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1543
CMI-2020-DataScience-A: 16
Which of the following are true? $\frac {2019}{2020} < \frac {2020}{2021}$ $x+\frac{1}{x} \geq 2$ for all $x>0$ $2^{60} >5^{24}$ $2^{314} <31^{42}$
Which of the following are true?$\frac {2019}{2020} < \frac {2020}{2021}$$x+\frac{1}{x} \geq 2$ for all $x>0$$2^{60} >5^{24}$$2^{314} <31^{42}$
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1544
CMI-2020-DataScience-A: 17
The identity $\frac{1}{(1-2r)}=\displaystyle\sum^{\infty} _{k=0} (2r)^k $ is true if and only if $r\neq \frac{1}{2}$ if and only if $0\leq r < \frac{1}{2}$ if and only if $-\frac{1}{2} \leq r<\frac{1}{2}$ if and only if $-\frac{1}{2}<r<\frac{1}{2}$
The identity$$\frac{1}{(1-2r)}=\displaystyle\sum^{\infty} _{k=0} (2r)^k $$is trueif and only if $r\neq \frac{1}{2}$if and only if $0\leq r < \frac{1}{2}$if and only if $-...
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2 answers
1545
CMI-2020-DataScience-A: 18
The sum and product of the roots of the polynomial $9x^2+171x-81$ are, respectively: $-19$ and $-9$ $19$ and $9$ $-9$ and $19$ $9$ and $-19$
The sum and product of the roots of the polynomial $9x^2+171x-81$ are, respectively:$-19$ and $-9$$19$ and $9$$-9$ and $19$$9$ and $-19$
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1547
CMI-2020-DataScience-A: 20
Which of the following inequalities are true? $e^x\geq(1+x)$ for $x\geq 0$ $e^x\leq(1+x)$ for $x<0$ $\text{In}(x)<(1+x)$ for $x>0$ $e^x<x^2$ for all real numbers $x$
Which of the following inequalities are true?$e^x\geq(1+x)$ for $x\geq 0$$e^x\leq(1+x)$ for $x<0$$\text{In}(x)<(1+x)$ for $x>0$$e^x<x^2$ for all real numbers $x$
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1548
CMI-2020-DataScience-B: 5
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2,\dots ,n\}$ to itself. We denote it using the notation $\begin{pmatrix}1 & 2 & & n \\ {\sigma(1)} & {\sigma(2)} &\dots & {\sigma(n)} \end{pmatrix},$ ...
A permutation $\sigma$ is a bijection from the set $[n]=\{1,2,\dots ,n\}$ to itself. We denote it using the notation$$\begin{pmatrix}1 & 2 & … & n \\ {\sigma(1)} & {\si...
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1556
CMI-2020-DataScience-B: 13
Let $R$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $R$ at random. What is the probability that the chosen relation is symmetric?
Let $R$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $R$ at random. What is the probability that the chosen relation is sy...
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1558
CMI-2020-DataScience-B: 15
For the function $f(x)=\text{ln}(x)/x$, show that the maximum value of $f(x)$ occurs when $x=e$. Use this to show that $x^e<e^x$ for all positive values of $x$.
For the function $f(x)=\text{ln}(x)/x$, show that the maximum value of $f(x)$ occurs when $x=e$. Use this to show that $x^e<e^x$ for all positive values of $x$.
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1559
CMI-2020-DataScience-B: 16
Given the set of letters $\text{\{a,b,c,d,e,f,g,h,i,j,k,l,m\}},$ ... $\text{bcjameflkihgd}$
Given the set of letters $\text{\{a,b,c,d,e,f,g,h,i,j,k,l,m\}},$ we can list out all permutations of these letters in lexicographic (dictionary) order. The first three pe...
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