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Recent questions tagged tifrmaths2014
3
votes
0
answers
1
TIFR-2014-Maths-B-10
How many maps $\emptyset:\mathbb{N}\cup \left\{0\right\}\rightarrow \mathbb{N} \cup \left\{0\right\}$ are there, with the property that $\emptyset(ab)=\emptyset(a)+\emptyset(b)$, for all $a, b \in \mathbb{N} \cup \left\{0\right\}$? None Finitely many Countably many Uncountably many
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
226
views
tifrmaths2014
set-theory&algebra
functions
1
vote
0
answers
2
TIFR-2014-Maths-B-9
Let $f : X \rightarrow Y$ be a continuous map between metric spaces. Then $f(X)$ is a complete subset of $Y$ if The space $X$ is compact The space $Y$ is compact The space $X$ is complete The space $Y$ is complete
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
159
views
tifrmaths2014
vector-space
non-gate
1
vote
0
answers
3
TIFR-2014-Maths-B-8
Let $X$ be a non-empty topological space such that every function $f : X \rightarrow \mathbb{R}$ is continuous. Then $X$ has the discrete topology $X$ has the indiscrete topology $X$ is compact $X$ is not connected
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
180
views
tifrmaths2014
vector-space
1
vote
0
answers
4
TIFR-2014-Maths-B-7
$X$ is a topological space of infinite cardinality which is homeomorphic to $X \times X$. Then $X$ is not connected $X$ is not compact $X$ is not homeomorphic to a subset of $R$ None of the above
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
147
views
tifrmaths2014
vector-space
non-gate
2
votes
0
answers
5
TIFR-2014-Maths-B-6
The number of irreducible polynomials of the form $x^{2}+ax+b$, with $a, b$ in the field $\mathbb{F}_{7}$ of $7$ elements is: 7 21 35 49
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
167
views
tifrmaths2014
polynomials
non-gate
1
vote
0
answers
6
TIFR-2014-Maths-B-5
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ and $\mathbb{Z}/4$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
275
views
tifrmaths2014
set-theory&algebra
group-theory
group-isomorphism
non-gate
2
votes
4
answers
7
TIFR-2014-Maths-B-4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
1.8k
views
tifrmaths2014
set-theory&algebra
group-theory
1
vote
0
answers
8
TIFR-2014-Maths-B-3
Let $S_{n}$ be the symmetric group of $n$ letters. There exists an onto group homomorphism From $S_{5}$ to $S_{4}$ From $S_{4}$ to $S_{2}$ From $S_{5}$ to $\mathbb{Z}/5$ From $S_{4}$ to $\mathbb{Z}/4$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
311
views
tifrmaths2014
set-theory&algebra
group-theory
group-isomorphism
non-gate
1
vote
0
answers
9
TIFR-2014-Maths-B-2
Let $f:\mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous map such that $f(x) = 0$ for only finitely many values of $x$. Which of the following is true? Either $f(x)\leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$ The map $f$ is onto The map $f$ is one-to-one None of the above
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
144
views
tifrmaths2014
functions
1
vote
0
answers
10
TIFR-2014-Maths-B-1
Let $f : [0, 1] \rightarrow [0, \infty)$ be continuous. Suppose $\int_{0}^{x} f(t) \text{d}t \geq f(x)$, for all $x \in [0, 1]$. Then No such function exists There are infinitely many such functions There is only one such function There are exactly two such functions
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
213
views
tifrmaths2014
set-theory&algebra
functions
1
vote
0
answers
11
TIFR-2014-Maths-A-20
Let $C$ denote the cube $\left[-1, 1\right]^{3} \subset \mathbb{R}^{3}$. How many rotations are there in $\mathbb{R}^{3}$ which take $C$ to itself? 6 12 18 24
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 17, 2015
by
makhdoom ghaya
180
views
tifrmaths2014
1
vote
1
answer
12
TIFR-2014-Maths-A-19
For $n \in \mathbb{N}$, we define $s_{n}=1^{3}+2^{3}+3^{3}+...+n^{3}$. Which of the following holds for all $n \in \mathbb{N}$? $s_{n}$ is an odd integer $s_{n} n^{2}(n+1)^{2}/4$ $s_{n} = n(n + 1)(2n + 1)/6$ None of the above
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 17, 2015
by
makhdoom ghaya
199
views
tifrmaths2014
quantitative-aptitude
1
vote
1
answer
13
TIFR-2014-Maths-A-18
What is the last digit of $97^{2013}$? 1 3 7 9
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 17, 2015
by
makhdoom ghaya
387
views
tifrmaths2014
quantitative-aptitude
unit-digit
1
vote
1
answer
14
TIFR-2014-Maths-A-17
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function and let $S$ be a non-empty proper subset of $R$. Which one of the following statements is always true? (Here $\bar{A}$ denotes the closure of $A$ and $A^{∘}$ denotes the interior of $A$ ... $f(\bar{S}) \supseteq \overline{f(S)}$ $f(S)^{∘} \supseteq f(S^{∘})$.
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
364
views
tifrmaths2014
functions
non-gate
1
vote
0
answers
15
TIFR-2014-Maths-A-16
$X$ is a metric space. $Y$ is a closed subset of $X$ such that the distance between any two points in $Y$ is at most $1$. Then $Y$ is compact Any continuous function from $Y \rightarrow \mathbb{R}$ is bounded $Y$ is not an open subset of $X$ none of the above
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
237
views
tifrmaths2014
linear-algebra
vector-space
non-gate
2
votes
1
answer
16
TIFR-2014-Maths-A-15
How many proper subgroups does the group $\mathbb{Z} ⊕ \mathbb{Z}$ have? $1$ $2$ $3$ Infinitely many
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
787
views
tifrmaths2014
group-theory
3
votes
1
answer
17
TIFR-2014-Maths-A-14
Let $G$ be a group and let $H$ and $K$ be two subgroups of $G$. If both $H$ and $K$ have $12$ elements, which of the following numbers cannot be the cardinality of the set $HK = \left\{hk : h \in H, k \in K\right\}$? $72$ $60$ $48$ $36$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
626
views
tifrmaths2014
set-theory&algebra
group-theory
1
vote
0
answers
18
TIFR-2014-Maths-A-13
Let $S$ be the set of all tuples $(x, y)$ with $x, y$ non-negative real numbers satisfying $x + y = 2n$, for a fixed $n \in \mathbb{N}$. Then the supremum value of $x^{2}y^{2}(x^{2}+y^{2})$ on the set $S$ is $3n^{6}$ $2n^{6}$ $4n^{6}$ $n^{6}$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
194
views
tifrmaths2014
set-theory&algebra
1
vote
0
answers
19
TIFR-2014-Maths-A-12
There exists a map $f : \mathbb{Z} \rightarrow \mathbb{Q}$ such that $f$ Is bijective and increasing Is onto and decreasing Is bijective and satisfies $f(n) \geq 0$ if $n \leq 0$ Has uncountable image
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
198
views
tifrmaths2014
functions
1
vote
1
answer
20
TIFR-2014-Maths-A-11
Let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$ (0-matrix), for some $k \in \mathbb{N}$. Then $A$ has to be the $0$ matrix Trace$(A)$ could be non-zero $A$ is diagonalizable $0$ is the only eigenvalue of $A$
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
293
views
tifrmaths2014
linear-algebra
matrix
2
votes
1
answer
21
TIFR-2014-Maths-A-10
Let $C\subset \mathbb{Z} \times\mathbb{Z}$ be the set of integer pairs $(a, b)$ for which the three complex roots $r_{1}, r_{2}$ and $r_{3}$ of the polynomial $p(x)=x^{3}-2x^{2}+ax-b$ satisfy $r^{3}_{1}+r^{3}_{2}+r^{3}_{3}=0$. Then the cardinality of $C$ is $|C| = \infty$ $|C| = 0$ $|C| = 1$ $1 < |C| < \infty$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
287
views
tifrmaths2014
set-theory
1
vote
1
answer
22
TIFR-2014-Maths-A-9
Let $A(\theta)=\begin{pmatrix} \cos \theta& \sin \theta \\ -\sin \theta& \cos \theta \end{pmatrix}$, where $\theta \in (0, 2\pi)$. Mark the correct statement below. $A(\theta)$ has eigenvectors in $\mathbb{R}^2$ for all $θ \in (0, 2\pi)$ $A(\theta)$ does not ... $θ \in (0, 2\pi)$ $A(\theta)$ has eigenvectors in $\mathbb{R}^2$ , for exactly $2$ values of $θ \in (0, 2\pi)$
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
340
views
tifrmaths2014
linear-algebra
matrix
eigen-value
1
vote
0
answers
23
TIFR-2014-Maths-A-8
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $|f(x)−f(y)| \geq \frac{1}{2}|x−y|$, for all $x, y \in \mathbb{R}$ . Then $f$ is both one-to-one and onto $f$ is one-to-one but may not be onto $f$ is onto but may not be one-to-one $f$ is neither one-to-one nor onto
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 17, 2015
by
makhdoom ghaya
236
views
tifrmaths2014
functions
1
vote
0
answers
24
TIFR-2014-Maths-A-7
Let $f_{n}(x)$, for $n \geq 1$, be a sequence of continuous non negative functions on $[0, 1]$ such that $\displaystyle \lim_{n \rightarrow \infty} \int_{0}^{1} f_{n}(x) \text{d}x$ ... $0$ point-wise $f_{n}$ will converge point-wise and the limit may be non-zero $f_{n}$ is not guaranteed to have a point-wise limit
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 14, 2015
by
makhdoom ghaya
206
views
tifrmaths2014
convergence
non-gate
1
vote
0
answers
25
TIFR-2014-Maths-A-6
Let $f:\left[0, 1\right]\rightarrow \mathbb{R}$ be a continuous function. Which of the following statements is always true? $\int_{0}^{1} f^{2}(x) \text{d}x = (\int_{0}^{1} f(x) \text{d}x)^{2}$ $\int_{0}^{1} f^{2}(x) \text{d}x \leq (\int_{0}^{1}| f(x) |\text{d}x)^{2}$ ... $\int_{0}^{1} f^{2}(x) \text{d}x ≰ (\int_{0}^{1} f(x) \text{d}x)^{2}$
makhdoom ghaya
asked
in
Calculus
Dec 14, 2015
by
makhdoom ghaya
242
views
tifrmaths2014
continuity
1
vote
1
answer
26
TIFR-2014-Maths-A-5
Let $a_{n}=(n+1)^{100} e^{-\sqrt{n}}$ for $n \geq 1$. Then the sequence $(a_{n})_{n}$ is Unbounded Bounded but does not converge Bounded and converges to $1$ Bounded and converges to $0$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 14, 2015
by
makhdoom ghaya
230
views
tifrmaths2014
convergence
non-gate
1
vote
0
answers
27
TIFR-2014-Maths-A-4
Let $f$ be the real valued function on $[0, \infty)$ defined by $f(x) = \begin{cases} x^{\frac{2}{3}}\log x& \text {for x > 0} \\ 0& \text{if x=0 } \end{cases}$ Then $f$ is discontinuous at $x = 0$ $f$ ... $f$ is uniformly continuous on $[0, \infty)$ $f$ is not uniformly continuous on $[0, \infty)$, but uniformly continuous on $(0, \infty)$
makhdoom ghaya
asked
in
Calculus
Dec 10, 2015
by
makhdoom ghaya
213
views
tifrmaths2014
continuity
2
votes
1
answer
28
TIFR-2014-Maths-A-3
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then $f$ is bounded $f$ is increasing $f$ is unbounded $f'$ is bounded
makhdoom ghaya
asked
in
Calculus
Dec 10, 2015
by
makhdoom ghaya
447
views
tifrmaths2014
differentiation
1
vote
0
answers
29
TIFR-2014-Maths-A-2
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous bounded function, then: $f$ has to be uniformly continuous There exists an $x \in \mathbb{R}$ such that $f(x) = x$ $f$ cannot be increasing $\displaystyle \lim_{x \rightarrow \infty} f(x)$ exists
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 10, 2015
by
makhdoom ghaya
236
views
tifrmaths2014
continuity
2
votes
1
answer
30
TIFR-2014-Maths-A-1
Let $A, B, C$ be three subsets of $\mathbb{R}$. The negation of the following statement For every $\epsilon > 1$, there exists $a \in A$ and $b \in B$ such that for all $c \in C, |a − c| < \epsilon$ and $|b − c| > \epsilon$ ... all $a \in A$ and $b \in B$ there exists $c \in C$ such that $|a − c| \geq \epsilon$ or $|b − c| \leq \epsilon$
makhdoom ghaya
asked
in
Mathematical Logic
Dec 10, 2015
by
makhdoom ghaya
268
views
tifrmaths2014
mathematical-logic
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Recent questions tagged tifrmaths2014
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Sure will provide it as soon as possible.
sir in the excel sheet of shedule of test link of...
The spreadsheet is up to date.
Can somebody give the details of how many topic...
@kabir5454 Anyway you should not be looking for...