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Recent questions and answers in Engineering Mathematics
+6
votes
8
answers
1
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
12 hours
ago
in
Combinatory
by
Lakshman Patel RJIT
Veteran
(
58.5k
points)

545
views
tifr2018
modulararithmetic
permutationandcombination
+18
votes
4
answers
2
GATE201421
The security system at an IT office is composed of $10$ computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed ... inspected are working. Let the probability that the system is deemed functional be denoted by p. Then $100$p = _____________.
answered
14 hours
ago
in
Probability
by
Kushagra गुप्ता
Active
(
4k
points)

3.7k
views
gate20142
probability
numericalanswers
normal
+50
votes
6
answers
3
GATE200625
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left  \left\{j \mid i\in X_j \right\} \right$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
answered
16 hours
ago
in
Set Theory & Algebra
by
Madhab
Loyal
(
5.7k
points)

3k
views
gate2006
settheory&algebra
normal
functions
+33
votes
6
answers
4
GATE2016226
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? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
answered
16 hours
ago
in
Set Theory & Algebra
by
arjuno
(
259
points)

4.8k
views
gate20162
settheory&algebra
relations
normal
+31
votes
8
answers
5
GATE2005IT36
Let $P(x)$ and $Q(x)$ ...
answered
2 days
ago
in
Mathematical Logic
by
Madhab
Loyal
(
5.7k
points)

4.5k
views
gate2005it
mathematicallogic
firstorderlogic
normal
+1
vote
1
answer
6
Made Easy Test Series 2019: Combinatory  Permutations And Combinations
in how many ways 6 letters can be placed in 6 envelopes such that at least 4 letters go into their corresponding envelopes ?
answered
2 days
ago
in
Combinatory
by
suvradip das
(
149
points)

194
views
discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
+37
votes
2
answers
7
GATE199116,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
answered
2 days
ago
in
Combinatory
by
Rishiryanemo
(
19
points)

1.6k
views
gate1991
permutationandcombination
normal
descriptive
catalannumber
0
votes
1
answer
8
ugc net 2018 july79
answered
4 days
ago
in
Mathematical Logic
by
mishrapankajs
(
11
points)

249
views
+26
votes
4
answers
9
GATE20012.1
How many $4$digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
answered
4 days
ago
in
Combinatory
by
Kushagra गुप्ता
Active
(
4k
points)

3.8k
views
gate2001
permutationandcombination
normal
+39
votes
7
answers
10
GATE200544
What is the minimum number of ordered pairs of nonnegative 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
5 days
ago
in
Combinatory
by
Kushagra गुप्ता
Active
(
4k
points)

4.7k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
0
votes
1
answer
11
ISRO202056
For the distributions given below : Which of the following is correct for the above distributions ? Standard deviation of $A$ is significantly lower than standard deviation of $B$ Standard deviation of $A$ is slightly lower than standard deviation of $B$ Standard ... $B$ Standard deviation of $A$ is significantly higher than standard deviation of $B$
answered
5 days
ago
in
Probability
by
Tuhin Dutta
Boss
(
10.5k
points)

143
views
isro2020
probability
standarddeviation
normal
+1
vote
1
answer
12
ISRO202076
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$ Then $(A \cup B’) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
answered
5 days
ago
in
Set Theory & Algebra
by
habedo007
Active
(
2.8k
points)

107
views
isro2020
discretemathematics
settheory&algebra
sets
easy
+1
vote
1
answer
13
ISRO202073
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish
answered
5 days
ago
in
Mathematical Logic
by
chirudeepnamini
Active
(
4.3k
points)

137
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+29
votes
4
answers
14
GATE2015337
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} \text{ for } i = 1, 2, 3$. Define another random variable $Y = X_1X_2 \oplus X_3$, where $\oplus$ denotes XOR. Then $Pr[Y=0 \mid X_3 = 0] =$______.
answered
6 days
ago
in
Probability
by
arjuno
(
259
points)

3.3k
views
gate20153
probability
randomvariable
normal
numericalanswers
+2
votes
1
answer
15
GO2019FLT111
Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation? $F(x) = \frac{1}{1xx^2}$ $a_n=a_{n1}+3, n>0, a_0=1$ $a_n=a_{n1}+a_{n2}, n>1, a_0=1, a_1=1$ $a_n=2n+3, n>1$ $a_n=2a_{n1}+3, n>1, a_0=1$
answered
Jan 12
in
Set Theory & Algebra
by
blackcloud
(
459
points)

303
views
go2019flt1
generatingfunctions
settheory&algebra
+23
votes
5
answers
16
GATE201134
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$
answered
Jan 11
in
Probability
by
arjuno
(
259
points)

3.6k
views
gate2011
probability
normal
+24
votes
8
answers
17
GATE200724
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
answered
Jan 11
in
Probability
by
arjuno
(
259
points)

4.7k
views
gate2007
probability
easy
uniformdistribution
+15
votes
7
answers
18
GATE200550
Let $G(x) = \frac{1}{(1x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $x < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
answered
Jan 9
in
Combinatory
by
arjuno
(
259
points)

1.8k
views
gate2005
normal
generatingfunctions
+15
votes
5
answers
19
GATE200827
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer science the next ... , what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
answered
Jan 9
in
Probability
by
JashanArora
Loyal
(
6.1k
points)

2.2k
views
gate2008
probability
normal
+21
votes
6
answers
20
GATE2005IT34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q  1)$ $pq$ $\left ( p^{2}1 \right ) (q  1)$ $p(p  1) (q  1)$
answered
Jan 9
in
Set Theory & Algebra
by
arjuno
(
259
points)

2k
views
gate2005it
settheory&algebra
normal
numbertheory
+6
votes
5
answers
21
CMI2012A07
A man has three cats. At least one is male. What is the probability that all three are male? $\frac{1}{2}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{3}{8}$
answered
Jan 9
in
Probability
by
JashanArora
Loyal
(
6.1k
points)

497
views
cmi2012
probability
+28
votes
2
answers
22
GATE20035
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
answered
Jan 9
in
Combinatory
by
arjuno
(
259
points)

2.6k
views
gate2003
permutationandcombination
normal
+1
vote
2
answers
23
MadeEasy Test Series: Calculus  Limits
How it solve this ?
answered
Jan 9
in
Calculus
by
Mayank Harbola
(
17
points)

216
views
madeeasytestseries
calculus
limits
engineeringmathematics
0
votes
1
answer
24
ISI2016MMA9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(XY)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
answered
Jan 8
in
Probability
by
Ayan Kumar Pahari
(
311
points)

54
views
isi2016mmamma
probability
randomvariable
poissondistribution
expectation
+13
votes
6
answers
25
TIFR2010B38
Suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up. One coin is chosen at random and flipped. What is the probability that after the flip the majority of the coins(i.e., at least two of them) will have heads facing up? ... $\left(\frac{1}{4}\right)$ $\left(\frac{1}{4}+\frac{1}{8}\right)$ $\left(\frac{2}{3}\right)$
answered
Jan 8
in
Probability
by
Navneet Singh Tomar
Junior
(
729
points)

1k
views
tifr2010
probability
binomialdistribution
+2
votes
1
answer
26
GO2019FLT153
A class of first year B.tech students is composed of four batches A, B, C and D, each consisting of $30$ students. It is found that the sessional marks of students in Engineering Drawing in batch C have a mean of $6.6$ and standard deviation of $2.3$. The mean and the standard ... Due to this, the marks of a student in batch C are changed from $8.5$ to $6.0$ $7.0$ $8.0$ $9.0$
answered
Jan 7
in
Probability
by
Dharmendra Tiwari
Junior
(
629
points)

199
views
go2019flt1
statistics
probability
+16
votes
10
answers
27
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
answered
Jan 6
in
Combinatory
by
Çșȇ ʛấẗẻ
Active
(
1.9k
points)

6.9k
views
gate2018
generatingfunctions
normal
permutationandcombination
+47
votes
5
answers
28
GATE2007IT25
What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ? $1$ $2$ $3$ $n$
answered
Jan 6
in
Graph Theory
by
endurance1
(
13
points)

5.4k
views
gate2007it
graphtheory
spanningtree
normal
+6
votes
4
answers
29
ISRO201437
The probability that two friends are born in the same month is ____ ? 1/6 1/12 1/144 1/24
answered
Jan 6
in
Probability
by
Satbir
Boss
(
23.7k
points)

3.9k
views
probability
isro2014
+1
vote
3
answers
30
ISI2019MMA27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
answered
Jan 6
in
Combinatory
by
Navneet Singh Tomar
Junior
(
729
points)

2.8k
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
31
Kenneth Rosen Edition 7th Exercise 1.7 Question 7 (Page No. 91)
Use a direct proof to show that every odd integer is the difference of two squares.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

22
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
1
answer
32
Kenneth Rosen Edition 7th Exercise 1.7 Question 15 (Page No. 91)
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

12
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
33
Kenneth Rosen Edition 7th Exercise 1.7 Question 11 (Page No. 91)
Prove or disprove that the product of two irrational numbers is irrational.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

18
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
1
answer
34
Kenneth Rosen Edition 7th Exercise 1.7 Question 10 (Page No. 91)
Use a direct proof to show that the product of two rational numbers is rational.
answered
Jan 5
in
Mathematical Logic
by
vedantbonde19
(
29
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+29
votes
4
answers
35
GATE2015254
Let $X$ and $Y$ denote the sets containing 2 and 20 distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being onetoone is ______.
answered
Jan 4
in
Set Theory & Algebra
by
shivam001
Junior
(
959
points)

2.7k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+24
votes
3
answers
36
GATE19962.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, xy)$. The inverse function of $f$ is given by $f^{1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{xy}\right)$ ... $f^{1}(x,y)=\left [ 2\left(xy\right),2\left(x+y\right) \right ]$
answered
Jan 4
in
Set Theory & Algebra
by
shivam001
Junior
(
959
points)

2.6k
views
gate1996
settheory&algebra
functions
normal
+2
votes
2
answers
37
matrix groups
Which of the following is true? Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers. Every diagonal matrix is group under multiplication operation, where all elements of diagonal are non zero numbers. Every ... addition operation where all elements are real numbers. Both (a) and b) isn't a b c all are correct?
answered
Jan 4
in
Linear Algebra
by
Sahin
(
361
points)

382
views
grouptheory
+15
votes
3
answers
38
Mathematics: GATE 2013 ECA27
Let A be an mxn matrix and B an nxm matrix. It is given that determinant ( Im + AB ) = determinant ( In + BA ) , where Ik is the k k identity matrix. Using the above property, the determinant of the matrix given below is ... A) 2 B) 5 C) 8 D) 16
answered
Jan 4
in
Linear Algebra
by
Satbir
Boss
(
23.7k
points)

1.3k
views
gate2013ec
linearalgebra
engineeringmathematics
normal
determinant
+70
votes
8
answers
39
GATE201238
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
answered
Jan 3
in
Graph Theory
by
JashanArora
Loyal
(
6.1k
points)

11.2k
views
gate2012
graphtheory
normal
markstoall
counting
+46
votes
4
answers
40
GATE200479
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2  3n)}{ 2}$ edges ? $^{\left(\frac{n^2n}{2}\right)}C_{\left(\frac{n^23n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^23n}{2} \right )}}.\left(n^2n\right)}C_k\\$ $^{\left(\frac{n^2n}{2}\right)}C_n\\$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2n}{2}\right)}C_k$
answered
Jan 3
in
Graph Theory
by
JashanArora
Loyal
(
6.1k
points)

4.8k
views
gate2004
graphtheory
permutationandcombination
normal
counting
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