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+5
votes
1
answer
1
Gilbert Strang
How many n*n (0,1) matrix are invertable ? PS: original question in book is for 2*2
asked
Oct 23
in
Linear Algebra

85
views
matrix
gilbertstrang
linearalgebra
+1
vote
0
answers
2
Self Doubt
Let < G, * > be a finite group and let H1 and H2 be it's sub group as per lagrange theorem we know order of sub group divides order of group, my doubt is, is it possible that we can have multiple subgroup of same cardinality for a particular group ? $\left  H1 \right =\left  H2 \right $
asked
Oct 21
in
Set Theory & Algebra

39
views
groups
#grouptheory
#discrete
+1
vote
1
answer
3
Tremblay and Manohar
S={2,a,{3},4} and R={{a},3,4,1} indicate whether the following are true or false 1) $\varnothing \subset R$ 2)$\varnothing \subseteq \left \{ \left \{ a \right \} \right \}\subseteq R\subseteq E$ E=Universal Set 3) $\left \{ \varnothing \right \}\subseteq S$ 4) $\varnothing \in R$ I think 1,2 are true and 3 is false and about 4 nothing is clear
asked
Jul 26
in
Set Theory & Algebra

90
views
discretemathematics
settheory&algebra
+1
vote
1
answer
4
Set Theory Doubt
Want to verify let set $\left  A \right =n$ and $\left  B \right =m$ Then $max(m,n)\leq \left  A\cup B \right \leq (m+n)$ $0\leq \left  A\cap B \right \leq min(m,n)$ $0\leq \left  A B \right \ ... here $\bigoplus$ is symmetric difference $0\leq \left  \overline{A} \right \leq U$ here $\overline{A}$ is compliment of A and U is universal Set
asked
Jul 25
in
Set Theory & Algebra

63
views
discretemathematics
settheory&algebra
sets
0
votes
1
answer
5
IIITHPGEE 2017
Consider 3 card one having both side painted red another having both side printed black and last having one side black and another side red, 3 cards are put in a hat and are mixed properly, now one card in picked and put down on table, its face up color is red what is probability that another side will be black.
asked
Apr 30
in
Probability

170
views
iiithpgee
probability
0
votes
1
answer
6
PGEE 2017
P1: Number of onetoone function from A$\bigotimes A$ is 1. P2: Function A>B is bijective C>D is bijective then AC and BD is also bijective. P3: Consider set A,B,C,D then ($A\cup B\cap C\cup D) == (A\cap B\cup C\cap D$) which of above statement are true and which are false
asked
Apr 30
in
Set Theory & Algebra

135
views
iiithpgee
discretemathematics
settheory&algebra
0
votes
2
answers
7
PGEE 2017
Consider a graph where vertex having number 2 to 12 (including 2 and 12), there is an edge between two vertex x and y iff x divides y What would be maximum path length between any two vertices of graph ?
asked
Apr 30
in
Graph Theory

132
views
iiithpgee
graphtheory
+1
vote
1
answer
8
PGEE 2017
Consider a graph where vertex having number 2 to 12 (including 2 and 12), there is an edge between two vertex x and y iff x divides y Which vertex will have highest in degree ?
asked
Apr 30
in
Graph Theory

70
views
iiithpgee
graphtheory
0
votes
0
answers
9
PGEE 2017
Consider a graph where vertex having number 2 to 12 (including 2 and 12), there is an edge between two vertex x and y iff x divides y Find number of strongly connected components
asked
Apr 30
in
Graph Theory

73
views
iiithpgee
graphtheory
connectedcomponents
+1
vote
2
answers
10
PGEE 2017
$\int_{3}^{3} \left  X+1 \right dx$
asked
Apr 30
in
Calculus

88
views
iiithpgee
calculus
+1
vote
0
answers
11
ISI 2013 Subjective
Q C4 b) If it is known that the language L1=$\left \{ 0^{n}1^{n}2^{i}\mid n\neq i \right \}$ is not a context free language (CFL). Now consider the language L2=$\left \{ 0^{i}1^{n}2^{n}\mid i\neq ... not CFL by converting L2 into L1 by applying two operation, both know to be closed on CFLs. What are two operation you will use for this construction.
asked
Apr 5
in
Theory of Computation

70
views
isi2013
theoryofcomputation
contextfreelanguages
+1
vote
1
answer
12
ISI 2004 MIII
Q23 If $\textit{f}(x)=x^{2}$ and g(x)=x sinx +cosx then A) f and g agree at no point B) f and g agree at exactly one point C) f and g agree at exactly two point D) f and g agree at more then two point
asked
Apr 5
in
Calculus

131
views
isi2004
engineeringmathematics
functions
+2
votes
1
answer
13
ISI 2004 MIII
Q22 If $\textit{f}(x)=\frac{\sqrt{3}sinx}{2+cosx}$ then the range of $\textit{f}(x)$ is A) the interval [1,$\frac{\sqrt{3}}{2}$] B) the interval [$\frac{\sqrt{3}}{2}$,1] C) the interval [1.1] D) none of the above
asked
Apr 5
in
Calculus

93
views
isi2004
engineeringmathematics
functions
+1
vote
0
answers
14
ISI 2004 MIII
Let X be an nonempty set and let P(X) denote the collection of all subset of X. Define $\textit{f}:\textit{X*P(X)}\rightarrow \mathbb{R}$ by f(x,A) = $\left\{\begin{matrix} 1 if x \epsilon A & \\ 0 if x\not\epsilon A & \end{matrix}\right.$ Then $f\left ( x,A\cup B ... 1 C) f(x,A)+f(x,B)  f(x,A).f(x,B). D) f(x,A)+ $\left  f(x,A)f(x,B) \right $
asked
Apr 5
in
Mathematical Logic

121
views
isi2004
discretemathematics
+1
vote
3
answers
15
Gate math book
Find the sum of n terms of the series $log a+ log \frac{a^{2}}{b} + log \frac{a^{3}}{b^{2}}+ ...$ to n terms
asked
Apr 5
in
Mathematical Logic

95
views
engineeringmathematics
+1
vote
1
answer
16
ISI 2004 MIII
Q14 The inequality $\frac{2gx+x^{2}}{1x+x^{2}}\leq 3$ is true for all the value of x if and only if A) $1\leq g\leq 7$ B) $1\leq g\leq 1$ C) $6\leq g\leq 7$ D) $1\leq g\leq 7$
asked
Apr 4
in
Set Theory & Algebra

94
views
isi2004
inequality
+1
vote
2
answers
17
ISI 2004 MIII
Q13 Let X= $\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+...+\frac{1}{3001}$. Then A) X$< 1$ B) X>$\frac{3}{2}$ C) $1< X< \frac{3}{2}$ D) none of the above
asked
Apr 4
in
Calculus

151
views
isi2004
engineeringmathematics
integration
+2
votes
1
answer
18
ISI 2004 MIII
Q12 The maximum possible value of xy2z3 subjected to condition x,y,z$\geq 0$ and x+y+z=3 is A) 1 B) $\frac{9}{8}$ C) $\frac{9}{4}$ D) $\frac{27}{16}$
asked
Apr 4
in
Calculus

134
views
isi2004
engineeringmathematics
maximaminima
0
votes
1
answer
19
ISI 2004 MIII
Q11 If $\alpha 1,\alpha 2,\dots,\alpha n$ are the positive numbers then $\frac{a1}{a2}+\frac{a2}{a3}+\dots+\frac{an1}{an}+\frac{an}{a1}$ is always A) $\geq n$ B) $\leq n$ C) $\leq n^{\frac{1}{2}}$ D) None of the above
asked
Apr 4
in
Set Theory & Algebra

106
views
isi2004
settheory&algebra
numbertheory
+1
vote
1
answer
20
ISI 2004 MIII
Q10 The equation $p\left ( x \right ) = \alpha$ where $p\left ( x \right ) = x^{4}+4x^{3}2x^{2}12x$ has four distinct real root if and only if A) $p\left ( 3 \right )<\alpha$ B) $p\left ( 1 \right )>\alpha$ C) $p\left ( 1 \right )<\alpha$ D) $p\left ( 3 \right )<\alpha <p\left ( 1 \right )$
asked
Apr 3
in
Set Theory & Algebra

45
views
isi2004
polynomials
+1
vote
1
answer
21
ISI 2004 MIII
Q9 The equation' $\frac{1}{3}+\frac{1}{2}s^{2}+\frac{1}{6}s^{3}=s$ has A) exactly three solution in [0.1] B) exactly one solution in [0,1] C) exactly two solution in [0,1] D) no solution in [0,1]
asked
Apr 3
in
Set Theory & Algebra

53
views
isi2004
polynomials
+1
vote
1
answer
22
ISI 2004 MIII
Q8 If $\alpha 1,\alpha 2,\alpha 3....\alpha n$ be the roots of $x^{n}+1=0$, then $\left ( 1\alpha 1 \right )*\left ( 1\alpha 2 \right )...\left ( 1\alpha n \right )$ is equal to A) 1 B) 0 C) n D) 2
asked
Apr 3
in
Set Theory & Algebra

30
views
isi2004
polynomials
+2
votes
2
answers
23
ISI 2004 MIII
Q7 The equation $x^{6}5x^{4}+16x^{2}72x+9=0$ has A) Exactly two distinct real roots B) Exactly three distinct real roots C) Exactly four distinct real roots D) six different real roots
asked
Apr 3
in
Set Theory & Algebra

112
views
isi2004
polynomials
+1
vote
1
answer
24
ISI 2004 MIII
Q6 If the equation $x^{4}+ax^{3}+bx^{2}+cx+1=0$ (where a,b,c are real number) has no real roots and if at least one of the root is of modulus one, then A) b=c B) a=c C) a=b D) none of this
asked
Apr 3
in
Set Theory & Algebra

32
views
isi2004
polynomials
0
votes
1
answer
25
ISI 2004 MIII
Q5 $x^{2}+x+1$ is a factor of $\left ( x+1 \right )^{n}x^{n}1$ whenever A) n is odd B) n is odd and multiple of 3 C) n is an even multiple of 3 D) n is odd and not a multiple of 3
asked
Apr 3
in
Set Theory & Algebra

32
views
factors
isi2004
engineeringmathematics
+7
votes
3
answers
26
ISI 2004 MIII
In how many ways can three person, each throwing a single die once, make a score of 11 22 27 24 38
asked
Apr 3
in
Combinatory

271
views
permutationsandcombinations
isi2004
+5
votes
4
answers
27
ISI 2004 MIII
A subset S of set of numbers {2,3,4,5,6,7,8,9,10} is said to be good if has exactly 4 elements and their gcd=1, Then number of good subset is 126 125 123 121
asked
Apr 3
in
Combinatory

220
views
permutationsandcombinations
isi2004
+7
votes
3
answers
28
ISI 2004 MIII
A club with x members is organized into four committees such that each member is in exactly two comittees, any two committees have exactly one member in common . Then $x$ has exactly two values both between 4 and 8. exactly one value and this lies between 4 and 8. exactly two values both between 8 and 16. exactly one value and this lies between 8 and 16.
asked
Apr 3
in
Combinatory

158
views
permutationsandcombinations
isi2004
+4
votes
2
answers
29
ISI 2004 MIII
The number of permutation of {1,2,3,4,5} that keep at least one integer fixed is. 81 76 120 60
asked
Apr 3
in
Combinatory

159
views
permutationsandcombinations
isi2004
0
votes
2
answers
30
Graph Theory
let G=(V,E) be an connected graph, let $\left  V \right = n$ Find largest value of n such that i) G is complete & ii) G is bipartite with valid proof
asked
Apr 2
in
Algorithms

94
views
graphtheory
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