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 tifrmaths2022
0
votes
1
answer
1
TIFR Mathematics 2022 | Part B | Question: 1
Answer whether the following statements are True or False. $\mathbb{R}^{2} \backslash \mathbb{Q}^{2}$ is connected but not path-connected.
admin
asked
in
Others
Sep 9
by
admin
117
views
tifrmaths2022
true-false
0
votes
0
answers
2
TIFR Mathematics 2022 | Part B | Question: 2
Answer whether the following statements are True or False. If $X$ is a connected metric space, and $F$ is a subring of $C(X, \mathbb{R})$ that is a field, then every element of $C(X, \mathbb{R})$ that belongs to $F$ is a constant function.
admin
asked
in
Others
Sep 9
by
admin
72
views
tifrmaths2022
true-false
0
votes
0
answers
3
TIFR Mathematics 2022 | Part B | Question: 3
Answer whether the following statements are True or False. Let $K \subseteq[0,1]$ be the Cantor set. Then there exists no injective ring homomorphism $C([0,1], \mathbb{R}) \rightarrow C(K, \mathbb{R})$.
admin
asked
in
Others
Sep 9
by
admin
46
views
tifrmaths2022
true-false
0
votes
0
answers
4
TIFR Mathematics 2022 | Part B | Question: 4
Answer whether the following statements are True or False. There exists a metric space $(X, d)$ such that the group of isometries of $X$ is isomorphic to $\mathbb{Z}$.
admin
asked
in
Others
Sep 9
by
admin
34
views
tifrmaths2022
true-false
0
votes
0
answers
5
TIFR Mathematics 2022 | Part B | Question: 5
Answer whether the following statements are True or False. Let $A \subset \mathbb{R}^{2}$ be a nonempty subset such that any continuous function $f: A \rightarrow \mathbb{R}$ is constant. Then $A$ is a singleton set.
admin
asked
in
Others
Sep 9
by
admin
24
views
tifrmaths2022
true-false
0
votes
0
answers
6
TIFR Mathematics 2022 | Part B | Question: 6
Answer whether the following statements are True or False. For a nilpotent matrix $A \in \mathrm{M}_{n}(\mathbb{R})$, let \[ \exp (A):=\sum_{n=0}^{\infty} \frac{A^{n}}{n !}=\mathrm{Id}+\frac{A}{1 !}+\frac{A^{2}}{2 !}+\cdots \in \mathrm{M}_{n}(\mathbb{R}) \] If $A$ is a nilpotent matrix such that $\exp (A)=\mathrm{Id}$, then $A$ is the zero matrix.
admin
asked
in
Others
Sep 9
by
admin
38
views
tifrmaths2022
true-false
0
votes
0
answers
7
TIFR Mathematics 2022 | Part B | Question: 7
Answer whether the following statements are True or False. There exists $A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \in \mathrm{M}_{2}(\mathbb{R})$, with $A^{2}=A \neq 0$, such that $|a|+|b|<1 \quad \text{and} \quad|c|+|d|<1.$
admin
asked
in
Others
Sep 9
by
admin
38
views
tifrmaths2022
true-false
0
votes
0
answers
8
TIFR Mathematics 2022 | Part B | Question: 8
Answer whether the following statements are True or False. If $A \in \mathrm{M}_{3}(\mathbb{C})$ is such that $A^{i}$ has trace zero for all positive integers $i$, then $A$ is nilpotent.
admin
asked
in
Others
Sep 9
by
admin
30
views
tifrmaths2022
true-false
0
votes
0
answers
9
TIFR Mathematics 2022 | Part B | Question: 9
Answer whether the following statements are True or False. For any finite cyclic group $G$, there exists a prime power $q$ such that $G$ is a subgroup of $\mathbb{F}_{q}^{\times}.$
admin
asked
in
Others
Sep 9
by
admin
25
views
tifrmaths2022
true-false
0
votes
0
answers
10
TIFR Mathematics 2022 | Part B | Question: 10
Answer whether the following statements are True or False. There are only finitely many isomorphism classes of finite nonabelian groups, all of whose proper subgroups are abelian.
admin
asked
in
Others
Sep 9
by
admin
30
views
tifrmaths2022
true-false
0
votes
0
answers
11
TIFR Mathematics 2022 | Part B | Question: 11
Answer whether the following statements are True or False. Every subring of a unique factorization domain is a unique factorization domain.
admin
asked
in
Others
Sep 9
by
admin
27
views
tifrmaths2022
true-false
0
votes
0
answers
12
TIFR Mathematics 2022 | Part B | Question: 12
Answer whether the following statements are True or False. Let $f_{1}, f_{2}, f_{3}, f_{4} \in \mathbb{R}[x]$ be monic polynomials each of degree exactly two. Then there exist a real polynomial $p \in \mathbb{R}[x]$ and a subset $\{i, j\} \subset\{1,2,3,4\}$ with $i \neq j$, such that $f_{i} \circ p=c f_{j}$ for some $c \in \mathbb{R}$.
admin
asked
in
Others
Sep 9
by
admin
33
views
tifrmaths2022
true-false
0
votes
0
answers
13
TIFR Mathematics 2022 | Part B | Question: 13
Answer whether the following statements are True or False. There exists a finite abelian group $G$ such that the group Aut$(G)$ of automorphisms of $G$ is isomorphic to $\mathbb{Z} / 7 \mathbb{Z}$.
admin
asked
in
Others
Sep 9
by
admin
24
views
tifrmaths2022
true-false
0
votes
0
answers
14
TIFR Mathematics 2022 | Part B | Question: 14
Answer whether the following statements are True or False. There exists an integral domain $R$ and a surjective homomorphism $R \rightarrow R$ of rings that is not injective.
admin
asked
in
Others
Sep 9
by
admin
26
views
tifrmaths2022
true-false
0
votes
0
answers
15
TIFR Mathematics 2022 | Part B | Question: 15
Answer whether the following statements are True or False. There exists $f \in C([0,1], \mathbb{R})$ satisfying the following two conditions: $\int_{0}^{1} f(x) d x=1$; and $\lim _{n \rightarrow \infty} \int_{0}^{1} f(x)^{n} d x=0$.
admin
asked
in
Others
Sep 9
by
admin
28
views
tifrmaths2022
true-false
0
votes
0
answers
16
TIFR Mathematics 2022 | Part B | Question: 16
Answer whether the following statements are True or False. Let $a_{n} \geq 0$ for each positive integer $n$. If the series $\sum_{n=1}^{\infty} \sqrt{a_{n}}$ converges, then so does the series $\sum_{n=1}^{\infty} \frac{a_{n}}{n^{1 / 4}}$.
admin
asked
in
Others
Sep 9
by
admin
23
views
tifrmaths2022
true-false
0
votes
0
answers
17
TIFR Mathematics 2022 | Part B | Question: 17
Answer whether the following statements are True or False. There exists a differentiable function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that \[ \lim _{x \rightarrow \infty} f(x)=2 \quad \text { and } \quad \lim _{x \rightarrow \infty} f^{\prime}(x)=1 .\]
admin
asked
in
Others
Sep 9
by
admin
19
views
tifrmaths2022
true-false
0
votes
0
answers
18
TIFR Mathematics 2022 | Part B | Question: 18
Answer whether the following statements are True or False. Let $f:[0,1] \rightarrow[0, \infty)$ be continuous on $[0,1]$ and twice differentiable in $(0,1)$. If $f^{\prime \prime}(x)=7 f(x)$ for all $x \in(0,1)$, then $f(x) \leq \max \{f(0), f(1)\}$ for all $x \in[0,1]$.
admin
asked
in
Others
Sep 9
by
admin
25
views
tifrmaths2022
true-false
0
votes
1
answer
19
TIFR Mathematics 2022 | Part B | Question: 19
Answer whether the following statements are True or False. There are $N$ balls in a box, out of which $n$ are blue $(1 < n < N)$ and the rest are red. Balls are drawn from the box one by one at random, and discarded. Then the ... in the first $n$ drawn is the same as the probability of picking all the red balls in the first $(N - n)$ draws.
admin
asked
in
Others
Sep 9
by
admin
61
views
tifrmaths2022
true-false
0
votes
0
answers
20
TIFR Mathematics 2022 | Part B | Question: 20
Answer whether the following statements are True or False. The set $\{f(x) \in \mathbb{R}[x] \mid f(n) \in \mathbb{Z}$ for all $n \in \mathbb{Z}\}$ is uncountable.
admin
asked
in
Others
Sep 9
by
admin
30
views
tifrmaths2022
true-false
0
votes
0
answers
21
TIFR Mathematics 2022 | Part A | Question: 1
Consider the following properties of a metric space $(X, d)$ : $(X, d)$ is complete as a metric space. For any sequence $\left\{Z_{n}\right\}_{n \in \mathbb{N}}$ of closed nonempty subsets of $X$, such that $Z_{1} \supseteq Z_{2} \supseteq$ ... (I). (I) does not imply (II) but (II) implies (I). (I) does not imply (II) and (II) does not imply (I).
admin
asked
in
Others
Sep 9
by
admin
30
views
tifrmaths2022
0
votes
0
answers
22
TIFR Mathematics 2022 | Part A | Question: 2
Consider the following assertions: $\left\{(x, y) \in \mathbb{R}^{2} \mid x y=1\right\}$ is connected. $\left\{(x, y) \in \mathbb{C}^{2} \mid x y=1\right\}$ is connected. Which of the following sentences is true? Both (I) and (II) are true. (I) is true but (II) is false. (I) is false but (II) is true. Both (I) and (II) are false.
admin
asked
in
Others
Sep 9
by
admin
33
views
tifrmaths2022
0
votes
0
answers
23
TIFR Mathematics 2022 | Part A | Question: 3
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]$ ? $0$ $1$ $2$ $\infty$
admin
asked
in
Others
Sep 9
by
admin
29
views
tifrmaths2022
0
votes
0
answers
24
TIFR Mathematics 2022 | Part A | Question: 4
Let $A$ be an element of $\mathrm{M}_{4}(\mathbb{R})$ with characteristic polynomial $t^{4}-t$. What is the characteristic polynomial of $A^{2}$ ? $t^{4}-t$ $t^{4}-2 t^{3}+t^{2}$ $t^{4}-t^{2}$ None of the other three options
admin
asked
in
Others
Sep 9
by
admin
39
views
tifrmaths2022
0
votes
0
answers
25
TIFR Mathematics 2022 | Part A | Question: 7
What is the cardinality of the set of $\theta \in[0,2 \pi)$ such that the linear map $\mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ given by the matrix: \[ \left(\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right) \] has an eigenvector in $\mathbb{R}^{2}$ ? $1$ $2$ $4$ $\infty$
admin
asked
in
Others
Sep 9
by
admin
24
views
tifrmaths2022
0
votes
0
answers
26
TIFR Mathematics 2022 | Part A | Question: 8
Let $p$ be a prime number, and let $A$ equal $\left(\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right)$, viewed as a $2 \times 2$ matrix with integer entries. What is the smallest positive integer $n$ such that the matrix $A^{n}$ is congruent to the $2 \times 2$ identity matrix modulo $p$? $p^{2}-1$ $p-1$ $p$ $p+1$
admin
asked
in
Others
Sep 9
by
admin
23
views
tifrmaths2022
0
votes
0
answers
27
TIFR Mathematics 2022 | Part A | Question: 9
What is the largest value of $n$ for which there exists a set $\left\{A_{1}, \ldots, A_{n}\right\}$ of (distinct) nonzero matrices in $\mathrm{M}_{2}(\mathbb{C})$ such that $A_{i}^{*} A_{j}$ has trace zero for all $1 \leq i < j \leq n?$ $1$ Greater than $1$ but at most $4$ Greater than $4$ but finite $\infty$
admin
asked
in
Others
Sep 9
by
admin
24
views
tifrmaths2022
0
votes
0
answers
28
TIFR Mathematics 2022 | Part A | Question: 10
Let $p$ be a prime number. What is the number of elements in the group $\mathbb{Q} / \mathbb{Z}$ that have order exactly $p$? $0$ $p=1$ $p$ $\infty$
admin
asked
in
Others
Sep 9
by
admin
21
views
tifrmaths2022
0
votes
0
answers
29
TIFR Mathematics 2022 | Part A | Question: 11
Consider the real polynomial \[ f(x)=x^{11}-x^{7}+x^{2}-1 \] Which of the following sentences is correct? $f(x)$ has exactly one positive root. $f(x)$ has exactly two positive roots. $f(x)$ has at least three positive roots. None of the other three options.
admin
asked
in
Others
Sep 9
by
admin
24
views
tifrmaths2022
0
votes
0
answers
30
TIFR Mathematics 2022 | Part A | Question: 12
Consider polynomials \[ f_{1}(x, y)=\sum_{i, j=0}^{\infty} a_{i j} x^{i} y^{j} \quad \text { and } \quad f_{2}(x, y)=\sum_{i, j=0}^{\infty} b_{i j} x^{i} y^{j} \in \mathbb{R}[x, y] \] (where $a_{i j}=b_{i j}=0$ ... $(i, j)$ with $i+j=3$. $a_{i j}=b_{i j}$ if $i+j \leq 3$, but we may not have $f_{1}=f_{2}$.
admin
asked
in
Others
Sep 9
by
admin
25
views
tifrmaths2022
Page:
1
2
next »
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
POWER GRID CORPORATION OF INDIA LIMITED
INSTITUTE OF BANKING PERSONNEL SELECTION
GATE Overflow books for TIFR, ISRO, UGCNET and NIELIT
RECRUITMENT IN OIL AND GAS CORPORATION LIMITED
Aptitude Overflow Book
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
(647)
Exam Queries
(841)
Tier 1 Placement Questions
(17)
Job Queries
(74)
Projects
(9)
Unknown Category
(855)
Recent questions tagged tifrmaths2022
Recent Blog Comments
@abir_banerjee Thanks Abir. I'm third year...
@nolan_keats Currently I am in third year...
@abir_banerjee thank you Abir.Supposing you...
@nolan_keats just a suggestion as I also...
@abir_banerjee Hope I can do this in span of one...