Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Recent questions tagged isi2020-pcb-mathematics
0
votes
0
answers
1
ISI 2020 | PCB Mathematics | Question: 5.2
Deduce that if $N, H, K$ are normal subgroups of a group $G$ such that $ N \bigcap H=N \bigcap K=H \bigcap K=\left\{e_{G}\right\} $ and $G=H K$, then $N$ is an Abelian group.
Lakshman Patel RJIT
asked
in
Others
Aug 25
by
Lakshman Patel RJIT
26
views
isi2020-pcb-mathematics
descriptive
0
votes
0
answers
2
ISI 2020 | PCB Mathematics | Question: 1
Let $\epsilon>0$. Prove that there exists $n_{0} \in \mathbb{N}$ such that $ n \geq n_{0} \Rightarrow 2-\epsilon<\frac{2 n+1}{n+2}<2+\epsilon. $
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
20
views
isi2020-pcb-mathematics
descriptive
0
votes
0
answers
3
ISI 2020 | PCB Mathematics | Question: 2
Show that the sequence $\left\{x_{n}\right\}, n>0$, defined by $ x_{n}=\int_{1}^{n} \frac{\cos (t)}{t^{2}} d t $ is convergent.
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
20
views
isi2020-pcb-mathematics
descriptive
0
votes
1
answer
4
ISI 2020 | PCB Mathematics | Question: 3
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$. Prove that $I+A$ is an invertible matrix, where $I$ is the $(n \times n)$ identity matrix. Find the characteristic polynomial of $A$.
Lakshman Patel RJIT
asked
in
Linear Algebra
Aug 8
by
Lakshman Patel RJIT
55
views
isi2020-pcb-mathematics
descriptive
linear-algebra
matrix
0
votes
1
answer
5
ISI 2020 | PCB Mathematics | Question: 4
Let $c$ be a positive real number for which the equation $ x^{4}-x^{3}+x^{2}-(c+1) x-\left(c^{2}+c\right)=0 $ has a real root $\alpha$. Prove that $c=\alpha^{2}-\alpha$.
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
28
views
isi2020-pcb-mathematics
descriptive
0
votes
0
answers
6
ISI 2020 | PCB Mathematics | Question: 5.1
Prove that if $N$ and $K$ are normal subgroups of a group $G$ such that $N \cap K=\left\{e_{G}\right\}$, then $x y=y x, \forall x \in N, \forall y \in K$.
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
33
views
isi2020-pcb-mathematics
descriptive
0
votes
1
answer
7
ISI 2020 | PCB Mathematics | Question: 6
Find all possible integers $n$ for which $n^{2}+20 n+15$ is a perfect square.
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
81
views
isi2020-pcb-mathematics
descriptive
0
votes
1
answer
8
ISI 2020 | PCB Mathematics | Question: 7
Let $A=\{1,2,3, \cdots, 50\}$. In how many ways can three distinct numbers $x<y<z$ be chosen from $A$ such that the product $x y z$ is divisible by $125?$
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
79
views
isi2020-pcb-mathematics
descriptive
0
votes
0
answers
9
ISI 2020 | PCB Mathematics | Question: 8
Prove that the function defined by $ f(x)=\sum_{n=0}^{\infty}\left(\frac{x^{n}}{n !}\right)^{2} $ is continuous on $\mathbb{R}$, for any real number $x$.
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
19
views
isi2020-pcb-mathematics
descriptive
0
votes
0
answers
10
ISI 2020 | PCB Mathematics | Question: 9
Let $X_{i} \sim\left(i . i . d\right.$.) Bernoulli $\left(\frac{\lambda}{n}\right), n \geq \lambda \geq 0$. $Y_{i} \sim\left(\right. i. i. d.)$ Poisson $\left(\frac{\lambda}{n}\right),\left\{X_{i}\right\}$ and $\left\{Y_{i}\right\}$ ... $\dfrac{T_{n}}{S_{n}}$ as $n \rightarrow \infty.$
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
13
views
isi2020-pcb-mathematics
descriptive
0
votes
0
answers
11
ISI 2020 | PCB Mathematics | Question: 10
Prove that if $T_{1}, T_{2}, \ldots, T_{k}$ are pairwise-intersecting subtrees of a tree $T$, then $T$ has a vertex that belongs to all of $T_{1}, T_{2}, \ldots, T_{k}$.
Lakshman Patel RJIT
asked
in
Others
Aug 8
by
Lakshman Patel RJIT
17
views
isi2020-pcb-mathematics
descriptive
To see more, click for the
full list of questions
or
popular tags
.
Subscribe to GATE CSE 2023 Test Series
Subscribe to GO Classes for GATE CSE 2023
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Life happens, just chill and do hardwork
ISRO RECRUITMENT FOR SCIENTIST B THROUGH GATE
POWER GRID CORPORATION OF INDIA LIMITED
INSTITUTE OF BANKING PERSONNEL SELECTION
GATE Overflow books for TIFR, ISRO, UGCNET and NIELIT
Subjects
All categories
General Aptitude
(2.4k)
Engineering Mathematics
(9.1k)
Digital Logic
(3.2k)
Programming and DS
(5.8k)
Algorithms
(4.5k)
Theory of Computation
(6.6k)
Compiler Design
(2.3k)
Operating System
(4.9k)
Databases
(4.5k)
CO and Architecture
(3.7k)
Computer Networks
(4.5k)
Non GATE
(1.3k)
Others
(2.4k)
Admissions
(648)
Exam Queries
(841)
Tier 1 Placement Questions
(17)
Job Queries
(74)
Projects
(9)
Unknown Category
(855)
Recent questions tagged isi2020-pcb-mathematics
Recent Blog Comments
Maximum age limit changed from 35 yrs. to 28...
Hmm, sir totally getting your point ☺️☺️....
yes, that's fine. But saying so in a public forum...
@gatecse Sir , I know you are correct. I just...
@Deepanshu I have to disagree there...