Permutation

Q.

How many numbers greater than $24000$can be formed by using digits $1,2,3,4,5$when no digit is repeated?

1. $36$

2. $60$

3. $84$

4. $120$

Q. The digits of a three-digit positive integer are in A.P. and their sum is $15$. The number obtained by reversing the digits is $594$ less than the original number. Then the number is

1. $452$
2. $852$
3. $1252$
4. $1652$

Q. If all the letters of the word $"SECRET"$ are arranged in all possible ways and written out in alphabetical(dictionary) order, then the rank of the given word $"SECRET"$ will be

Q. If $3$ dice are rolled, then the number of possible outcomes in which at least one dice shows $5$ is

Q. Let $A=\{x_1,x_2,x_3,\dots ,x_8\},B=\{y_1,y_2,y_3\}$ then the total number of functions from $A$ to $B$ such that all the elements of $B$ has atleast one pre image and there are exactly four elements in $A$ having image as $y_3,$ are

1. $14\times {}^8{C}_4$
2. $24\times {}^8{C}_4$
3. $14\times {}^4{C}_4$
4. $16\times {}^4{C}_4$

Q. A debate club consists of $6$ girls and $4$ boys. A team of $4$ members is to be selected from this club including a selection of a captain (from among these four members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

1. $380$
2. $320$
3. $260$
4. $95$

Q. If the letters of the word $SACHIN$ are arranged in all possible ways and these words(with or without meaning) are written out as in dictionary, then the position of the word $SACHIN$ will be

1. $601$
2. $600$
3. $603$
4. $602$

Q. The sum of all the different four digit numbers that can be formed with the digits $2,3,4,5$ taken all at a time is

1. $93324$
2. $93240$
3. $9324$
4. none of these

Q. $n$-digit numbers are formed using only three digits $2,5$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed, is :

1. $6$
2. $7$
3. $8$
4. $9$

Q. Using 3, 4, 5, 6, 7, 8(repetition allowed) how many numbers between 3000 and 4000 can be formed which are divisible by 5?

1. 18
2. 20
3. 36
4. 12

Q. The letters of the word COCHIN are arranged and all the words are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is:

1. $360$
2. $192$
3. $96$
4. $48$

Q. If $(n+1)!=12(n-1)!$, then the value of $n$ is

1. $2$
2. $3$
3. $4$
4. $5$

Q. Consider all the permutations of the word $BENGALURU$. The number of words in which vowels occur at even places is given as $A$ and the number of words in which the letters of the word $GLUE$ appear together in that order is given as $B$. Find the value of $A-B$

1. $1440$
2. $720$
3. $2160$
4. $1200$

Q. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be a member of same team, is :

1. 200
2. 300
3. 350
4. 500

Q. The number of integers greater than a million (Ten lakhs) that can be formed using the digits
$2,3,0,3,4,2,3$ is

1. $240$
2. $320$
3. $360$
4. $300$

Q.

Find the total number of 9 digit numbers which have all different digits.

1. 3265920

2. 3267720

3. $9\times 9!$

4. $9\times 10!$

Q. The number of different signals can be given by using any number of flags from $4$ flags of different colours is

1. $24$
2. $256$
3. $64$
4. $60$

Q. If a $5$ digit number is made using all the digits from $1,3,4,6,8$, such that all the digits of number from $1$st position to $5$th should not be in increasing order, then the position of number ${}^{\prime \prime }{63184}^{\prime \prime }$ after listing all the numbers formed in ascending order is

1. $77$
2. $78$
3. $79$
4. $80$

Q. If $18$ guests have to be seated, half on each side of a long table. $4$ particular guests desire to sit on one particular side and $3$ on the other side, then the number of ways in which the sitting arrangements can be made is

1. ${}^{11}{C}_3\cdot (9!{)}^2$
2. ${}^{11}{C}_4\cdot (9!{)}^2$
3. $(9!{)}^2$
4. ${}^{11}{C}_5\cdot (9!{)}^2$

Q. A letter lock consists of three rings each marked with ten different letters. Then how many ways it is possible to make an unsuccessful attempt to open the lock.

1. 29
2. 30
3. 999
4. 1000

Q. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

1. $603$
2. $601$
3. $600$
4. $602$

Q. If a $6$ digits number's are formed using the digits $0,1,3,3,6,7$ and arranged in ascending order, then the position of the number ${}^{\prime \prime }{631307}^{\prime \prime }$ is

Q. If $(n+1)!=12(n-1)!$, then the value of $n$ is

1. $2$
2. $3$
3. $4$
4. $5$