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Recent questions and answers in TIFR

1 1 vote
1 1 answer
524
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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 subg...
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0 0 votes
2 2 answers
666
666 views
TIFR-2012-Maths-B: 17
True/False Question:If the equation$$xyz=1$$holds in a group $G$, does it follow that$$yxz=1$$.
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1 1 vote
1 1 answer
737
737 views
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 $...
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0 0 votes
1 1 answer
570
570 views
TIFR-2013-Maths-A: 3
True/False Question :The equation $x^{3}+3x-4=0$ has exactly one real root.
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0 0 votes
1 1 answer
602
602 views
TIFR-2012-Maths-D: 32
True/False Question:The polynomial $X^{8}+1$ is irreducible in $\mathbb{R}\left [ X \right ]$.
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0 0 votes
1 1 answer
577
577 views
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...
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0 0 votes
1 1 answer
809
809 views
TIFR-2012-Maths-B: 11
True/False Question:The automorphism group $Aut\left ( \mathbb{Z}/2\times \mathbb{Z}/2 \right )$ is abelian.
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0 0 votes
1 1 answer
563
563 views
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-...
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1 1 vote
1 1 answer
669
669 views
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.
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0 0 votes
1 1 answer
735
735 views
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 $\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+\left | z...
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1 1 vote
1 1 answer
1.0k
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TIFR-2012-Maths-D: 31
True/False Question:$f : \left [ 0,\infty \right ]\rightarrow \left [ 0,\infty \right ]$ is continuous and bounded then $f$ has a fixed point.
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0 0 votes
1 1 answer
590
590 views
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 \l...
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0 0 votes
1 1 answer
587
587 views
TIFR-2018-Maths-B: 9
What are the last $3$ digits of $2^{2017}$?$072$$472$$512$$912.$
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0 0 votes
0 0 answers
393
393 views
TIFR-2012-Maths-D: 35
True/False Question:Given any integer $n\geq 2$, we can always finds an integer $m$ such that each of the $n-1$ consecutive integers $m+2,m+3,\dots,m+n$ are composite.
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0 0 votes
0 0 answers
411
411 views
TIFR-2012-Maths-D: 36
True/False Question:The $10 \times 10 $ matrix $\begin{pmatrix} v_{1}w_{1} & \cdots&v_{1}w_{10} \\ v_{2}w_{2}& \cdots & v_{2}w_{10}\\ v_{10}w_{1}&\cdots & v_{10}w_{10} \e...
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0 0 votes
0 0 answers
291
291 views
TIFR-2012-Maths-D: 37
True/False Question:If every continuous function on $X\subset \mathbb{R}^{2}$ is bounded, then $X$ is compact.
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0 0 answers
348
348 views
TIFR-2012-Maths-D: 38
True/False Question:The graph of $xy=1$ is $\mathbb{C}^{2}$ is connected.
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0 0 votes
0 0 answers
369
369 views
TIFR-2012-Maths-D: 40
True/False Question:Consider the differential equations (with $y$ is a function of $x$)$\begin{matrix} \frac{dy}{dx} & = & y\\ y\left ( 0 \right ) & = & 0 \end{matrix}$$\...
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368
368 views
TIFR-2012-Maths-C: 21
True/False Question:Let $f : \mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous function. Then the derivative $\frac{\partial ^{2}f}{\partial x\partial y}$ can exist w...
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0 0 votes
0 0 answers
366
366 views
TIFR-2012-Maths-C: 22
True/False Question:If $f$ is continuous on $\left [ 0,1 \right ]$ and if $\int_{0}^{1}f\left ( x \right )x^{n}dx=0$ for $n=1,2,3,\cdots .$ .Then $\int_{0}^{1}f^{2}\left...
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0 0 votes
0 0 answers
410
410 views
TIFR-2012-Maths-C: 23
True/False Question:Suppose that $f \in \mathfrak{L}^{2} \left ( \mathbb{R} \right )$. Then $f \in \mathfrak{L}^{1} \left ( \mathbb{R} \right )$.
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302
302 views
TIFR-2012-Maths-C: 24
True/False Question:The Integral$$\int_{-\infty }^{+\infty }\frac{e^{-x}}{1+x^{2}}\:dx$$is convergent.
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0 0 answers
345
345 views
TIFR-2012-Maths-C: 25
True/False Question:If $A\subset \mathbb{R}$ and open then the interior of the closure $\overset{-0}{A}$is $A$.
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0 0 answers
391
391 views
TIFR-2012-Maths-C: 26
True/False Question:If $f \in C^{\infty }$ and $f^{\left ( k \right )}\left ( 0 \right )=0$ for all integer $k\geq 0$, then $f\equiv 0$.
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0 0 votes
0 0 answers
337
337 views
TIFR-2012-Maths-C: 27
True/False Question:Let $f:\left [ 0,1 \right ]\rightarrow \left [ 0,1 \right ]$be continuous then $f$ assumes the value $\int_{0}^{1}f^{2}\left ( t \right )dt$ somewher...
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0 0 votes
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362
362 views
TIFR-2012-Maths-C: 28
True/False Question:Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function such that$$\underset{h\rightarrow 0}{lim }\:\frac{f\left ( x+h \right )-f\left ( x-h \right )}{...
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0 0 votes
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314
314 views
TIFR-2012-Maths-C: 29
True/False Question:The functions $f\left ( x \right )=x\left | x \right |$ and $x\left | sin\:x \right |$ are not differentiable at $x=0$.
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0 0 answers
362
362 views
TIFR-2012-Maths-C: 30
True/False Question:The composition of two uniformly continuous functions need not always be uniformly continuous.
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366
366 views
TIFR-2012-Maths-B: 14
True/False Question:$A\in M_{2}\left ( \mathbb{C} \right )$and $A$ is nilpotent then $A^{2}=0$.
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349
349 views
TIFR-2012-Maths-B: 15
True/False Question:Let $P$ be an $n \times n $ matrix whose row sums equal $1$. Then for any positive integer $m$ the row sums of the matrix $p^{m}$ equal $1$.
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0 0 votes
0 0 answers
298
298 views
TIFR-2012-Maths-B: 16
True/False Question:There is a non trivial group homomorphism from $C$ to $R$.
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0 0 votes
0 0 answers
337
337 views
TIFR-2012-Maths-B: 18
True/False Question:Any $3\times3$ and $5\times5$ skew-symmetric matrices have always zero determinants.
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1 1 vote
0 0 answers
721
721 views
TIFR-2012-Maths-B: 19
True/False Question:The rank of the matrix$$\begin{bmatrix} 11 &12 &13 &14 \\ 21& 22 &23 & 24\\ 31& 32 &33 &34 \\ 41&42 & 43 & 44 \end{bmatrix}$$is $2$.
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0 0 votes
0 0 answers
367
367 views
TIFR-2012-Maths-B: 20
True/False Question:The number $2$ is a prime in $\mathbb{Z}\left [ i \right ]$.
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1 1 answer
936
936 views
Exam Approach
As I have no prior knowledge of TIFR pattern then any suggestion from any experienced practitioner of TIFR that how much time to be given for Section A and Section B of...
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0 0 votes
1 1 answer
1.0k
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TIFR Exam Pattern
If anyone had analysed the previous TIFR papers, which subjects/topics of GATE they dont or rarely ask ?Please do share.
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0 0 votes
1 1 answer
4.3k
4.3k views
TIFR Answer keys
Anyone have answer keys for tifr gs 2010/2011 ?and 2012- 2018 Question papers without answers marked.kindly share.
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2 2 votes
1 answers 1 answer
1.2k
1.2k views
TIFR CSS GS-2017
How many distinct ways are there to split 50 identical coins among three people so that each person gets atleast 5 coins??
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2 2 votes
1 answers 1 answer
8.2k
8.2k views
TIFR 2017 - How to prepare for TIFR and what are the future placement opportunities?
Dear Fellow Mates,I will be sitting for GATE and TIFR both this year. I don't have much clue about TIFR but I have looked up about it on their site and know the rules, sy...
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