Factorial

Q.

The value of 5! is _____

Q.

The sum of the digits in the unit place of all numbers formed with the help of $3,4,5,6$ taken all at a time is

1. $18$

2. $432$

3. $108$

4. $144$

Q. We have to choose $11$ players for cricket team from $8$ batsmen, $6$ bowlers, $4$ all rounders and $2$ wicket keepers. Number of selections, when two particular batsmen do not want to play when a particular bowler will play, is

1. ${}^{17}{C}_{10}+{}^{19}{C}_{11}$
2. ${}^{17}{C}_{10}+{}^{19}{C}_{11}+{}^{17}{C}_{11}$
3. ${}^{17}{C}_{10}+{}^{20}{C}_{11}$
4. ${}^{19}{C}_{10}+{}^{19}{C}_{11}$

Q.

In how many ways a team of 10 players out of 22 players can be made if 6 particular players are always to be included and 4 particular players are always excluded.

1. 

2. 

3. 

4. 

Q.

The number of numbers that can be formed by the digits 1, 2, 3, 4, 3, 2, 1 with the odd digits at odd places is

1. 430

2. 18

3. 36

4. None of these

Q.

Make correct statements by filling in the symbols $\subset$ or $\subset ̸$ in the blank spaces:

(i) {2, 3, 4} ..................... {1, 2, 3, 4, 5}

(ii) {a, b, c} ..................... {b, c, d}

(iii) {x : x is a student of Class XI of your school} ......... {x : x student of your school}

(iv) {x : x is a circle in the plane} ........... {x : x is a circle in the same plane with radius 1 unit}

(v) {x : x is a triangle in a plane} ........... {x : x is a rectangle in the same plane}

(vi) {x : x is an equilateral triangle in a plane} ............ {x : is a triangle in the same plane}

(vii) {x : x is an even natural number} .......... {x : x is an integer}

Q.

Find the remainder when 5k-1 is divided by 5, where k is a positive integer

__

Q. 1. Evaluate

Q. 8!3. Compute 61x2!

Q. 2.Ís 3 ! + 4-71?

Q. $A,B,C$ are three persons among $7$ persons who speak at a function. The number of ways in which it can be done if ${}^{\prime }{A}^{\prime }$ speaks before ${}^{\prime }{B}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ speaks before ${}^{\prime }{C}^{\prime }$ is

Q. Write the negation of the following statements:
(i) p : For every positive real number $x$ the number $x-1$ is also positive
(ii) q : All cats scratch
(iii) r : For every real number $x$, either $x>1$ or $x<1$
(iv) s : There exist a number $x$ such that $0<x<1$

Q. The maximum number of permutations of $2n$ letters in which there are only $a^{\prime }s$ and $b^{\prime }s,$ taken all at a time is given by

1. ${}^{2n}{C}_n$
2. $\frac{2}{1}\cdot \frac{6}{2}\cdot \frac{10}{3}\cdot \cdots \frac{4n-6}{n-1}\cdot \frac{4n-2}{n}$
3. $\frac{n+1}{1}\cdot \frac{n+2}{2}\cdot \frac{n+3}{3}\cdot \frac{n+4}{4}\cdot \cdots \frac{2n-1}{n-1}\cdot \frac{2n}{n}$
4. $\frac{2^n[1\cdot 3\cdot 5\cdots (2n-3\left)\right(2n-1\left)\right]}{n!}$

Q.

Find the intersection of each of the following pairs of sets :

(i) X = {1, 3, 5} and Y = {1, 2, 3}

(ii) A = {a, e, i, o, u} and B = {a, b, c}

(iii) A = {x : x is a natural number and multiple of 3} and B = {x : x is a natural number less than 6}

(iv) A = {x : x is a natural number and 1 < x $\le$ 6} and B = {x : is a natural number and 6 < x < 10}

(v) A = {1, 2, 3} and $B=\Phi$

Q. The product of r consecutive positive integers is divisible by
(a) r !
(b) (r − 1) !
(c) (r + 1) !
(d) none of these.

Q. Total number of different signals that can be made using atleast $3$ flags from $5$ flags of different colours is

Q.

The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all at a time is

1. 18

2. 432

3. 108

4. 144

Q. Seven athletes are participating in a race. If there are three prizes $Gold,Silver$ and $Bronze$, then the number of ways in which the prizes can be distributed to the athletes is

1. $35$
2. $105$
3. $210$
4. $420$

Q. The number of permutations of the word $AUROBIND$ in which vowels appear in the alphabetical order, is

1. ${}^8{P}_4$
2. ${}^8{C}_4$
3. $4!\times {}^8{C}_4$
4. $5!\times {}^8{C}_5$

Q.

The number of numbers that can be formed by the digits 1, 2, 3, 4, 3, 2, 1 with the odd digits at odd places is

1. 430
   

2. 36
   

3. 18
   

4. None of these

Q.

The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all at a time is

1. 18

2. 108

3. 144

4. 432

Q.

Eleven animals of a circus have to be placed in eleven cages one in each cage. If 4 of the cages are too small for 6 of the animals, find the number of ways of caging the animals.___

Q.

The value of $2^n\left\{\mathrm{1.3.5.....}\right(2n-3\left)\right(2n-1\left)\right\}$ is

1. $\frac{\left(2n\right)!}{n!}$

2. $\frac{\left(2n\right)!}{2^n}$

3. $\frac{n!}{\left(2n\right)!}$

4. $\frac{(2n-1)!}{n!}$

Q.

Find the total number of ways of selecting five letters from the letters of the word INDEPENDENT.___

Q.

The number of ways in which ten candidates $A_1,A_2,A_3......A_{10}$ can be ranked if $A_1$ and $A_2$ are next to each other is

1. 2!.9!
   

2. 2!.8!

3. 2!.11!
   

4. 2!.10!
   

Q. The remainder when $2!+4!+6!+8!+...+50!$ is divided by $18$ is

Q.

The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all at a time is

1. 18

2. 108

3. 432

4. 144

Q. The value of 1+ 1.1! + 2.2! + 3.3! + .......... + n.n! is

1. (n+1)!+1
2. (n+1)!–1
3. (n+1) !
4. (n–1) !

Q.

The value of $2^n\left\{\mathrm{1.3.5.....}\right(2n-3\left)\right(2n-1\left)\right\}$ is

1. 

2. 

3. 

4. 

Q.

Eleven animals of a circus have to be placed in eleven cages one in each cage. If 4 of the cages are too small for 6 of the animals, find the number of ways of caging the animals.___