Search results for tifrmaths2014

2 votes
4 answers
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1 votes
1 answer
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Let $a_{n}=(n+1)^{100} e^{-\sqrt{n}}$ for $n \geq 1$. Then the sequence $(a_{n})_{n}$ isUnboundedBounded but does not converge Bounded and converges to $1$Bounded and con...
2 votes
1 answer
3
How many proper subgroups does the group $\mathbb{Z} ⊕ \mathbb{Z}$ have? $1$$2$ $3$ Infinitely many
1 votes
1 answer
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3 votes
1 answer
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2 votes
1 answer
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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 unboun...
1 votes
0 answers
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1 votes
1 answer
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1 votes
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14
Which of the following groups are isomorphic? $\mathbb{R}$ and $C$ $\mathbb{R}^{*}$ and $C^{*}$ $S_{3}\times \mathbb{Z}/4$ and $S_{4}$ $\mathbb{Z}/2\times \mathbb{Z}/2$ a...
1 votes
1 answer
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2 votes
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18
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