Register
Filter

Recent questions in Others

0 votes
0 answers
1301
TIFR2021-Maths-B: 8
Let $f:[0,1]\rightarrow{\mathbb{R}}$ be a monotone increasing (not necessarily continuous) function such that $f(0)>0$ and $f(1)<1$. Then there exists $x\in[0,1]$ such that $f(x)=x$.
Let $f:[0,1]\rightarrow{\mathbb{R}}$ be a monotone increasing (not necessarily continuous) function such that $f(0)>0$ and $f(1)<1$. Then there exists $x\in[0,1]$ such th...
User Avatar
0 votes
0 answers
1302
TIFR2021-Maths-B: 9
The set $\{(x,y)\in \mathbb{N}\times\mathbb{N}| x^y \text{ divides } y^x,\:x\neq y,\:xy\neq0,\:x\neq1\}$ is finite.
The set$$\{(x,y)\in \mathbb{N}\times\mathbb{N}| x^y \text{ divides } y^x,\:x\neq y,\:xy\neq0,\:x\neq1\}$$is finite.
User Avatar
0 votes
0 answers
1303
TIFR2021-Maths-B: 10
Suppose a line segment of a fixed length $L$ is given. It is possible to construct a triangle of perimeter $L$, whose angles are $105^{\circ},\: 45^{\circ} \text{ and } 30^{\circ}$, using only a straight edge and a compass.
Suppose a line segment of a fixed length $L$ is given. It is possible to construct a triangle of perimeter $L$, whose angles are $105^{\circ},\: 45^{\circ} \text{ and } 3...
User Avatar
1 votes
0 answers
1304
TIFR2021-Maths-B: 11
The real vector space $M_n(\mathbb{R})$ cannot be spanned by nilpotent matrices, for any positive integer $n$.
The real vector space $M_n(\mathbb{R})$ cannot be spanned by nilpotent matrices, for any positive integer $n$.
User Avatar
0 votes
0 answers
1305
TIFR2021-Maths-B: 12
Let $S \subseteq M_n(\mathbb{R})$ be a nonempty finite set closed under matrix multiplication. Then there exists $A\in S$ such that the trace of $A$ is an integer.
Let $S \subseteq M_n(\mathbb{R})$ be a nonempty finite set closed under matrix multiplication. Then there exists $A\in S$ such that the trace of $A$ is an integer.
User Avatar
0 votes
0 answers
1306
TIFR2021-Maths-B: 13
Given a linear transformation $T:\mathbb{Q}^4\rightarrow\mathbb{Q}^4$, there exists a nonzero proper subspace $V$ of $\mathbb{Q}^4$ such that $T(V)\underline\subset V.$
Given a linear transformation $T:\mathbb{Q}^4\rightarrow\mathbb{Q}^4$, there exists a nonzero proper subspace $V$ of $\mathbb{Q}^4$ such that $T(V)\underline\subset V.$
User Avatar
0 votes
0 answers
1307
TIFR2021-Maths-B: 14
If G is a finite group such that the group $\text{Aut}(G)$ of automorphisms of $G$ is cyclic, then $G$ is abelian.
If G is a finite group such that the group $\text{Aut}(G)$ of automorphisms of $G$ is cyclic, then $G$ is abelian.
User Avatar
0 votes
0 answers
1308
TIFR2021-Maths-B: 15
There exists a countable group having uncountably many subgroups.
There exists a countable group having uncountably many subgroups.
User Avatar
0 votes
0 answers
1309
TIFR2021-Maths-B: 16
There exists a nonzero ideal $I \subseteq \mathbb{Z}[i]$ such that the quotient ring $\mathbb{Z}[i]/I$ is infinite $($here $i$ is a square root of $-1$ in $\mathbb{C})$.
There exists a nonzero ideal $I \subseteq \mathbb{Z}[i]$ such that the quotient ring $\mathbb{Z}[i]/I$ is infinite $($here $i$ is a square root of $-1$ in $\mathbb{C})$.
User Avatar
0 votes
0 answers
1310
TIFR2021-Maths-B: 17
There exists an injective ring homomorphism from the ring $\mathbb{Q}[x,y]/(x^2-y^2)$ into the ring $\mathbb{Q}[x,y]/(x-y^2)$.
There exists an injective ring homomorphism from the ring $\mathbb{Q}[x,y]/(x^2-y^2)$ into the ring $\mathbb{Q}[x,y]/(x-y^2)$.
User Avatar
0 votes
0 answers
1311
TIFR2021-Maths-B: 18
The set $\{n\in\mathbb{N} | n \text{ divides } a^3-1, \text{ for all integers } \text{$a$ such that gcd}(a,n)=1\}$ is infinite.
The set $$\{n\in\mathbb{N} | n \text{ divides } a^3-1, \text{ for all integers } \text{$a$ such that gcd}(a,n)=1\}$$is infinite.
User Avatar
0 votes
0 answers
1312
TIFR2021-Maths-B: 19
The set of polynomials in the ring $\mathbb{Z}[x]$, the sum of whose coefficients is zero, forms an ideal of the ring $\mathbb{Z}[x]$.
The set of polynomials in the ring $\mathbb{Z}[x]$, the sum of whose coefficients is zero, forms an ideal of the ring $\mathbb{Z}[x]$.
User Avatar
0 votes
0 answers
1313
TIFR2021-Maths-B: 20
Let $c_1,c_2>0,$ and let $f,g:\mathbb{R}\rightarrow\mathbb{R}$ be functions (not assumed to be continuous) such that for all $x\in \mathbb{R}$ $f(x+c_1)=f(x) \text{ and } g(x+c_2)=g(x).$ Further, assume that $\displaystyle \lim_{x\rightarrow\infty}(f(x)-g(x))=0.$ Then $f=g.$
Let $c_1,c_2>0,$ and let $f,g:\mathbb{R}\rightarrow\mathbb{R}$ be functions (not assumed to be continuous) such that for all $x\in \mathbb{R}$$$f(x+c_1)=f(x) \text{ and }...
User Avatar
0 votes
1 answer
1315
all tests and quiz are paid or not
all test is paid or not
all test is paid or not
User Avatar
4 votes
6 answers
1318
UGC NET CSE | December 2019 | Part 2 | Question: 3
The Boolean expression $AB+A \overline{B}+\overline{A}C+AC$ is unaffected by the value of the Boolean variable _________. $A$ $B$ $C$ $A, B$ and $C$
The Boolean expression $AB+A \overline{B}+\overline{A}C+AC$ is unaffected by the value of the Boolean variable _________.$A$$B$$C$$A, B$ and $C$
User Avatar
Page: