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+6
votes
1
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 _______
answered
Jan 2
in
Linear Algebra

3.4k
views
gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+2
votes
2
$\textbf{NTA NET dec 2019 ( Recurrence relation)}$
$\text{Give asymptotic upper and lower bound for $\mathbf{T(n)}$ given below.}\;\text{Assume $\mathrm {T(n)}$ is constant for $\mathrm {n\le 2}.$}$ $\large{\mathrm{T(n) = 4T\left (\sqrt n \right ) + \lg^2 n}}$ ... $4)\;\;\mathrm{T(n) = \theta (\lg (\lg n)\lg n)}$
answered
Jan 2
in
Algorithms

133
views
#recurrencerelations
0
votes
3
ISI 2004 MIII
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X.$ Define $\textit{f}:\textit{X$\times$ $\mathcal{P}$(X)}\rightarrow \mathbb{R}$ by $f(x,A) = \begin{cases} 1 \text{ if } x \in A & \\ 0 \text{ if } x \notin A & \end{cases}$ ... $f(x,A)+f(x,B)  f(x,A) \cdot f(x,B)$ $f(x,A)+ \mid f(x,A)  f(x,B) \mid$
answered
Dec 31, 2019
in
Set Theory & Algebra

151
views
isi2004
functions
+1
vote
4
GATE19879f
Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
answered
Dec 30, 2019
in
Set Theory & Algebra

216
views
gate1987
groupisomorphism
settheory&algebra
nongate
+1
vote
5
ISI2018DCG25
There are three circles of equal diameter ($10$ units each) as shown in the figure below. The straight line $PQ$ passes through the centres of all the three circles. The straight line $PR$ is a tangent to the third circle at $C$ ... $B$ as shown in the figure.Then the length of the line segment $AB$ is $6$ units $7$ units $8$ units $9$ units
answered
Sep 19, 2019
in
Geometry

29
views
isi2018dcg
circle
lines
nongate
0
votes
6
CMI2018A2
Akash, Bharani, Chetan and Deepa are invited to a party. If Bharani and Chetan attend, then Deepa will attend too. If Bharani does not attend, then Akash will not attend. If Deepa does not attend, which of the following is true? Chetan does not attend Akash does not attend either (A) or (B) none of the above
answered
Sep 16, 2019
in
Numerical Ability

53
views
cmi2018
logicalreasoning
+7
votes
7
GATE2007IT76
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 nonempty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c1}$
answered
Jul 20, 2019
in
Combinatory

1.5k
views
gate2007it
permutationandcombination
normal
recurrence
+3
votes
8
TIFR2014A13
Let $L$ be a line on the two dimensional plane. $L'$s intercepts with the $X$ and $Y$ axes are respectively $a$ and $b$. After rotating the coordinate system (and leaving $L$ untouched), the new intercepts are $a'$ and $b'$ ... $\frac{b}{a}+\frac{a}{b}=\frac{b'}{a'}+\frac{a'}{b'}$. None of the above.
answered
Jun 9, 2019
in
Numerical Ability

271
views
tifr2014
geometry
cartesiancoordinates
+3
votes
9
GATE198816i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lowertriangular with all diagonal elements equal to 1, $U$ is uppertriangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 & 9 \\ 4 & 6 & 5 \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
answered
Jun 8, 2019
in
Linear Algebra

371
views
gate1988
normal
descriptive
linearalgebra
matrices
+2
votes
10
Differentiability
$\varphi \left ( x \right )=x^{2}\cos \frac{1}{x}$ when $x\neq 0$ $=0$ when $x=0$ Is it differentiable at $x=0$? Is it continuous ?
answered
Jun 7, 2019
in
Calculus

64
views
calculus
discretemathematics
+4
votes
11
GATE200727
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above
answered
Jun 6, 2019
in
Linear Algebra

3.7k
views
gate2007
linearalgebra
normal
vectorspace
+2
votes
12
GATE2017 ME1: GA8
Let $S_1$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x  1 \mid \leq 2$ and $\mid y+2 \mid \leq 3$. Let $S_2$ be the plane figure given by the inequalities $xy \geq 2, \: y \geq 1$, and $x \leq 3$. Let $S$ be the union of $S_1$ and $S_2$. The area of $S$ is. $26$ $28$ $32$ $34$
answered
Jun 5, 2019
in
Numerical Ability

145
views
gate2017me1
generalaptitude
numericalability
geometry
+3
votes
13
GATE2017 ME1: GA5
$P$, $Q$ and $R$ talk about $S's$ car collection. $P$ states that $S$ has at least $3$ cars. $Q$ believes that $S$ has less than $3$ cars. $R$ indicates that to his knowledge, $S$ has at least one car. Only one of $P, Q$ and $R$ is right. The number of cars owned by $S$ is. $0$ $1$ $3$ Cannot be determined.
answered
Jun 4, 2019
in
Numerical Ability

128
views
gate2017me1
generalaptitude
logicalreasoning
+5
votes
14
GATE2019 CE1: GA3
On a horizontal ground, the base of a straight ladder is $6$ m away from the base of a vertical pole. The ladder makes an angle of $45^{\circ}$ to the horizontal. If the ladder is resting at a point located at onefifth of the height of the pole from the bottom, the height of the pole is ______ meters. $15$ $25$ $30$ $35$
answered
Jun 4, 2019
in
Numerical Ability

113
views
gate2019ce1
generalaptitude
numericalability
geometry
+3
votes
15
GATE2019 EC: GA9
Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the hour hand moved by $210$ degrees on the clock. $Q$ stopped working when the hour ... . After paying the consultants, the client shall have USD _______ remaining in the budget. $000.00$ $166.67$ $300.00$ $433.33$
answered
Jun 4, 2019
in
Numerical Ability

135
views
gate2019ec
generalaptitude
numericalability
clocktime
+3
votes
16
GATE2019 ME1: GA3
A worker noticed that the hour hand on the factory clock had moved by $225$ degrees during her stay at the factory. For how long did she stay in the factory? $3.75$ hours $4$ hours and $15$ mins $8.5$ hours $7.5$ hours
answered
Jun 4, 2019
in
Numerical Ability

168
views
gate2019me1
generalaptitude
numericalability
clocktime
+2
votes
17
GATE2018 CE1: GA8
Which of the following function(s) is an accurate description of the graph for the range(s) indicated? $y=2x+4 \text{ for } 3 \leq x \leq 1$ $y= \mid x1 \mid \text{ for } 1 \leq x \leq 2$ $y= \mid\mid x \mid 1 \mid \text{ for } 1 \leq x \leq 2$ $y=1 \text{ for } 2 \leq x \leq 3$ i, ii and iii only i, ii and iv only i and iv only ii and iv only
answered
Jun 3, 2019
in
Numerical Ability

126
views
gate2018ce1
generalaptitude
numericalability
graphicaldata
+1
vote
18
GATE2017 ME2: GA9
All people in a certain island are either 'Knights' or 'Knaves' and each person knows every other person's identity. Knights never lie, and Knaves ALWAYS lie. $P$ says "Both of us are Knights". $Q$ says "None of us are Knaves". Which one of the ... $P$ and $Q$ are Knaves. The identities of $P, Q$ cannot be determined.
answered
Jun 3, 2019
in
Verbal Ability

172
views
gate2017me2
verbalability
logicalreasoning
statementsfollow
+4
votes
19
GATE2017 EC1: GA5
Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences? At least one bench is a table At least one shelf is a bench At least one chair is a table All benches are chairs Only i Only ii Only ii and iii Only iv
answered
Jun 2, 2019
in
Verbal Ability

158
views
gate2017ec1
generalaptitude
verbalability
statementsfollow
+2
votes
20
GATE2015118
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
answered
Jun 2, 2019
in
Linear Algebra

3.2k
views
gate20151
linearalgebra
matrices
numericalanswers
0
votes
21
Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?
answered
May 30, 2019
in
Mathematical Logic

167
views
mathematicallogic
propositionallogic
discretemathematics
+1
vote
22
Kenneth Rosen Edition 7th Exercise 1.2 Question 34 (Page No. 24)
Five friends have access to a chat room. Is it possible to determine who is chatting if the following information is known? Either Kevin or Heather, or both, are chatting. Either Randy or Vijay, but not both, are ... either both chatting or neither is. If Heather is chatting, then so are Abby and Kevin. Explain your reasoning.
answered
May 29, 2019
in
Mathematical Logic

70
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
+1
vote
23
Kenneth Rosen Edition 7th Exercise 1.2 Question 33 (Page No. 24)
Steve would like to determine the relative salaries of three coworkers using two facts. First, he knows that if Fred is not the highest paid of the three, then Janice is. Second, he knows that if Janice is not the lowest paid, ... and Janice from what Steve knows? If so, who is paid the most and who the least? Explain your reasoning.
answered
May 29, 2019
in
Mathematical Logic

41
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
24
Kenneth Rosen Edition 7th Exercise 1.2 Question 32 (Page No. 23)
The police have three suspects for the murder of Mr. Cooper: Mr. Smith, Mr Jones, Mr. Williams. Smith Jones, and Williams each declare that they did not kill Cooper. Smith also states that Cooper was friend of Jones and that ... telling the truth, but the statements of the guilty man may or may not b true? innocent men do not lie?
answered
May 29, 2019
in
Mathematical Logic

49
views
kennethrosen
discretemathematics
mathematicallogic
0
votes
25
Kenneth Rosen Edition 7th Exercise 1.2 Question 23 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if ... what these people are, can you draw any conclusions? $A$ says We are both knaves and $B$ says nothing.
answered
May 28, 2019
in
Mathematical Logic

28
views
kennethrosen
discretemathematics
mathematicallogic
0
votes
26
Kenneth Rosen Edition 7th Exercise 1.2 Question 22 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if they ... determine what these people are, can you draw any conclusions ? Both $A$ and $B$ say I am a knight.
answered
May 28, 2019
in
Mathematical Logic

24
views
kennethrosen
discretemathematics
mathematicallogic
+1
vote
27
Kenneth Rosen Edition 7th Exercise 1.2 Question 20 (Page No. 23)
relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth always lie. You encounter two people. A and B. Determine, if possible, what A and B are if they address you in the ways ... can you draw any conclusions? A says The two of us are both knights and B says A is knave.
answered
May 28, 2019
in
Mathematical Logic

69
views
kennethrosen
discretemathematics
mathematicallogic
descriptive
0
votes
28
Kenneth Rosen Edition 7th Exercise 1.2 Question 19 (Page No. 23)
Relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, $A$ and $B$. Determine, if possible, what $A$ and $B$ are if they address ... can you draw any conclusions ? $A$ says At least one of us is a knave and $B$ says nothing.
answered
May 28, 2019
in
Mathematical Logic

37
views
kennethrosen
discretemathematics
mathematicallogic
descriptive
logicalreasoning
0
votes
29
Kenneth Rosen Edition 7th Exercise 1.2 Question 17 (Page No. 23)
When three professors are seated in a restaurant, the hostess asks them: Does everyone want coffee ? The first professor says: I do not know. The second professor then says: I do not know. Finally, the third ... The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?
answered
May 28, 2019
in
Mathematical Logic

42
views
kennethrosen
discretemathematics
mathematicallogic
+2
votes
30
GATE2019 ME2: GA4
The product of three integers $X$, $Y$ and $Z$ is $192$. $Z$ is equal to $4$ and $P$ is equal to the average of $X$ and $Y$. What is the minimum possible value of $P$? $6$ $7$ $8$ $9.5$
answered
May 24, 2019
in
Numerical Ability

116
views
gate2019me2
generalaptitude
numericalability
numericalcomputation
+3
votes
31
GATE2011 AG: GA7
Given that $f(y)=\frac{ \mid y \mid }{y},$ and $q$ is nonzero real number, the value of $\mid f(q)f(q) \mid $ is $0$ $1$ $1$ $2$
answered
May 15, 2019
in
Numerical Ability

205
views
generalaptitude
numericalability
gate2011ag
absolutevalue
+1
vote
32
Allen Career Institute: Spanning tree
Let $G$ be a simple undirected complete and weighted graph with vertex set $V = {0, 1, 2, . 99.}$ Weight of the edge $(u, v)$ is $\left  uv \right $ where $0\leq u, v\leq 99$ and $u\neq v$. Weight ... tree is______________ Doubt:Here asking for maximum weight spanning tree. So, there weight will be $0$ to every node. Isnot it? but answer given 7351.
answered
Mar 29, 2019
in
Graph Theory

87
views
discretemathematics
+2
votes
33
Proposition LogicRosen(7e)
Show that these statements are inconsistent: “If Miranda does not take a course in discrete mathematics, then she will not graduate.” “If Miranda does not graduate, then she is not qualified for the job.” “If Miranda reads this book, then she is qualified for the job.” “Miranda does not take a course in discrete mathematics but she reads this book.” how to approach?
answered
Mar 27, 2019
in
Mathematical Logic

125
views
mathematicallogic
discretemathematics
kennethrosen
propositionallogic
+5
votes
34
ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{2}$ $b)3\left ( 13x \right )^{2}$ $c)2\left ( 1+3x \right )^{3}$ $d)2\left ( 13x \right )^{3}$
answered
Mar 9, 2019
in
Combinatory

111
views
generatingfunctions
discretemathematics
+5
votes
35
GATE20151GA7
Select the alternative meaning of the underlined part of the sentence. The chain snatchers took to their heels when the police party arrived. Took shelter in a thick jungle Open indiscriminate fire Took to flight Unconditionally surrendered
answered
Dec 29, 2018
in
Verbal Ability

986
views
gate20151
verbalability
meaning
easy
+7
votes
36
GATE199011b
The following program computes values of a mathematical function $f(x)$. Determine the form of $f(x)$. main () { int m, n; float x, y, t; scanf ("%f%d", &x, &n); t = 1; y = 0; m = 1; do { t *= (x/m); y += t; } while (m++ < n); printf ("The value of y is %f", y); }
answered
Oct 24, 2018
in
Algorithms

418
views
gate1990
descriptive
algorithms
identifyfunction
+9
votes
37
ISI2017MMA13
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
Aug 24, 2018
in
Calculus

337
views
isi2017mma
engineeringmathematics
calculus
differentiation
+3
votes
38
GATE201137
Which of the given options provides the increasing order of asymptotic complexity of functions $f_1, f_2, f_3$ and $f_4$? $f_1(n) = 2^n$ $f_2(n) = n^{3/2}$ $f_3(n) = n \log_2 n$ $f_4(n) = n^{\log_2 n}$ $f_3, f_2, f_4, f_1$ $f_3, f_2, f_1, f_4$ $f_2, f_3, f_1, f_4$ $f_2, f_3, f_4, f_1$
answered
Jun 23, 2018
in
Algorithms

2.4k
views
gate2011
algorithms
asymptoticnotations
normal
+6
votes
39
Matrix
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$ satisfies the following polynomial $A^{5}4A^{4}7A^{3}+11A^{2}2A+kI=0$ Then the value of k is ______________
answered
May 27, 2018
in
Linear Algebra

562
views
linearalgebra
matrices
engineeringmathematics
+7
votes
40
CMI 2018 (Probability)
Suppose you have two coins $A$ and $B$ the probability of head in $A$ is $\dfrac{1}{4}$ and the probability of head in $B$ is $\dfrac{3}{4}$. Now, suppose you have chosen a coin and tossed it two times. The output was head and head. What is the probability that you chose the coin $B$.
answered
May 17, 2018
in
Probability

211
views
usercmi2018
usermod
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