Dearrangement

Q. There are four balls of different colors and four boxes of colors same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own color is ___.

Q. There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is

1. $9$
2. $8$
3. $16$
4. None of these

Q. What numbers should be added to $\frac{-5}{8}$ so as to get $\frac{-3}{2}$?

1. $-\frac{5}{8}$
2. $\frac{7}{8}$
3. $-\frac{1}{8}$
4. $-\frac{7}{8}$

Q. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2, the number of ways it can be done is -

1. 265
2. 264
3. 53
4. 67

Q.

If 5 letters are taken out of 5 different envelopes. In how many ways, can they be reinserted in the envelopes so that no letter goes to its original envelopes?

1. 9

2. 44

3. 120

4. 24

Q. A printer alloted consecutive integers to all the pages of a book starting with 1 .In this process the sum of pages is $1275$. Then the total number of pages in that book is

1. $50$
2. $51$
3. $100$
4. $101$

Q. Calculate the mean of the distribution given below using the short cut method.

Marks	$11-20$	$21-30$	$31-40$	$41-50$	$51-60$	$61-70$	$71-80$
No. of students	$2$	$6$	$10$	$12$	$9$	$7$	$4$

Q.

5 countries president and prime minister went for summit. If all 5 prime minister shake hand to president at random, in how many ways they can shake hand if none of the same country PM shake hand to that country president.

1. 9

2. 44

3. 120

4. 24

Q. There are four balls of different colors and four boxes of colors same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own color is .....

Q. $A,B$ and $C$ can do a job in $11,20$ and $55$ days respectively. How soon can the work be done if $A$ is assisted by $B$ and $C$ on alternate days?

1. $7$ days
2. $9$ days
3. $8$ days
4. $10$ days

Q. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

1. 264
2. 265
3. 53
4. 67

Q. Find the sum of the first $12$ natural numbers each of which is a multiple of $7$.

Q. Supposing $4$ letters are placed in $4$ different envelopes. In how many ways can they be taken out from their original envelopes and distributed among the $4$ different envelopes so that no letter remains in its original envelope?

1. $7$
2. $8$
3. None of these
4. $9$