Five boys and five girls are writing an examination in a hall in which $5$ benches are arranged in a row and only two students are to be seated on every bench at either of its ends. If the seating arrangement is to be such that no two boys or no two girls sit together as neighbours (a student should not have a student of same gender either on left or right),then the total number of such arrangements is
- A$28800$
- B$14400$
- C$240$
- D$480$
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Let $5$-digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed,and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.
DifficultJEE MAIN 2023
View SolutionThe number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is
Let $x$ and $y$ be two $2$-digit numbers such that $y$ is obtained by reversing the digits of $x$. Suppose they also satisfy $x^2-y^2=m^2$ for some positive integer $m$. The value of $x+y+m$ is
Consider all possible permutations of the letters of the word $ENDEANOEL$. Match the Statements / Expressions in $Column I$ with the Statements / Expressions in $Column II$.
$Column I$ $Column II$ $(A)$ The number of permutations containing the word $ENDEA$ is $(p)$ $5!$ $(B)$ The number of permutations in which the letter $E$ occurs in the first and the last positions is $(q)$ $2 \times 5!$ $(C)$ The number of permutations in which none of the letters $D, L, N$ occurs in the last five positions is $(r)$ $7 \times 5!$ $(D)$ The number of permutations in which the letters $A, E, O$ occur only in odd positions is $(s)$ $21 \times 5!$
| $Column I$ | $Column II$ |
| $(A)$ The number of permutations containing the word $ENDEA$ is | $(p)$ $5!$ |
| $(B)$ The number of permutations in which the letter $E$ occurs in the first and the last positions is | $(q)$ $2 \times 5!$ |
| $(C)$ The number of permutations in which none of the letters $D, L, N$ occurs in the last five positions is | $(r)$ $7 \times 5!$ |
| $(D)$ The number of permutations in which the letters $A, E, O$ occur only in odd positions is | $(s)$ $21 \times 5!$ |
$^{80}C_{40}$ is not divisible by -
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