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1
vote
1
answer
1
TIFR-2012-Maths-A: 1
True/False Question: If $H_{1}$ & $H_{2}$ are subgroups of a group $G$ then $H_{1} .H_{2}=\left \{ h_{1} h_{2}\in G \mid h_{1}\in H_{1},h_{2}\in H_{2}\right \}$ is a subgroup of $G$.
soujanyareddy13
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TIFR
Aug 30, 2020
by
soujanyareddy13
273
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tifrmaths2012
0
votes
2
answers
2
TIFR-2012-Maths-B: 17
True/False Question: If the equation $xyz=1$ holds in a group $G$, does it follow that $yxz=1$.
soujanyareddy13
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TIFR
Aug 30, 2020
by
soujanyareddy13
266
views
tifrmaths2012
0
votes
1
answer
3
TIFR-2019-Maths-B: 5
True/False Question : Suppose $A,B,C$ are $3\times3$ real matrices with Rank $A =2$, Rank $B=1$, Rank $C=2$. Then Rank $(ABC)=1$.
soujanyareddy13
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TIFR
Aug 29, 2020
by
soujanyareddy13
268
views
tifrmaths2019
true-false
1
vote
1
answer
4
TIFR-2012-Maths-D: 34
True/False Question: If a rectangle $R:=\left \{ \left ( x,y \right ) \in \mathbb{R}^{2}\mid A\leq x\leq B,C\leq y\leq D\right \}$ can be covered (allowing overlaps ) by $25$ discs of radius $1$ then it can also be covered by $101$ dics of radius $\frac{1}{2}.$
soujanyareddy13
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TIFR
Aug 30, 2020
by
soujanyareddy13
447
views
tifrmaths2012
1
vote
1
answer
5
TIFR-2012-Maths-D: 31
True/False Question: $f : \left [ 0,\infty \right ]\rightarrow \left [ 0,\infty \right ]$ is continuous and bounded then $f$ has a fixed point.
soujanyareddy13
asked
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TIFR
Aug 30, 2020
by
soujanyareddy13
714
views
tifrmaths2012
0
votes
1
answer
6
TIFR-2013-Maths-A: 3
True/False Question : The equation $x^{3}+3x-4=0$ has exactly one real root.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
316
views
tifrmaths2013
true-false
1
vote
1
answer
7
TIFR-2012-Maths-D: 33
True/False Question: The matrix $\begin{pmatrix} 1 & \pi &3 \\ 0& 2&4 \\ 0&0 &3 \end{pmatrix}$ is diagonalisable.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
374
views
tifrmaths2012
0
votes
1
answer
8
TIFR-2012-Maths-D: 39
True/False Question: If $z_{1},z_{2},z_{3},z_{4}\in \mathbb{C}$ satisfy $z_{1}+z_{2}+z_{3}+z_{4}=0$ and $\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+\left | z_{3} \right |^{2}+\left | z_{4} \right |^{2}=1$ ... $2$.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
375
views
tifrmaths2012
0
votes
1
answer
9
TIFR-2012-Maths-D: 32
True/False Question: The polynomial $X^{8}+1$ is irreducible in $\mathbb{R}\left [ X \right ]$.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
294
views
tifrmaths2012
0
votes
0
answers
10
TIFR-2018-Maths-B: 8
Consider the following four sets of maps $f:\mathbb{Z}\rightarrow \mathbb{Q}$: $\{f:\mathbb{Z}\rightarrow \mathbb{Q} \mid f$ is bijective and increasing$\}$, $\{f:\mathbb{Z}\rightarrow \mathbb{Q} \mid f$ is onto and increasing$\}$ ... $\}$. How many of these sets are empty? $0$ $1$ $2$ $3$
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
540
views
tifrmaths2018
0
votes
1
answer
11
TIFR-2012-Maths-B: 12
True/False Question: Let $V$ be the vector space of consisting polynomials of $\mathbb{R}\left [ t \right ]$ of deg$\leq 2$. The map $T:V\rightarrow V$ sending $f\left ( t \right )$ to $f\left ( t \right )+{f}'\left ( t \right )$ is invertible.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
328
views
tifrmaths2012
0
votes
1
answer
12
TIFR-2012-Maths-B: 11
True/False Question: The automorphism group $Aut\left ( \mathbb{Z}/2\times \mathbb{Z}/2 \right )$ is abelian.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
470
views
tifrmaths2012
1
vote
0
answers
13
TIFR-2012-Maths-B: 19
True/False Question: The rank of the matrix $\begin{bmatrix} 11 &12 &13 &14 \\ 21& 22 &23 & 24\\ 31& 32 &33 &34 \\ 41&42 & 43 & 44 \end{bmatrix}$ is $2$.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
452
views
tifrmaths2012
0
votes
1
answer
14
TIFR-2012-Maths-B: 13
True/False Question: The polynomials $\left ( t-1 \right )\left ( t-2 \right ),\left ( t-2 \right )\left ( t-3 \right ),\left ( t-3 \right )\left ( t-4 \right ),\left ( t-4 \right )\left ( t-6 \right )\in \mathbb{R}\left [ t \right ]$ are linearly independent.
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
294
views
tifrmaths2012
0
votes
0
answers
15
TIFR-2018-Maths-B: 11
Consider a cube $C$ centered at the origin in $\mathbb{R^{3}}$. The number of invertible linear transformation of $\mathbb{R^{3}}$ which map $C$ onto itself is $72$ $48$ $24$ $12$
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
444
views
tifrmaths2018
0
votes
1
answer
16
TIFR-2019-Maths-B: 2
True/False Question : If $A \in M_{10} \left ( \mathbb{R} \right )$ satisfies $A^{2}+A+I=0$, then $A$ is invertible.
soujanyareddy13
asked
in
TIFR
Aug 29, 2020
by
soujanyareddy13
328
views
tifrmaths2019
true-false
0
votes
1
answer
17
TIFR-2020-Maths-A: 2
Consider the set of continuous functions $f:\left [ 0,1 \right ]\rightarrow \mathbb{R}$ that satisfy: $\int_{0}^{1}f\left ( x \right )\left ( 1-f\left ( x \right ) \right )dx=\frac{1}{4}.$ Then the cardinality of this set is: $0$. $1$. $2$. more than $2$.
soujanyareddy13
asked
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TIFR
Aug 28, 2020
by
soujanyareddy13
484
views
tifrmaths2020
0
votes
1
answer
18
TIFR-2018-Maths-A: 7
True/False Question : In the vector space $\left \{ f \mid f : \left [ 0,1 \right ] \rightarrow \mathbb{R}\right \}$ of real-valued functions on the closed interval $\left [ 0,1 \right ]$, the set $S=\left \{ sin\left ( x \right ) , cos\left ( x \right ),tan\left ( x \right )\right \}$ is linearly independent.
soujanyareddy13
asked
in
TIFR
Aug 29, 2020
by
soujanyareddy13
321
views
tifrmaths2018
true-false
0
votes
1
answer
19
TIFR-2017-Maths-A: 30
True/False Question : The matrices $\begin{pmatrix} x &0 \\ 0 & y \end{pmatrix} and \begin{pmatrix} x &1 \\ 0 & y \end{pmatrix}, x\neq y,$ for any $x,y \in \mathbb{R}$ are conjugate in $M_{2}\left ( \mathbb{R} \right )$ .
soujanyareddy13
asked
in
TIFR
Aug 30, 2020
by
soujanyareddy13
306
views
tifrmaths2017
true-false
0
votes
1
answer
20
TIFR-2017-Maths-A: 29
True/False Question : Let $y\left ( t \right )$ be a real valued function defined on the real line such that ${y}'=y \left ( 1-y \right )$, with $y\left ( 0\right ) \in \left [ 0,1 \right ]$. Then $\lim_{t\rightarrow \infty }y\left ( t \right )=1$ .
soujanyareddy13
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TIFR
Aug 30, 2020
by
soujanyareddy13
273
views
tifrmaths2017
true-false
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