MCQ
The smallest positive integer $n$ for which $n! <\Big(\frac{\text{n+1}}{2}\Big)^\text{n}$ holds, is:
  • A
    $1$
  • $2$
  • C
    $3$
  • D
    $4$

Answer

Correct option: B.
$2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If the points $A(3,{\rm{ }}4),\,B(7,{\rm{ }}7),\,C(a,{\rm{ }}b)$ be collinear and $AC = 10$, then $(a,{\rm{ }}b)$=
$\mathop {\lim }\limits_{n \to \infty } \left( {\frac{{{{\left( {n + 1} \right)}^{1/3}}}}{{{n^{4/3}}}} + \frac{{{{\left( {n + 2} \right)}^{1/3}}}}{{{n^{4/3}}}} + .... + \frac{{{{\left( {2n} \right)}^{1/3}}}}{{{n^{4/3}}}}} \right)$ is equal to
The eccentricity of the ellipse $9{x^2} + 5{y^2} - 30y = 0$, is
Let $a_1, a_2, \ldots \ldots, a_n$ be in A.P. If $a_5=2 a_3$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots . \cdot \frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to $..........$.
The greatest integer which divides the number ${101^{100}} - 1$, is
An organization awarded $48$ medals in event '$A$',$25$ in event '$B$ ' and $18$ in event ' $C$ '. If these medals went to total $60$ men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
Let the line $y - \sqrt 3 x + 3 = 0$ cuts the parabola $2y^2 = 2x + 3$ at $A$ and $B$ . If $P(\sqrt 3,0)$ , then value of $|PA -PB|$ is [where $PA$ denotes distance between points $P$ and $A$]
If $ \mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2\mathrm{x}+\mathrm{b}(\mathrm{x}<\alpha)\\\mathrm{x}+\mathrm{d}(\mathrm{\text{x}}\geq\alpha)\end{array}\right.$ is such that $ \lim_\limits{\text{x} \rightarrow \text{a}}\text{f}(\text{x}=\text{L}),$ then $L.$
Every body in a room shakes hands with everybody else. The total number of hand shakes is $66.$ The total number of persons in the room is.
If in a family, there is at least one boy among three children, then the probability of two boys and one girl in the family is :