JEE MAIN - Mathematics (2016 (Offline) - No. 16)
If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :
$${46^{th}}$$
$${59^{th}}$$
$${52^{nd}}$$
$${58^{th}}$$
Explicaţie
Clearly, number of words start with $$A = {{4!} \over {2!}} = 12$$
Number of words start with $$L = 4! = 24$$
Number of words start with $$M = {{4!} \over {2!}} = 12$$
Number of words start with $$SA = {{3!} \over {2!}} = 3$$
Number of words start with $$SL = 3! = 6$$
Note that, next word will be "SMALL"
Hence, the position of word "SMALL" is 58th.