The letters of the word ‘INDIA’ are arranged as in a dictionary. What are the $1^{\text {st }}, 13^{\text {th }}, 49^{\text {th }}$ and $60^{\text {th }}$ words?
Alphabetical arrangement of letters: A,D,I,N
$\Rightarrow 1^{\text {st }}$ word: ADIIN
To find other words:
Case 1: words starting with A
Number of words $=\frac{4 !}{2 !}=12$
$\Rightarrow 13^{\text {th }}$ word starts with D and is DAllN
Case 2: words starting with D
Number of words $=\frac{4 !}{2 !}=12$
Case 3: Words starting with I
Number of words $=4 !=24$
$\Rightarrow(12+12+24+1)^{\text {th }}=49^{\text {th }}$ word starts with $\mathrm{N}$ and is $\mathrm{NAllD}$
Case 4: Words starting with N
Number of words $=\frac{4 !}{2 !}=12$
$\Rightarrow(48+12)^{\text {th }}$ word is the last word which starts with $\mathrm{N}$
$\Rightarrow 60^{\text {th }}$ word $=$ NDIIA
1st word: ADIIN
$13^{\text {th }}$ word: DAllN
$9^{\text {th }}$ word: NAllD
$60^{\text {th }}$ word: NDIIA