Permutation

Q. The rank of the word $SUCCESS$, If all possible permutations of the word $SUCCESS$ are arranged in dictionary order is

1. $341$
2. $331$
3. $351$
4. $361$

Q.

What is the value of ${}^4{C}_2$?

Q. The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is

1. 216
2. 120
3. 192
4. 72

Q.

In a survey of 100 students, the number of students studying the various languages were found to be : English only 18, English but not Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, no language 24. Find :

(i) How many students were studying Hindi ?

(ii) How many students were studying English and Hindi ?

Q.

What is the factorial of $\left(n+1\right)$?

Q. If three dice are rolled, then total number of possible outcomes is

Q.

All possible four digit numbers are formed using the digits $0,1,2,3$, so that no number has repeated digits. The number of even numbers among them is?

1. $9$

2. $18$

3. $10$

4. None of these

Q.

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together ?

Q. The total number of permutations of the letters of the word “BANANA” is

1. 60
2. 120
3. 720
4. 24

Q.

There are 6 books of physics, 3 of chemistry and 4 of biology. Number of ways in which these books can be placed on a shelf if the books of the same subject are to be together is

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.

How many numbers are there between 100 and 1000 in which all the digits are distinct?

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. 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 5 digit numbers which are divisible by 4, with digits from the set $\{1,2,3,4,5\}$ and the repetition of digits is allowed, is.

Q.

The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is

1. None of these

2. 4!

3. $4!\times 3!$

4. $3!\times 3!$

Q.

Write all possible $3$-digit numbers using $8,7,0$(only once) and arrange them in ascending and descending orders.

Q. How many three digit numbers more than 700 that can be formed using the digits 2, 3, 4, 6, 7(repetition allowed).

1. 25
2. 18
3. 20
4. 12

Q. There are $7$ greetings cards, each of a different colour and $7$ envelopes of same $7$ colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly $4$ of the cards go into envelopes of respective colour is

1. $3!{}^7{C}_3{}^4{C}_3$
2. $3!{}^4{C}_4$
3. ${}^7{C}_3$
4. $2\cdot {}^7{C}_3$

Q.

A letter lock consists of three rings each narked with 10 different letters. In how many nays it is possible to make an unsuccessful attempt to open the lock ?

Q. The number of arrangements of the letters of the word $BANANA$ in which two $N^{\prime }s$ do not appear adjacently is :

1. $40$
2. $60$
3. $100$
4. $80$

Q.

How many $10$-digit numbers can be written by using digits $9$ and $2$?

1. ${}^{10}C_1+{}^{9}C_2$

2. $2^{10}$

3. ${}^{10}C_2$

4. $10!$

Q. The number of $4$ digit numbers without repetition that can be formed using the digits $1,2,3,4,5,6,7$ in which each number has two odd digits and two even digits is

1. $450$
2. $432$
3. $436$
4. $454$

Q.

The number of ordered triplets of positive integers which are solutions of the equation $x+y+z=100$ is$?$

1. $6005$

2. $4851$

3. $5081$

4. None of these

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

Q.

If $x^2+2x+n>10$ for all real numbers $x$, then which of the following conditions is correct?

1. $n<11$

2. $n=10$

3. $n=11$

4. $n>11$

5. $n<-11$

Q.

In a plane there are 10 points out of which 4 are collinear, then the number of triangles that can be formed by joining these points are

1. 60

2. 116

3. 115

4. 105

Q. The number of arrangements of the letters of the word CALCUTTA

1. 10, 080
2. 40, 320
3. 2520
4. 5040

Q.

Find the Number of ways such that 5 boys and 5 girls sit together such that boys and girls are in alternate positions

Q.

How many different 4 digit number licence plates can be made if

i. Repetition is not allowed

ii. Repetition is allowed