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Introduction to Linear Algebra 4th edition Problem Set 1.1
How many corner does a cube have in 4 dimensions? How many 3D faces? Now by observation we can tell that, an ndimensional cube has $2^n$ corners. 1D cube which is a line have $2^1$ corners 2D cube which is a square have $2^2$ ... . but this is the question i'm not able to answer. How every Ncube have $2n$ cubes of dimension (N1)?
asked
23 hours
ago
in
Linear Algebra
by
Mk Utkarsh
Boss
(
36.8k
points)

13
views
linearalgebra
0
votes
0
answers
2
JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that F is oneone For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
asked
Feb 17
in
Set Theory & Algebra
by
vivek_mishra
Junior
(
585
points)

78
views
jest
functions
sets
0
votes
3
answers
3
TIFR2020B11
Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$
asked
Feb 11
in
Graph Theory
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

68
views
tifr2020
engineeringmathematics
graphtheory
graphcoloring
0
votes
1
answer
4
TIFR2020A13
What is the area of the largest rectangle that can be inscribed in a circle of radius $R$? $R^{2}/2$ $\pi \times R^{2}/2$ $R^{2}$ $2R^{2}$ None of the above
asked
Feb 11
in
Calculus
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

22
views
tifr2020
0
votes
1
answer
5
TIFR2020A12
The hour needle of a clock is malfunctioning and travels in the anticlockwise direction, i.e., opposite to the usual direction, at the same speed it would have if it was working correctly. The minute needle is working correctly. Suppose the the two needles show the correct time at ... $\dfrac{10}{11}$ hour $\dfrac{11}{12}$ hour $\dfrac{12}{13}$ hour $\dfrac{19}{22}$ hour One hour
asked
Feb 11
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

33
views
tifr2020
0
votes
0
answers
6
TIFR2020A11
Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above
asked
Feb 11
in
Probability
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

24
views
tifr2020
0
votes
1
answer
7
TIFR2020A10
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
asked
Feb 10
in
Probability
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

46
views
tifr2020
engineeringmathematics
probability
0
votes
0
answers
8
TIFR2020A8
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly global minimum inside $(0,1).$ What can you say about the behaviour of the first derivative $f'$ and and second derivative $f''$ on ... is zero at atleast one point $f'$ is zero at atleast two points, $f''$ is zero at atleast two points
asked
Feb 10
in
Calculus
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

24
views
tifr2020
engineeringmathematics
calculus
maximaminima
0
votes
1
answer
9
TIFR2020A7
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent of the other ... . $\dfrac{17}{2401}$ $\dfrac{48}{2401}$ $\dfrac{105}{2401}$ $\dfrac{175}{2401}$ $\dfrac{294}{2401}$
asked
Feb 10
in
Probability
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

25
views
tifr2020
engineeringmathematics
probability
independentevents
0
votes
0
answers
10
TIFR2020A4
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
asked
Feb 10
in
Probability
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

21
views
tifr2020
engineeringmathematics
probability
uniformdistribution
0
votes
1
answer
11
TIFR2020A5
Let $A$ be am $n\times n$ invertible matrix with real entries whose column sums are all equal to $1.$ Consider the following statements: Every column in the matrix $A^{2}$ sums to $2.$ Every column in the matrix $A^{3}$ sums to $3.$ Every column in the matrix $A^{1}$ ... $(1)\:\text{or}\:(2)$ all the $3$ statements $(1),(2),$ and $(3)$ are correct
asked
Feb 10
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

42
views
tifr2020
engineeringmathematics
linearalgebra
matrices
0
votes
0
answers
12
TIFR2020A3
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f'_{a}(w) = 0\},$ where the polynomial function $f_{a}(x)$ ... is a $d$dimensional vector subspace of $\mathbb{R}^{d+1}$ $S$ is a $(d1)$dimensional vector subspace of $\mathbb{R}^{d+1}$ None of the other options
asked
Feb 10
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

18
views
tifr2020
engineeringmathematics
linearalgebra
vectorspace
0
votes
0
answers
13
TIFR2020A2
Let $M$ be a real $n\times n$ matrix such that for every nonzero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
asked
Feb 10
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

30
views
tifr2020
engineeringmathematics
linearalgebra
rankofmatrix
eigenvalue
0
votes
1
answer
14
TIFR2020A1
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
asked
Feb 10
in
Probability
by
Lakshman Patel RJIT
Veteran
(
60.8k
points)

30
views
tifr2020
engineeringmathematics
probability
expectation
0
votes
1
answer
15
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 $B$
asked
Jan 13
in
Probability
by
Satbir
Boss
(
25.1k
points)

281
views
isro2020
probability
standarddeviation
normal
+2
votes
1
answer
16
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
asked
Jan 13
in
Mathematical Logic
by
Satbir
Boss
(
25.1k
points)

306
views
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+1
vote
1
answer
17
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 $(A \cup \bar{B}) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
asked
Jan 13
in
Set Theory & Algebra
by
Satbir
Boss
(
25.1k
points)

176
views
isro2020
discretemathematics
settheory&algebra
sets
easy
0
votes
1
answer
18
$\textbf{NTA NET DEC 2019 (group)}$
Consider the following statements: $\mathbf{S_1:}\;\;$If a group $\mathbf{(G,*)}$ is of order $\mathbf n$ and $\mathrm {a \in G}$ is such that $\mathrm {a^m=e}$ for some integer $\mathrm {m \le n}$ then $\mathbf m$ must divide $\mathbf n$ ... $(3)\;\;\;\text{Niether}\; \mathrm{S_1}\;\text{nor}\;\mathrm{S_2}$
asked
Dec 29, 2019
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.4k
points)

126
views
ugcnetdec2019ii
grouptheory
+1
vote
1
answer
19
NTA NET DEC2019( shortest distance)
Consider a weighted directed graph. The current shortest distance from sources S to node x is represented by d[v] = 29 . d[u] = 15 , w[u,v] = 12. What is the updated value of d[v]based on current information? 1) 29 2) 27 3) 25 4) 17
asked
Dec 22, 2019
in
Graph Theory
by
Sanjay Sharma
Boss
(
49.4k
points)

104
views
+1
vote
0
answers
20
Variation on Birthday Problem
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.
asked
Nov 12, 2019
in
Probability
by
Ayush Upadhyaya
Boss
(
30.6k
points)

189
views
probability
+3
votes
0
answers
21
The Interesting combination sum problems
Find the number of possible solutions for $x,y,z$ for each the following cases. $Case\ 1.$ Case of unlimited repetition. $x + y +z = 10$ and $x \geq 0\ , y \geq 0,\ z \geq 0 $ $Case\ 2 $ Case of unlimited repetition with variable lower bounds $x + y +z = 10$ and ... variable. $x + y +z = 10$ and $8 \geq x \geq 1\ , \ 20 \geq y \geq 2 \ , 12 \geq z \geq 3\ $
asked
Nov 1, 2019
in
Combinatory
by
Satbir
Boss
(
25.1k
points)

227
views
permutationandcombination
+1
vote
0
answers
22
Gravner probability
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
asked
Oct 23, 2019
in
Probability
by
ajaysoni1924
Boss
(
11k
points)

103
views
gravner
probability
engineeringmathematics
+2
votes
2
answers
23
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\left( 1+\dfrac{C_0}{C_1} \right) \left( 1+\dfrac{C_1}{C_2} \right) \cdots \left( 1+\dfrac{C_{n1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $ \frac{(n+1)^n}{n!} $
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
434k
points)

190
views
isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
1
answer
24
ISI2014DCG2
Let $a_n=\bigg( 1 – \frac{1}{\sqrt{2}} \bigg) \cdots \bigg( 1 – \frac{1}{\sqrt{n+1}} \bigg), \: n \geq 1$. Then $\underset{n \to \infty}{\lim} a_n$ equals $1$ does not exist equals $\frac{1}{\sqrt{\pi}}$ equals $0$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
434k
points)

127
views
isi2014dcg
calculus
limits
+4
votes
4
answers
25
ISI2014DCG3
$\underset{x \to \infty}{\lim} \left( \frac{3x1}{3x+1} \right) ^{4x}$ equals $1$ $0$ $e^{8/3}$ $e^{4/9}$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
434k
points)

166
views
isi2014dcg
calculus
limits
+3
votes
2
answers
26
ISI2014DCG4
$\underset{n \to \infty}{\lim} \dfrac{1}{n} \bigg( \dfrac{n}{n+1} + \dfrac{n}{n+2} + \cdots + \dfrac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
434k
points)

130
views
isi2014dcg
calculus
limits
+1
vote
1
answer
27
ISI2014DCG5
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is nonempty none of the above
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

112
views
isi2014dcg
sets
+2
votes
2
answers
28
ISI2014DCG6
If $f(x)$ is a real valued function such that $2f(x)+3f(x)=154x$, for every $x \in \mathbb{R}$, then $f(2)$ is $15$ $22$ $11$ $0$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
434k
points)

107
views
isi2014dcg
calculus
functions
+2
votes
3
answers
29
ISI2014DCG7
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[1 , \sqrt{3}{/2}]$ the interval $[\sqrt{3}{/2}, 1]$ the interval $[1, 1]$ none of these
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
434k
points)

65
views
isi2014dcg
calculus
functions
range
+1
vote
3
answers
30
ISI2014DCG8
If $M$ is a $3 \times 3$ matrix such that $\begin{bmatrix} 0 & 1 & 2 \end{bmatrix}M=\begin{bmatrix}1 & 0 & 0 \end{bmatrix}$ and $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
Veteran
(
434k
points)

142
views
isi2014dcg
linearalgebra
matrices
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