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Discrete Mathematics Q&A Archive of January 5, 2025

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January 5 of 2025

Civil Service Numerical Test Candidate Guide Questions The table below show information about the average daily hours of sunshine for four cities in four months \begin{tabular}{lrrrrr} \hline Month & London & New York & Berlin & Sydney \\ \hline January & 1 & 6 & 2 & 9 \\ \hline April & 5 & 8…
Civil Service Numerical Test Candidate Guide (opens in new window) Questions The table below show information about the average daily hours of sunshine for four cities in four months of the year. \begin{tabular}{lrrrrr} & London & New York & Berlin & Sydney \\ \hline Month & 1 & 6 & 2 & 9…
Numerical Test Questions Candidate Guide (opens in new wind The table below shows the population of a small country, broken down by region. \begin{tabular}{|c|c|c|c|} \hline Region Region A & \begin{tabular}{l} Total \\ Population \end{tabular} & \begin{tabular}{l} Total \\ Population less…
Civil Service Numerical Test Questions Candidate Guide (gpens in new w The table below shows the population of a small country, broken down by region. All people aged 65 plus years are entitled to a state pension of \( \$ 150 \) per week as part of the country's provision for olde citizens.…
\begin{tabular}{|c|c|c|c|c|c|} \hline \multirow[t]{2}{*}{Day of the week} & Number of staff on site atst & Number of ff on site ats & Number of aff on site ats & Number of aff on site at & Total staff on site during \\ \hline & 08:00 & 09:00 & 17:00 & 18:30 & the day \\ \hline Monday & 8 & 61 &…
290 I Intermediate Algebra 3. How many sums can be made of 4 one rupee notes, 6 five rupee note 4. How many factors can there be of the number 2310 ? 5. In how many ways can 3 parcels of 4 things from 15 dissimilar things 6. Given 5 different green dyes, 4 different blue dyes and 3 different \(…
Suppose that \( f \) is an entire function of finite order, that is, there exist \( A, B, \rho>0 \) such that \[ |f(z)| \leq A e^{B|z|^{p}} \] Assume also that \( f \) has at most a finite number of zeros. Show that \( f \) can be written as \[ f(z)=p(z) e^{q(z)} \quad \forall z \in…
Let \( P(z) \) be a (complex) polynomial such that \( P(0) \neq 1 \). Use Jensen's formula to show that the set of zeroes of the function \( f(z)=e^{z}-P(z) \) is not finite.
Let \( B(z) \) be the Blaschke product with zeroes at the points \( \alpha_{n}=1-\frac{1}{n^{2}} \), for \( n \in \mathbb{N} \). Show that \( B(z) \) defines a holomorphic function on the unit disk. Prove that \( \lim _{r \rightarrow 1} B(r)=0 \), where \( 0<r<1 \). Hint: Show the…
Prove that \[ \prod_{n=1}^{\infty} \frac{e^{1 / n}}{1+\frac{1}{n}}=e^{C} \] 9 where \[ C=\lim _{N \rightarrow \infty}\left(\sum_{k=1}^{N} \frac{1}{k}-\log N\right) \] is the Euler constant.
Prove that \( A \Delta B=(A \cup B)-(A \cap B) \) for \( A, B \subseteq U= \) universal set
70. For how many integer values of \( x \) is \( \frac{2 x^{2}-10 x-4}{x^{2}-4 x+3} \) an integer? (a) 4 (b) 5 (c) 6 (d) 7
b) \( \lim _{x \rightarrow 0} \frac{\ln \left(1+x^{2}\right)}{1-\cos x} \)
b) \( \lim _{x \rightarrow 0} \frac{\ln \left(1+x^{2}\right)}{1-\cos x} \)
1. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set \( \mathrm{A}=\{1,2,3, \ldots, 13,14\} \) defined as \[ \mathrm{R}=\{(x, y): 3 x-y=0\} \] (ii) Relation R in the set N of natural numbers defined as \[ \mathrm{R}=\{(x, y):…