For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?

  • [KVPY 2013]
  • A

    $S_n$ has a multiple of $19$

  • B

    $S_n$ has a prime

  • C

    $S_n$ has at least four multiples of $5$

  • D

    $S_n$ has at most six primes

Similar Questions

Examine whether the following statements are true or false :

$\{ x:x$ is an even natural number less than $6\}  \subset \{ x:x$ is a natural mumber which divide $36\} $

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\}  \ldots \{ x:x$ student of your school $\} $

Write the following sets in the set-builder form :

$\{ 3,6,9,12\}$

The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is

Write the following intervals in set-builder form :

$\left( {6,12} \right]$