Recent questions and answers in Engineering Mathematics

+14 votes

5 answers

1

TIFR2013-A-9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above.

answered 27 minutes ago in Combinatory by Verma Ashish Loyal (9.1k points) | 798 views

0 votes

2 answers

2

UGC NET NOV 2017 PAPER III Q-59
59. Consider the following two well-formed formulas in prepositional logic. F1 : P ⇒ ¬ P F2 : (P ⇒ ¬ P) ∨ (¬ P ⇒ P) Which of the following statements is correct ? (1) F1 is Satisfiable, F2 is valid (2) F1 is unsatisfiable, F2 is Satisfiable (3) F1 is unsatisfiable, F2 is valid (4) F1 and F2 both are Satisfiable

answered 35 minutes ago in Discrete Mathematics by GoalSet1 (97 points) | 581 views

0 votes

2 answers

3

UGC NET NOV 2017 PAPER III Q-58
58. “If X, then Y unless Z” is represented by which of the following formulae in propositional logic ? (1) (X ∧ Y) → ¬ Z (2) (X ∧ ¬ Z) → Y (3) X → (Y ∧ ¬ Z) (4) Y → (X ∧ ¬ Z)

answered 39 minutes ago in Discrete Mathematics by GoalSet1 (97 points) | 428 views

+19 votes

4 answers

4

GATE2000-5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?

answered 16 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 1.4k views

+4 votes

7 answers

5

TIFR2018-B-1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$

answered 21 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 377 views

+2 votes

6 answers

6

GATE2019-21
The value of $3^{51} \text{ mod } 5$ is _____

answered 22 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 2.7k views

+22 votes

3 answers

7

GATE2000-2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having 1 equivalence class $R$ is an equivalence relation having 2 equivalence classes $R$ is an equivalence relation having 3 equivalence classes

answered 1 day ago in Set Theory & Algebra by MRINMOY_HALDER Active (1.7k points) | 2.7k views

+26 votes

6 answers

8

GATE2014-2-51
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.

answered 1 day ago in Graph Theory by King Suleiman Junior (629 points) | 3.6k views

+1 vote

2 answers

9

Continuity and Differentiability
If the function f(x) =[(x-2)3 /a] sin(x-2) + acos(x-2), [.] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘a’ range: (A) a ϵ (-∞,∞) (B) a ϵ [64, ∞) (C) a ϵ [128, ∞) (D) Not defined

answered 1 day ago in Calculus by moharanaguruprasad (11 points) | 319 views

+1 vote

1 answer

10

set theory

answered 2 days ago in Set Theory & Algebra by Debadrita Talapatra (11 points) | 48 views

+25 votes

3 answers

11

GATE2014-3-1
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.

answered 6 days ago in Mathematical Logic by sohailkhan (47 points) | 2.4k views

+9 votes

4 answers

12

TIFR2012-A-20
There are $1000$ balls in a bag, of which $900$ are black and $100$ are white. I randomly draw $100$ balls from the bag. What is the probability that the $101$st ball will be black? $9/10$ More than $9/10$ but less than $1$. Less than $9/10$ but more than $0$. $0$ $1$

answered 6 days ago in Probability by !KARAN Active (1.8k points) | 629 views

+34 votes

5 answers

13

GATE2005-44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$

answered Aug 15 in Combinatory by JashanArora (93 points) | 3.9k views

+25 votes

4 answers

14

GATE2009-22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators

answered Aug 9 in Set Theory & Algebra by spike500 (29 points) | 1.8k views

0 votes

1 answer

15

recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N-1) - T(N-2) B)T(N) = T(N-1) + T(N-2) C)T(N) = N+1 D) None of these

answered Aug 8 in Mathematical Logic by Rohit Suryanarayan (15 points) | 439 views

+2 votes

1 answer

16

ISI MTECH CS 2019 INTERVIEW question
As due to rain, the match between the teams in ICC world cup got canceled , So lets the total team be 10, exclude semi finals and finals , consider only league match, What is the total number of matches that played between the teams ... many ways those n matches can be conducted ? Source : https://gateoverflow.in/blog/8548/isi-mtech-cs-2019-interview-experience

answered Aug 8 in Combinatory by Shaik Masthan Veteran (61.9k points) | 74 views

+52 votes

4 answers

17

GATE2003-33
Consider the following formula and its two interpretations $I_1$ and $I_2$. $\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]$ $I_1$ : Domain: the set of ... , $I_1$ does not Neither $I_1$ nor $I_2$ satisfies $\alpha$ Both $I_1$ and $I_2$ satisfies $\alpha$

answered Aug 6 in Mathematical Logic by MRINMOY_HALDER Active (1.7k points) | 4k views

+1 vote

2 answers

18

Graph Connectivity
Consider the given statements S1: In a simple graph G with 6 vertices, if degree of each vertex is 2, then Euler circuit exists in G. S2:In a simple graph G, if degree of each vertex is 3 then the graph G is connected. Which of the following is/are true?

answered Aug 5 in Graph Theory by IamDRD (11 points) | 162 views

+15 votes

5 answers

19

GATE2005-IT-3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}$ $-1$ $0$ $1$ $2$

answered Aug 5 in Linear Algebra by Satbir Boss (17.2k points) | 1.8k views

+1 vote

2 answers

20

#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edge-disjoint Hamiltonian cycles in $K_7$ is $3$ (b) If $G$ is a simple graph with $6$ vertices and the degree of each vertex is at least $3$, then the Hamiltonian cycle exists in ... simple graph with $5$ vertices and $7$ edges, then the Hamiltonian cycle exists in $G$ Please help me understand all the options.

answered Aug 1 in Graph Theory by Raghava45 (333 points) | 65 views

+1 vote

3 answers

21

UGCNET-June2015-II-5
Consider a Hamiltonian Graph(G) with no loops and parallel edges. Which of the following is true with respect to this graph (G)? deg (v) $\geq$ n/2 for each vertex of G $\mid E(G) \mid \geq $1/2 (n-1)(n-2)+2 edges deg(v) + deg(w) $\geq$ n fr every v and $\omega$ not connected by an edge a and b b and c a and c a, b, and c

answered Aug 1 in Graph Theory by tripu (11 points) | 1.9k views

+9 votes

3 answers

22

GATE2002-1.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$

answered Jul 31 in Linear Algebra by thambu (11 points) | 831 views

0 votes

1 answer

23

Probability - Gravner-49.c
You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enough to accommodate any number of balls.) (c) What is the probability that each urn contains all three colors?

answered Jul 31 in Probability by blackcloud (79 points) | 20 views

0 votes

1 answer

24

MADE EASY
The Necessary condition to diagonalize a matrix is that A) ITS all eigen values should be distdist B) its eigen vectors should be indeindepent C) its eigen values should be real D) matrix is non singular

answered Jul 30 in Linear Algebra by Jyotish Ranjan (11 points) | 51 views

+1 vote

1 answer

25

UGCNET-June-2019-II-69
Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a real-valued function $f:V \times V \rightarrow R$: $P_1$: For all $u, v, \in V, \: f(u,v)=-f(v,u)$ $P_2$: $\underset{v \in V}{\Sigma} f(u,v)=0$ for all $u \in V$ Which one of the following is/are correct? Only $P_1$ Only $P_2$ Both $P_1$ and $P_2$ Neither $P_1$ nor $P_2$

answered Jul 29 in Graph Theory by abhinav kumar (17 points) | 31 views

+2 votes

3 answers

26

ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple non-empty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two non-empty and non-overlapping subsets $S$ and $T$. Which of the following is true? There are at least two edges that ... $S$ and one end point in $T$ There are exactly one edge that have one end point in $S$ and one end point in $T$

answered Jul 26 in Graph Theory by gvjha3 (11 points) | 95 views

+11 votes

13 answers

27

TIFR2012-A-1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What probability should Anthony ... $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above

answered Jul 25 in Probability by Arghya Mukherjee (17 points) | 1.5k views

0 votes

1 answer

28

Gate 2002 - ME
Which of the following functions is not differentiable in the domain $[-1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x-1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,-x)$

answered Jul 24 in Calculus by Arif_Faizan (35 points) | 64 views

0 votes

1 answer

29

ISI2018-MMA-28
Consider the following functions $f(x)=\left\{\begin{matrix} 1 &, if\ |x| \leq 1 \\ 0 & ,if\ |x|>1 \end{matrix}\right.$ ... at $ 1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $ 2$ $h_1$ has discontinuity at $ 2$ and $h_2$ has discontinuity at $ 1$.

answered Jul 24 in Calculus by Arif_Faizan (35 points) | 41 views

+1 vote

1 answer

30

graph theory(basic doubt)
Q.1)How many nonisomorphic simple graph are there with 6 vertices and 4 edges??

answered Jul 24 in Graph Theory by gorya506 (163 points) | 56 views

+41 votes

7 answers

31

GATE2014-2-47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$

answered Jul 24 in Linear Algebra by srestha Veteran (113k points) | 9.4k views

+1 vote

2 answers

32

UGCNET-June-2019-II-3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$

answered Jul 23 in Combinatory by Lakshman Patel RJIT Boss (45.1k points) | 115 views

+1 vote

3 answers

33

Suppose that 100 people enter a contest and that different winners are selected at random for first, second, and third prizes. What is the probability that Michelle wins one of these prizes if she is one of the contestants?

answered Jul 21 in Probability by mohan123 Junior (663 points) | 926 views

+13 votes

4 answers

34

GATE2007-IT-76
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n -2$, where $c > 0$. Suppose there exists a non-empty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1-\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c-1}$

answered Jul 20 in Combinatory by ankitgupta.1729 Boss (14k points) | 1.2k views

0 votes

1 answer

35

Probability
Suppose that a bag contains 8 blue cubes and 4 green cubes. We draw 2 cubes from the bag without replacement. It is given that blue balls are of weight 1Kg and green balls are of weight 0.5 Kg. Suppose that the probability that a given cube in the bag ... is its weight divided by the sum of the weights of all cubes currently in the bag. What is the probability that both cubes are blue.

answered Jul 20 in Probability by bankeshk (27 points) | 43 views

0 votes

1 answer

36

Probability
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys?

answered Jul 20 in Mathematical Logic by bankeshk (27 points) | 36 views

0 votes

1 answer

37

Kenneth Rosen Edition 7th Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to it-self is one-to-one. Give an example of an decreasing function from $R$ to itself that is not one-to-one

answered Jul 17 in Set Theory & Algebra by chirudeepnamini (219 points) | 11 views

+1 vote

2 answers

38

Probability-GFG
In a bunch of $13$ T-shirts only $1$ is of Medium size, which is correct fit for the searching person. Each time wrong size is picked, the person throws it away and pick the next T-shirt. What is the probability that the correct size T-shirt can be searched in $8^{th}$ attempt ? My attempt : $\frac{1}{13}$ where i went wrong ?

answered Jul 16 in Probability by arjun0001 (21 points) | 330 views

+8 votes

8 answers

39

Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

answered Jul 14 in Combinatory by srestha Veteran (113k points) | 2.2k views

+36 votes

7 answers

40

GATE2003-40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$

answered Jul 14 in Graph Theory by PRANAV M (143 points) | 3.5k views

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