Permutation: n Different Things Taken All at a Time When All Are Not Different.

Q.

The Largest $4$ Digits Odd Number

Q. All the rearrangements for the letters of the word $DEMAND$ are written without including any word that has two $D^{\prime }s$ appearing together. If all these are arranged in dictionary order, then the rank of the word $DEMAND$ is

1. $36$
2. $74$
3. $42$
4. $86$

Q.

The total no. of permutations of $\mathrm{n}(\mathrm{n}>1)$ different things have taken not more than $\mathrm{r}$ at a time, when each thing may be repeated any number of times is$?$

1. $\frac{\mathrm{n}\left({\mathrm{n}}^{\mathrm{r}}-1\right)}{\left(\mathrm{n}-1\right)}$

2. $\frac{\left({\mathrm{n}}^{\mathrm{r}}-1\right)}{(\mathrm{n}-1)}$

3. $\frac{\mathrm{n}({\mathrm{r}}^{\mathrm{n}}-1)}{(\mathrm{n}-1)}$

4. $\frac{\mathrm{n}(\mathrm{n}-\mathrm{r})}{(\mathrm{n}-1)}$

Q. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL are arranged in a dictionary. Then the position of the word SMALL is : -

1. $52nd$
2. $58th$
3. $46th$
4. $59th$

Q. 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 ?

1. ${46}^{th}$
2. ${59}^{th}$
3. ${52}^{th}$
4. ${58}^{th}$

Q. The number of anagrams of the word ${}^{\prime }COLOURFU{L}^{\prime }$ is

1. $45359$
2. $45360$
3. $45361$
4. none of these

Q. Number of permutations of three different things $A,B,C,D$ taking:-

1. 12
2. 24
3. 4
4. \N