967

How many bit strings with length not exceeding n, where n is a positive integer, consist entirely of 1's ?

why do we count here empty string also , it has no 1's , so what's the reason for counting this ?

radha gogia

2.1k views

radha gogia asked Mar 6, 2016

1 votes

1 answer

5968

the binary relation S=∅ on set A={1,2,3} is transitive and symmetric

SHEETAL KAUSHIK

2.1k views

SHEETAL KAUSHIK asked Mar 3, 2016

1 votes

1 answer

5969

In how many ways can 5 chocolates be chosen from an unlimited number of Cadbury,Five-star, and Perk chocolates?

we have to choose five chocolates,say, C1, C2, C3, C4 and C5. Now for C1 we can choose among three kinds of chocolates. Since the supply of chocolates is infinite, for C2...

radha gogia

4.6k views

radha gogia asked Feb 25, 2016

0 votes

2 answers

5970

permutations
The number of ways in which 6 rings can be worn on the four fingers of one hand is: a. 360 b. 4^6 c. 6C4 d. 6^4

The number of ways in which 6 rings can be worn on the four fingers of one hand is:a. 360b. 4^6c. 6C4d. 6^4

Desert_Warrior

1.2k views

Desert_Warrior asked Feb 17, 2016

0 votes

3 answers

5971

Circular Permutation
A class is composed of 2 brothers and 6 other boys. In how many ways can all the boys be seated at a round table so that the two brothers are not seated together? a. 3000 b.3600 c. 2050 d. 2600

A class is composed of 2 brothers and 6 other boys. In how many ways can all the boys beseated at a round table so that the two brothers are not seated together?a. 3000b....

Desert_Warrior

3.1k views

Desert_Warrior asked Feb 17, 2016

92 votes

9 answers

5972

GATE CSE 2016 Set 1 | Question: 28
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.

A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)...

Sandeep Singh

21.6k views

Sandeep Singh asked Feb 12, 2016

67 votes

10 answers

5973

GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.

Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.

Sandeep Singh

29.3k views

Sandeep Singh asked Feb 12, 2016

57 votes

17 answers

5974

GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.

The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.

Sandeep Singh

25.9k views

Sandeep Singh asked Feb 12, 2016

74 votes

8 answers

5975

GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.

Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...

Sandeep Singh

13.0k views

Sandeep Singh asked Feb 12, 2016

45 votes

4 answers

5976

GATE CSE 2016 Set 1 | Question: 2
Let $a_n$ be the number of $n$-bit strings that do NOT contain two consecutive $1's$. Which one of the following is the recurrence relation for $a_n$? $a_n = a_{n-1}+ 2a_{n-2}$ $a_n = a_{n-1}+ a_{n-2}$ $a_n = 2a_{n-1}+ a_{n-2}$ $a_n = 2a_{n-1}+ 2a_{n-2}$

Let $a_n$ be the number of $n$-bit strings that do NOT contain two consecutive $1's$. Which one of the following is the recurrence relation for $a_n$?$a_n = a_{n-1}+ 2a_{...

Sandeep Singh

9.5k views

Sandeep Singh asked Feb 12, 2016

70 votes

6 answers

5977

GATE CSE 2016 Set 2 | Question: 27
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$

Which one of the following well-formed formulae in predicate calculus is NOT valid ?$(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee ...

Akash Kanase

16.9k views

Akash Kanase asked Feb 12, 2016

50 votes

8 answers

5978

GATE CSE 2016 Set 2 | Question: 26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.

A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions:$P:$ $R$ ...

Akash Kanase

14.7k views

Akash Kanase asked Feb 12, 2016

85 votes

8 answers

5979

GATE CSE 2016 Set 2 | Question: 28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.

Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. ...

Akash Kanase

16.6k views

Akash Kanase asked Feb 12, 2016

44 votes

10 answers

5980

GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.

The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.

Akash Kanase

17.9k views

Akash Kanase asked Feb 12, 2016

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