Recent questions without answers

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153
Consider the sequence $\left\{a_{n}\right\}$ for $n \geq 1$ defined by\[a_{n}=\lim _{N \rightarrow \infty} \sum_{k=n}^{N} \frac{1}{k^{2}} .\]Which of the following statem...
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155
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156
What is the least positive integer $n>1$ such that $x^{n}$ and $x$ are conjugate, for every $x \in S_{11}$? Here, $S_{11}$ denotes the symmetric group on $11$ letters.$10...
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161
What is the number of distinct subfields of $\mathbb{C}$ isomorphic to $\mathbb{Q}[\sqrt[3]{2}]$?$1$$2$$3$Infinite
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162
Let $\mathbb{F}_{3}$ denote the finite field with 3 elements. What is the number of one dimensional vector subspaces of the vector space $\mathbb{F}_{3}^{5}$ over $\mathb...
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164
Consider the complex vector space$V=\{f \in \mathbb{C}[x] \mid f$ has degree at most 50 , and $f(i x)=-f(x)$ for all $x \in \mathbb{C}\}$.Then the dimension of $V$ equals...
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166
Can someone please explain how to calculate TLB size?
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168
I am unable to understand the language of the question , can someone help me??
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170
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171
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172
In it’s solution how are they obtaining x with the given operation? Should we not have 1 more register to keep x separate?
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173
Consider the following three functions defined for all positive integers $n \geq 0$.\[\begin{array}{l}f(n)=|\sin (n)+n|, \\g(n)=n, \\h(n)=|\sin (n)| .\end{array}\]Which o...