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Recent questions tagged non-gate
2
votes
0
answers
601
TIFR-2015-Maths-B-9
Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by $A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarrow \infty} f(x_{n}), \text {for some sequence} x_{n} \rightarrow +\infty\right\}$ Then the set A is necessarily. $A$ connected set $A$ compact set $A$ singleton set None of the above
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 21, 2015
by
makhdoom ghaya
340
views
tifrmaths2015
functions
non-gate
2
votes
0
answers
602
TIFR-2015-Maths-B-7
A complex number $\alpha \in \mathbb{C}$ is called algebraic if there is a non-zero polynomial $P(x) \in \mathbb{Q}\left[x\right]$ with rational coefficients such that $P(\alpha)=0$. Which of the following statements is true? There are only finitely many algebraic ... All complex numbers are algebraic $\sin (\frac{\pi}{3})+ \cos (\frac{\pi}{4}$) is algebraic None of the above
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 21, 2015
by
makhdoom ghaya
340
views
tifrmaths2015
set-theory&algebra
non-gate
1
vote
0
answers
603
TIFR-2015-Maths-B-4
Let $U_{1}\supset U_{2} \supset...$ be a decreasing sequence of open sets in Euclidean $3$-space $\mathbb{R}^{3}$. What can we say about the set $\cap U_{i}$ ? It is infinite. It is open. It is non-empty. None of the above.
makhdoom ghaya
asked
in
Linear Algebra
Dec 20, 2015
by
makhdoom ghaya
329
views
tifrmaths2015
linear-algebra
non-gate
3
votes
1
answer
604
TIFR-2015-Maths-A-15
The series $\sum_{n=1}^{\infty}\frac{\cos (3^{n}x)}{2^{n}}$ Diverges, for all rational $x \in \mathbb{R}$ Diverges, for some irrational $x \in \mathbb{R}$ Converges, for some but not all $x \in \mathbb{R}$ Converges, for all $x \in \mathbb{R}$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 20, 2015
by
makhdoom ghaya
338
views
tifrmaths2015
convergence
non-gate
2
votes
1
answer
605
TIFR-2015-Maths-A-11
Let $\left\{a_{n}\right\}$ be a sequence of real numbers. Which of the following is true? If $\sum a_{n}$ converges, then so does $\sum a_{n}^{4}$ If $\sum |a_{n}|$ converges, then so does $\sum a_{n}^{2}$ If $\sum a_{n}$ diverges, then so does $\sum a_{n}^{3}$ If $\sum |a_{n}|$ diverges, then so does $\sum a_{n}^{2}$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 20, 2015
by
makhdoom ghaya
358
views
tifrmaths2015
convergence
non-gate
1
vote
0
answers
606
TIFR-2015-Maths-A-10
For a group $G$, let Aut(G) denote the group of automorphisms of $G$. Which of the following statements is true? Aut$(\mathbb{Z})$ is isomorphic to $\mathbb{Z}_{2}$ If $G$ is cyclic, then Aut $(G)$ is cyclic. If Aut (G) is trivial, then $G$ is trivial. Aut $(\mathbb{Z})$ is isomorphic to $\mathbb{Z}$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 19, 2015
by
makhdoom ghaya
384
views
tifrmaths2015
group-theory
non-gate
3
votes
0
answers
607
TIFR-2015-Maths-A-9
Let $\left\{a_{n}\right\}$ be a sequence of real numbers such that $|a_{n+1}-a_{n}|\leq \frac{n^{2}}{2^{n}}$ for all $n \in \mathbb{N}$. Then The sequence $\left\{a_{n}\right\}$ may be unbounded. The sequence $\left\{a_{n}\right\}$ is bounded but may not converge. The sequence $\left\{a_{n}\right\}$ has exactly two limit points. The sequence $\left\{a_{n}\right\}$ is convergent.
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 19, 2015
by
makhdoom ghaya
381
views
tifrmaths2015
convergence
non-gate
2
votes
1
answer
608
TIFR-2015-Maths-A-4
Let $S$ be the collection of (isomorphism classes of) groups $G$ which have the property that every element of $G$ commutes only with the identity element and itself. Then $|S| = 1$ $|S| = 2$ $|S| \geq 3$ and is finite $|S| = \infty$
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 19, 2015
by
makhdoom ghaya
898
views
tifrmaths2015
group-theory
group-isomorphism
non-gate
1
vote
0
answers
609
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
310
views
tifrmaths2014
vector-space
non-gate
1
vote
0
answers
610
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
255
views
tifrmaths2014
vector-space
non-gate
2
votes
0
answers
611
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
351
views
tifrmaths2014
polynomials
non-gate
1
vote
0
answers
612
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
370
views
tifrmaths2014
set-theory&algebra
group-theory
group-isomorphism
non-gate
1
vote
0
answers
613
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
550
views
tifrmaths2014
set-theory&algebra
group-theory
group-isomorphism
non-gate
1
vote
1
answer
614
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
577
views
tifrmaths2014
functions
non-gate
1
vote
0
answers
615
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
366
views
tifrmaths2014
linear-algebra
vector-space
non-gate
1
vote
0
answers
616
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
323
views
tifrmaths2014
convergence
non-gate
1
vote
1
answer
617
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
463
views
tifrmaths2014
convergence
non-gate
1
vote
0
answers
618
TIFR-2011-Maths-B-12
Let $S$ be a finite subset of $\mathbb{R}^{3}$ such that any three elements in $S$ span a two dimensional subspace. Then $S$ spans a two dimensional space.
makhdoom ghaya
asked
in
Linear Algebra
Dec 10, 2015
by
makhdoom ghaya
436
views
tifrmaths2011
vector-space
non-gate
2
votes
0
answers
619
TIFR-2011-Maths-B-7
There is a non-trivial group homomorphism from $S_{3}$ to $\mathbb{Z}/3\mathbb{Z}$.
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 9, 2015
by
makhdoom ghaya
509
views
tifrmaths2011
group-theory
group-isomorphism
non-gate
1
vote
0
answers
620
TIFR-2011-Maths-B-3
There are n homomorphisms from the group $\mathbb{Z}/n\mathbb{Z}$ to the additive group of rationals $\mathbb{Q}$.
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 9, 2015
by
makhdoom ghaya
356
views
tifrmaths2011
group-theory
group-isomorphism
non-gate
1
vote
0
answers
621
TIFR-2011-Maths-A-23
The space of solutions of infinitely differentiable functions satisfying the equation $y" + y = 0$ is infinite dimensional.
makhdoom ghaya
asked
in
Linear Algebra
Dec 9, 2015
by
makhdoom ghaya
324
views
tifrmaths2011
vector-space
non-gate
2
votes
0
answers
622
TIFR-2011-Maths-A-18
Consider the map $T$ from the vector space of polynomials of degree at most $5$ over the reals to $R \times R$, given by sending a polynomial $P$ to the pair $(P(3), P' (3))$ where $P'$ is the derivative of $P$. Then the dimension of the kernel is $3$.
makhdoom ghaya
asked
in
Linear Algebra
Dec 9, 2015
by
makhdoom ghaya
388
views
tifrmaths2011
vector-space
non-gate
2
votes
1
answer
623
TIFR-2011-Maths-A-5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions Infinite number of solutions
makhdoom ghaya
asked
in
Calculus
Dec 9, 2015
by
makhdoom ghaya
463
views
tifrmaths2011
differentiation
non-gate
5
votes
2
answers
624
TIFR CSE 2015 | Part B | Question: 13
Two undirected graphs $G_{1}=(V_{1}, E_{1})$ and $G_{2}= (V_{2}, E_{2})$ are said to be isomorphic if there exist a bijection $\pi: V_{1} \rightarrow V_{2}$ such that for all $u, v \in V_{1}, (u, v) \in E_{1}$ ... $L$ is $NP$- hard. $L$ is undecidable. Only $(i)$ Only $(ii)$ Only $(iii)$ $(i)$ and $(ii)$ $(ii)$ and $(iii)$
makhdoom ghaya
asked
in
Algorithms
Dec 8, 2015
by
makhdoom ghaya
978
views
tifr2015
graph-theory
graph-isomorphism
p-np-npc-nph
non-gate
3
votes
1
answer
625
TIFR CSE 2014 | Part A | Question: 15
Consider the following statements: $b_{1}= \sqrt{2}$, series with each $b_{i}= \sqrt{b_{i-1}+ \sqrt{2}}, i \geq 2$, converges. $\sum ^{\infty} _{i=1} \frac{\cos (i)}{i^{2}}$ converges. $\sum ^{\infty} _{i=0} b_{i}$ ... $(3)$ but not $(1)$. Statements $(1)$ and $(3)$ but not $(2)$. All the three statements. None of the three statements.
makhdoom ghaya
asked
in
Calculus
Nov 14, 2015
by
makhdoom ghaya
650
views
tifr2014
convergence
non-gate
2
votes
0
answers
626
TIFR CSE 2014 | Part A | Question: 12
Let $f(x)= 2^{x}$. Consider the following inequality for real numbers $a, b$ and $0 < \lambda < 1$: $f(\lambda a + b) \leq \lambda f(a) + (1 - \lambda) f (\frac{b}{1 - \lambda})$. Consider the ... $(2)$. The above inequality holds under all the three conditions. The above inequality holds under none of the three conditions.
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 14, 2015
by
makhdoom ghaya
477
views
tifr2014
quantitative-aptitude
convex-sets-functions
non-gate
3
votes
1
answer
627
TIFR CSE 2013 | Part B | Question: 2
Consider polynomials in a single variable $x$ of degree $d$. Suppose $d < n/2$. For such a polynomial $p(x)$, let $C_{p}$ denote the $n$-tuple $(P\left ( i \right ))_{1 \leq i \leq n}$. For any two such distinct polynomials $p, q,$ the number of ... $d$ At most $n - d$ Between $d$ and $n - d$ At least $n - d$ None of the above.
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 6, 2015
by
makhdoom ghaya
643
views
tifr2013
polynomials
non-gate
2
votes
1
answer
628
TIFR CSE 2013 | Part A | Question: 7
For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ ... $\frac{1}{3}$ 1 3 $\frac{1}{2}$
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 4, 2015
by
makhdoom ghaya
620
views
tifr2013
quantitative-aptitude
complex-number
non-gate
5
votes
2
answers
629
TIFR CSE 2011 | Part B | Question: 40
Consider the class of object oriented languages. Which of the following is true? Pascal is an object oriented language. Object oriented languages require heap management. Object oriented languages cannot be implemented in ... languages are more powerful than declarative programming languages. Parallelism cannot be realized in object oriented languages.
makhdoom ghaya
asked
in
Object Oriented Programming
Oct 26, 2015
by
makhdoom ghaya
1.2k
views
tifr2011
programming
object-oriented-programming
non-gate
3
votes
0
answers
630
TIFR CSE 2011 | Part B | Question: 24
Consider the program x:=0; y:=0; (r1:=x; r2:=x; y:= if r1 = r2 then 1 ∥ r3:= y; x:= r3) Note that ∥ denotes the parallel operator. In which of the following cases can the program possibly ... in all sequential programming languages when the compiler appropriately translates the ∥ operator to interleaved statements in the sequential language. None of the above.
makhdoom ghaya
asked
in
Programming in C
Oct 20, 2015
by
makhdoom ghaya
505
views
tifr2011
programming
non-gate
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