Recent questions and answers in Engineering Mathematics

+18 votes

5 answers

1

GATE2000-1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$

answered 21 hours ago in Combinatory by Asim Siddiqui 4 Active (1.2k points) | 2.9k views

+1 vote

1 answer

2

Gatebook Test

answered 22 hours ago in Linear Algebra by aditi19 Active (4.9k points) | 43 views

0 votes

1 answer

3

Gatebook Test

answered 22 hours ago in Linear Algebra by aditi19 Active (4.9k points) | 44 views

+25 votes

4 answers

4

GATE2006-73
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$

answered 1 day ago in Graph Theory by shaktisingh (241 points) | 2.4k views

+38 votes

6 answers

5

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 3 days ago in Combinatory by techbd123 Active (1.4k points) | 4.2k views

+3 votes

2 answers

6

CMI2015-A-10
The school athletics coach has to choose 4 students for the relay team. He calculates that there are 3876 ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the ... taken into account? Between 12,000 and 25,000 Between 75,000 and 99,999 Between 30,000 and 60,000 More than 100,000

answered 3 days ago in Combinatory by chirudeepnamini Active (1.8k points) | 92 views

+21 votes

5 answers

7

GATE2018-27
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only

answered 3 days ago in Set Theory & Algebra by JashanArora Junior (827 points) | 4.6k views

+1 vote

2 answers

8

set theory

answered 4 days ago in Set Theory & Algebra by Spidey_guy (111 points) | 50 views

+50 votes

7 answers

9

GATE2016-2-28
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 with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.

answered 4 days ago in Set Theory & Algebra by Spidey_guy (111 points) | 4.8k views

+32 votes

8 answers

10

GATE1994-1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$

answered 4 days ago in Graph Theory by Saurabh666 (389 points) | 9.3k views

+11 votes

3 answers

11

GATE1996-1.6
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h) - f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 – h)}{h^2}$

answered 5 days ago in Calculus by neeraj2681 (33 points) | 1.3k views

0 votes

1 answer

12

Rosen 7e Recurrence Relation Exercise-8.1 Question no-25 page no-511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n-1 having odd number of 0s T(n)=T(n-1) Hence, we have T(n)=2T(n-1)

answered 6 days ago in Combinatory by anonymousgamer (11 points) | 53 views

+2 votes

3 answers

13

Made easy
What is the chromatic number of following graphs? 1) 2)

answered Oct 16 in Graph Theory by chirudeepnamini Active (1.8k points) | 167 views

+10 votes

2 answers

14

ISI2015-MMA-7
Suppose $X$ is distributed as Poisson with mean $λ.$ Then $E(1/(X + 1))$ is $\frac{e^{\lambda }-1}{\lambda }$ $\frac{e^{\lambda }-1}{\lambda +1}$ $\frac{1-e^{-\lambda }}{\lambda}$ $\frac{1-e^{-\lambda }}{\lambda + 1}$

answered Oct 14 in Probability by Gaurav Yadav (233 points) | 809 views

0 votes

1 answer

15

Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?

answered Oct 11 in Combinatory by shivamgo (11 points) | 29 views

+1 vote

1 answer

16

Mean Value Theorem
f(x) is a differentiable function that satisfies 5 ≤ f′(x) ≤ 14 for all x. Let a and b be the maximum and minimum values, respectively, that f(11)−f(3) can possibly have, then what is the value of a+b?

answered Oct 10 in Calculus by Nirmal Gaur Active (2k points) | 35 views

+8 votes

4 answers

17

GATE1989-3-v
Answer the following: Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

answered Oct 8 in Mathematical Logic by vupadhayayx86 Active (1.4k points) | 587 views

+3 votes

2 answers

18

TIFR2010-Maths-A-1
A cyclic group of order 60 has 12 Generators 15 Generators 16 Generators 20 Generators

answered Oct 6 in Set Theory & Algebra by Lakshman Patel RJIT Veteran (51.5k points) | 940 views

+2 votes

3 answers

19

TIFR-2014-Maths-B-4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above.

answered Oct 5 in Set Theory & Algebra by Harry Richie (17 points) | 328 views

+1 vote

1 answer

20

TIFR-2014-Maths-A-15
How many proper subgroups does the group $\mathbb{Z} &oplus; \mathbb{Z}$ have? $1$ $2$ $3$ Infinitely many

answered Oct 5 in Set Theory & Algebra by Harry Richie (17 points) | 182 views

+8 votes

5 answers

21

GATE2007-IT-80
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy-$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the ... largest or the smallest $y$-coordinate among all the points The difference between $x$-coordinates $P_{a}$ and $P_{b}$ is minimum None of the above

answered Oct 4 in Linear Algebra by sujeetkumar (11 points) | 1k views

+13 votes

2 answers

22

GATE2015-2-9
The number of divisors of $2100$ is ____.

answered Oct 3 in Set Theory & Algebra by JashanArora Junior (827 points) | 3.2k views

+5 votes

10 answers

23

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

answered Oct 3 in Combinatory by techbd123 Active (1.4k points) | 3k views

0 votes

1 answer

24

ISI2016-DCG-45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan^{2}\:x-x\:\tan\:x}{\sin\:x}$ is $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $0$ None of these

answered Oct 2 in Calculus by `JEET Loyal (8.2k points) | 19 views

+1 vote

1 answer

25

graph Theory
Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i,j):1<=i<=12,1<=j<=12}. There is an edge between (a, b) and (c, d) if |a-c|<=1 and |b-d|<=1. The number of edges in this graph is __________.

answered Oct 1 in Graph Theory by Mac2 (11 points) | 116 views

+5 votes

2 answers

26

GATE1995-25b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$

answered Sep 27 in Set Theory & Algebra by techbd123 Active (1.4k points) | 237 views

+31 votes

3 answers

27

GATE2001-2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $

answered Sep 26 in Graph Theory by HeartBleed Junior (691 points) | 3.9k views

+1 vote

1 answer

28

ISI2014-DCG-39
The function $f(x) = x^{1/x}, \: x \neq 0$ has a minimum at $x=e$; a maximum at $x=e$; neither a maximum nor a minimum at $x=e$; None of the above

answered Sep 24 in Calculus by `JEET Loyal (8.2k points) | 36 views

0 votes

1 answer

29

ISI2014-DCG-12
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these

answered Sep 24 in Calculus by Verma Ashish Boss (10.7k points) | 47 views

0 votes

1 answer

30

Kenneth Rosen Edition 7th Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $A-B=\left \{ 1,5,7,8 \right \}, B-A=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$

answered Sep 24 in Set Theory & Algebra by anurag_cs (41 points) | 15 views

0 votes

2 answers

31

Self-Doubt:Mathematical logic
“Every asymmetric relation is antisymmetric” Is this statement is True or False? I think it is false, because asymmetric relation never allows loops and antisymmetric relation allows loops. Am I not correct?

answered Sep 24 in Set Theory & Algebra by anurag_cs (41 points) | 31 views

+33 votes

9 answers

32

GATE2014-3-51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$

answered Sep 24 in Graph Theory by HeartBleed Junior (691 points) | 4.4k views

+1 vote

3 answers

33

ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$

answered Sep 23 in Linear Algebra by aditi19 Active (4.9k points) | 108 views

0 votes

2 answers

34

ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$

answered Sep 23 in Linear Algebra by aditi19 Active (4.9k points) | 73 views

0 votes

2 answers

35

ugc net 2018 july-80

answered Sep 23 in Probability by muthuct8 (11 points) | 185 views

+2 votes

3 answers

36

ISI2017-MMA-13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and is equal to $-5$ none of the above is necessarily true

answered Sep 22 in Calculus by techbd123 Active (1.4k points) | 277 views

+17 votes

6 answers

37

GATE1998-10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$

answered Sep 20 in Set Theory & Algebra by Gaurav Yadav (233 points) | 1.2k views

+24 votes

5 answers

38

GATE2016-1-05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______

answered Sep 19 in Linear Algebra by neeraj2681 (33 points) | 3.6k views

+10 votes

3 answers

39

GATE1997-14
Let $R$ be a reflexive and transitive relation on a set $A$. Define a new relation $E$ on $A$ as $E=\{(a, b) \mid (a, b) \in R \text{ and } (b, a) \in R \}$ Prove that $E$ is an equivalence relation on $A$. Define a relation $\leq$ on the equivalence classes of $E$ ... $\exists a, b$ such that $a \in E_1, b \in E_2 \text{ and } (a, b) \in R$. Prove that $\leq$ is a partial order.

answered Sep 19 in Set Theory & Algebra by Sambhrant Maurya Active (3.2k points) | 805 views

+15 votes

4 answers

40

GATE1994-3.8
Give a relational algebra expression using only the minimum number of operators from $(∪, −)$ which is equivalent to $R$ $∩$ $S.$

answered Sep 18 in Set Theory & Algebra by Anurag007 (11 points) | 830 views

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content	content:apple
exclude	-tag:apple
force match	+apple
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