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Previous GATE
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Previous GATE
+5
votes
2
answers
1
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
asked
Jun 6, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

406
views
gate1995
settheory&algebra
numericalanswers
sets
+2
votes
1
answer
2
Mathematics: GATE2017 EC222
Consider the random process: $X\left ( t \right )=U+Vt$ where $U$ is zeromean Gaussian random variable and $V$ is a random variable uniformly distributed between $0$ and $2.$ Assume $U$ and $V$ statistically independent. The mean value of random process at $t=2$ is ___________
asked
Jun 3, 2019
in
Probability
by
srestha
Veteran
(
119k
points)

168
views
gate2017ec2
probability
+2
votes
4
answers
3
GATE2017 EC
The rank of the matrix $\begin{bmatrix} 1 & 1 & 0 &0 & 0\\ 0 & 0 & 1 &1 &0 \\ 0 &1 &1 &0 &0 \\ 1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & 1 \end{bmatrix}$ is ________. Ans 5?
asked
Jun 1, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

297
views
discretemathematics
matrices
+10
votes
3
answers
4
GATE20195
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n1}$ $\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II
asked
Feb 7, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

3.1k
views
gate2019
engineeringmathematics
discretemathematics
permutationandcombination
+6
votes
5
answers
5
GATE20199
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is nonzero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
asked
Feb 7, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

2.3k
views
gate2019
engineeringmathematics
linearalgebra
determinant
+11
votes
3
answers
6
GATE201910
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
asked
Feb 7, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

3.5k
views
gate2019
engineeringmathematics
discretemathematics
settheory&algebra
grouptheory
+8
votes
9
answers
7
GATE201912
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n1)!$ $1$ $\frac{(n1)!}{2}$
asked
Feb 7, 2019
in
Graph Theory
by
Arjun
Veteran
(
431k
points)

4k
views
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+4
votes
6
answers
8
GATE201913
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^481}{2x^25x3}$ $1$ $53/12$ $108/7$ Limit does not exist
asked
Feb 7, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

2k
views
gate2019
engineeringmathematics
calculus
limits
+7
votes
10
answers
9
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
asked
Feb 7, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

4.1k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
+11
votes
8
answers
10
GATE201935
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
asked
Feb 7, 2019
in
Mathematical Logic
by
Arjun
Veteran
(
431k
points)

5.9k
views
gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
+6
votes
5
answers
11
GATE201938
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimumweight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
asked
Feb 7, 2019
in
Graph Theory
by
Arjun
Veteran
(
431k
points)

3.8k
views
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+7
votes
4
answers
12
GATE201944
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
asked
Feb 7, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

3.5k
views
gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+8
votes
3
answers
13
GATE201947
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______
asked
Feb 7, 2019
in
Probability
by
Arjun
Veteran
(
431k
points)

3.9k
views
gate2019
numericalanswers
engineeringmathematics
probability
uniformdistribution
+3
votes
4
answers
14
GATE201923
Two numbers are chosen independently and uniformly at random from the set $ [ 1, 2, \dots, 13]$. The probability (rounded off to $3$ decimal places ) that their $4bit$ (unsigned) binary representations have the same most significant bit is
asked
Feb 7, 2019
in
Probability
by
Ram Swaroop
Loyal
(
5.3k
points)

1.1k
views
gate2019
probability
0
votes
2
answers
15
GATE2019
What is the total number of different Hamiltonian cycles for the complete graph of n vertices?
asked
Feb 3, 2019
in
Graph Theory
by
Atul Sharma 1
(
81
points)

860
views
+2
votes
1
answer
16
GATE2016 37 Mathematics
Let $M = \begin{bmatrix} a & b &c \\ b &d & e\\ c & e & f \end{bmatrix}$ be a real matrix with eigenvalues 1, 0 and 3. If the eigenvectors corresponding to 1 and 0 are $\left ( 1,1,1 \right )^T$ and $\left ( 1,1, 0 \right )^T$ respectively, then the value of 3f is equal to _______.
asked
Oct 4, 2018
in
Linear Algebra
by
Mk Utkarsh
Boss
(
36.5k
points)

308
views
linearalgebra
eigenvalue
0
votes
0
answers
17
First Order Logic: GATE200541 ( From gate Overflow volume 1)
Can the answer to this be "âˆ€x âˆƒy (teacher (x) âˆ§ student (y) âˆ§ likes (y,x))" ?
asked
Sep 30, 2018
in
Mathematical Logic
by
rambo1987
(
19
points)

115
views
+3
votes
2
answers
18
GATE199810b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.
asked
Aug 12, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

394
views
gate1998
descriptive
settheory&algebra
relations
+29
votes
13
answers
19
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
asked
Feb 14, 2018
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

9.7k
views
gate2018
permutationandcombination
numericalanswers
+14
votes
4
answers
20
GATE201844
Consider Guwahati, (G) and Delhi (D) whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ and $P(L_G)$ denotes the ... , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____
asked
Feb 14, 2018
in
Probability
by
gatecse
Boss
(
17.5k
points)

4.6k
views
gate2018
probability
conditionalprobability
numericalanswers
+18
votes
9
answers
21
GATE201830
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ is between ... then $\mid ij \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II
asked
Feb 14, 2018
in
Graph Theory
by
gatecse
Boss
(
17.5k
points)

6.3k
views
gate2018
graphtheory
graphsearch
normal
+29
votes
3
answers
22
GATE201828
Consider the firstorder logic sentence $\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$ ... than or equal to $3$ There exists no model of $\varphi$ with universe size of greater than $7$ Every model of $\varphi$ has a universe of size equal to $7$
asked
Feb 14, 2018
in
Mathematical Logic
by
gatecse
Boss
(
17.5k
points)

7.8k
views
gate2018
mathematicallogic
normal
firstorderlogic
+29
votes
4
answers
23
GATE201826
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
asked
Feb 14, 2018
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

6.8k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
+27
votes
5
answers
24
GATE201827
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
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

5.5k
views
gate2018
settheory&algebra
countableuncountableset
normal
+11
votes
3
answers
25
GATE201817
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
asked
Feb 14, 2018
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

2.9k
views
gate2018
linearalgebra
eigenvalue
normal
numericalanswers
+18
votes
4
answers
26
GATE201818
The chromatic number of the following graph is _____
asked
Feb 14, 2018
in
Graph Theory
by
gatecse
Boss
(
17.5k
points)

2.9k
views
graphtheory
graphcoloring
numericalanswers
gate2018
+12
votes
4
answers
27
GATE201819
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

3.9k
views
gate2018
grouptheory
numericalanswers
settheory&algebra
+12
votes
6
answers
28
GATE201816
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
asked
Feb 14, 2018
in
Calculus
by
gatecse
Boss
(
17.5k
points)

4.8k
views
gate2018
calculus
integration
normal
numericalanswers
+10
votes
5
answers
29
GATE201815
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial ... probable and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
asked
Feb 14, 2018
in
Probability
by
gatecse
Boss
(
17.5k
points)

3.5k
views
gate2018
probability
normal
numericalanswers
+18
votes
10
answers
30
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
asked
Feb 14, 2018
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

7k
views
gate2018
generatingfunctions
normal
permutationandcombination
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