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TIFR Mathematics 2024 | Part B | Question: 13
Let $\text{G}$ be a proper subgroup of $(\mathbb{R},+)$ which is closed as a subset of $\mathbb{R}$. Then $G$ is generated by a single element.
Let $\text{G}$ be a proper subgroup of $(\mathbb{R},+)$ which is closed as a subset of $\mathbb{R}$. Then $G$ is generated by a single element.
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tifrmaths2024
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TIFR Mathematics 2024 | Part B | Question: 14
There exists a unique function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f$ is continuous at $x=0$, and such that for all $x \in \mathbb{R}$ \[ f(x)+f\left(\frac{x}{2}\right)=x . \]
There exists a unique function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f$ is continuous at $x=0$, and such that for all $x \in \mathbb{R}$\[f(x)+f\left(\frac{x}...
admin
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TIFR Mathematics 2024 | Part B | Question: 15
A map $f: V \rightarrow W$ between finite dimensional vector spaces over $\mathbb{Q}$ is a linear transformation if and only if $f(x)=f(x-a)+f(x-b)-f(x-a-b)$, for all $x, a, b \in V$.
A map $f: V \rightarrow W$ between finite dimensional vector spaces over $\mathbb{Q}$ is a linear transformation if and only if $f(x)=f(x-a)+f(x-b)-f(x-a-b)$, for all $x,...
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TIFR Mathematics 2024 | Part B | Question: 16
Let $R$ be the ring $\mathbb{C}[x] /\left(x^{2}\right)$ obtained as the quotient of the polynomial ring $\mathbb{C}[x]$ by its ideal generated by $x^{2}$. Let $R^{\times}$be the multiplicative group of units of this ring. Then there is an injective group homomorphism from $(\mathbb{Z} / 2 \mathbb{Z}) \times(\mathbb{Z} / 2 \mathbb{Z})$ into $R^{\times}$.
Let $R$ be the ring $\mathbb{C}[x] /\left(x^{2}\right)$ obtained as the quotient of the polynomial ring $\mathbb{C}[x]$ by its ideal generated by $x^{2}$. Let $R^{\times}...
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TIFR Mathematics 2024 | Part B | Question: 17
Let $A \in \mathrm{M}_{2}(\mathbb{Z})$ be such that $\left|A_{i j}(n)\right| \leq 50$ for all $1 \leq n \leq 10^{50}$ and all $1 \leq i, j \leq 2$, where $A_{i j}(n)$ denotes the $(i, j)$-th entry of the $2 \times 2$ matrix $A^{n}$. Then $\left|A_{i j}(n)\right| \leq 50$ for all positive integers $n$.
Let $A \in \mathrm{M}_{2}(\mathbb{Z})$ be such that $\left|A_{i j}(n)\right| \leq 50$ for all $1 \leq n \leq 10^{50}$ and all $1 \leq i, j \leq 2$, where $A_{i j}(n)$ den...
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TIFR Mathematics 2024 | Part B | Question: 18
Let $A, B$ be subsets of $\{0, \ldots, 9\}$. It is given that, on choosing elements $a \in A$ and $b \in B$ at random, $a+b$ takes each of the values $0, \ldots, 9$ with equal probability. Then one of $A$ or $B$ is singleton.
Let $A, B$ be subsets of $\{0, \ldots, 9\}$. It is given that, on choosing elements $a \in A$ and $b \in B$ at random, $a+b$ takes each of the values $0, \ldots, 9$ with ...
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TIFR Mathematics 2024 | Part B | Question: 19
If $f: \mathbb{R} \rightarrow \mathbb{R}$ is uniformly continuous, then there exists $M>0$ such that for all $x \in \mathbb{R} \backslash[-M, M]$, we have $f(x) < x^{100}$.
If $f: \mathbb{R} \rightarrow \mathbb{R}$ is uniformly continuous, then there exists $M>0$ such that for all $x \in \mathbb{R} \backslash[-M, M]$, we have $f(x) < x^{100}...
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TIFR Mathematics 2024 | Part B | Question: 20
If a sequence $\left\{f_{n}\right\}$ of continuous functions from $[0,1]$ to $\mathbb{R}$ converges uniformly on $(0,1)$ to a continuous function $f:[0,1] \rightarrow \mathbb{R}$, then $\left\{f_{n}\right\}$ converges uniformly on $[0,1]$ to $f$.
If a sequence $\left\{f_{n}\right\}$ of continuous functions from $[0,1]$ to $\mathbb{R}$ converges uniformly on $(0,1)$ to a continuous function $f:[0,1] \rightarrow \ma...
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OIL IT Senior officer
From where to get syllabus for OIL senior officer IT.
From where to get syllabus for OIL senior officer IT.
mk_007
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mk_007
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Jan 12
Study Resources
psu
syllabus
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UGC NET CSE | June 2008 | Part 2 | Question: 1
Which of the following does not define a tree? A tree is a connected acyclic graph. A tree is a connected graph with $n-1$ edges where ' $n$ ' is the number of vertices in the graph. A tree is an acyclic graph with $n-1$ edges where ' $n$ ' is the number of vertices in the graph. A tree is a graph with no cycles.
Which of the following does not define a tree?A tree is a connected acyclic graph.A tree is a connected graph with $n-1$ edges where ' $n$ ' is the number of vertices in ...
admin
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ugcnetcse-june2008-paper2
directed-acyclic-graph
tree
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UGC NET CSE | June 2008 | Part 2 | Question: 2
The complexity of Kruskal's minimum spanning tree algorithm on a graph with ' $n$ ' nodes and ' $e$ ' edges is : $\mathrm{O}(n)$ $\mathrm{O}(n \log n)$ $\mathrm{O}(e \log n)$ $\mathrm{O}(e)$
The complexity of Kruskal's minimum spanning tree algorithm on a graph with ' $n$ ' nodes and ' $e$ ' edges is :$\mathrm{O}(n)$$\mathrm{O}(n \log n)$$\mathrm{O}(e \log n)...
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ugcnetcse-june2008-paper2
kruskals-algorithm
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UGC NET CSE | June 2008 | Part 2 | Question: 3
If a code is t-error correcting, the minimum Hamming distance is equal to : $2 t+1$ $2 t$ $2 t-1$ $t-1$
If a code is t-error correcting, the minimum Hamming distance is equal to :$2 t+1$$2 t$$2 t-1$$t-1$
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ugcnetcse-june2008-paper2
hamming-code
error-correction
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UGC NET CSE | June 2008 | Part 2 | Question: 4
The set of positive integers under the operation of ordinary multiplication is : not a monoid not a group a group an Abelian group
The set of positive integers under the operation of ordinary multiplication is :not a monoidnot a groupa groupan Abelian group
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ugcnetcse-june2008-paper2
abelian-group
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UGC NET CSE | June 2008 | Part 2 | Question: 5
In a set of $8$ positive integers, there always exists a pair of numbers having the same remainder when divided by : $7$ $11$ $13$ $15$
In a set of $8$ positive integers, there always exists a pair of numbers having the same remainder when divided by :$7$$11$$13$$15$
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UGC NET CSE | June 2008 | Part 2 | Question: 6
An example of a tautology is : $x \vee y$ $x \mathrm{v}(\sim y)$ $x \mathrm{v}(\sim x)$ $(x=>y) \wedge(x<=y)$
An example of a tautology is :$x \vee y$$x \mathrm{v}(\sim y)$$x \mathrm{v}(\sim x)$$(x=>y) \wedge(x<=y)$
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UGC NET CSE | June 2008 | Part 2 | Question: 7
Among the logic families $\text{RTL, TTL, ECL}$ and $\text{CMOS}$, the fastest family is : $\text{ECL}$ $\mathrm{CMOS}$ $\text{TTL}$ $\text{RTL}$
Among the logic families $\text{RTL, TTL, ECL}$ and $\text{CMOS}$, the fastest family is :$\text{ECL}$$\mathrm{CMOS}$$\text{TTL}$$\text{RTL}$
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UGC NET CSE | June 2008 | Part 2 | Question: 8
The octal equivalent of the hexadecimal number $\mathrm{FF}$ is : $100$ $150$ $377$ $737$
The octal equivalent of the hexadecimal number $\mathrm{FF}$ is :$100$$150$$377$$737$
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UGC NET CSE | June 2008 | Part 2 | Question: 9
The characteristic equation of a $\mathrm{T}$ flip flop is given by : $\mathrm{Q}_{\mathrm{N}+1}=\mathrm{TQ}_{\mathrm{N}}$ $\mathrm{Q}_{\mathrm{N}+1}=\mathrm{T}+\mathrm{Q}_{\mathrm{N}}$ $\mathrm{Q}_{\mathrm{N}+1}=\mathrm{T} \oplus \mathrm{Q}_{\mathrm{N}}$ $\mathrm{Q}_{\mathrm{N}+1}=\overline{\mathrm{T}}+\mathrm{Q}_{\mathrm{N}}$
The characteristic equation of a $\mathrm{T}$ flip flop is given by :$\mathrm{Q}_{\mathrm{N}+1}=\mathrm{TQ}_{\mathrm{N}}$$\mathrm{Q}_{\mathrm{N}+1}=\mathrm{T}+\mathrm{Q}_...
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ugcnetcse-june2008-paper2
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UGC NET CSE | June 2008 | Part 2 | Question: 10
The idempotent law in Boolean algebra says that: $\sim(\sim x)=x$ $x+x=x$ $x+x y=x$ $x(x+y)=x$
The idempotent law in Boolean algebra says that:$\sim(\sim x)=x$$x+x=x$$x+x y=x$$x(x+y)=x$
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UGC NET CSE | June 2008 | Part 2 | Question: 11
What is the effect of the following $\text{C}$ code? for(int i=1 ; i ≤ 5 ; i = i + 1/2) printf(" % d,", i); It prints $1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5$, and stops It prints $1, 2, 3, 4, 5$, and stops It prints $1, 2, 3, 4, 5$, and repeats forever It prints $1, 1, 1, 1, 1$, and repeats forever
What is the effect of the following $\text{C}$ code?for(int i=1 ; i ≤ 5 ; i = i + 1/2) printf(" % d,", i);It prints $1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5$, and stopsIt pri...
admin
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ugcnetcse-june2008-paper2
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