Home
Class 12
MATHS
Find the number of permutations of the s...

Find the number of permutations of the set {1,2,3,4} in which no two adjacent positions are filled by consecutive integers ( increasing orders).

Text Solution

Verified by Experts

The correct Answer is:
18
Let the equation of line be (y-2) = m(x-8) where `m lt 0.`
`rArr P-= (8-(2)/(m), 0)" and " Q -=(0 ,2-8m)`
`"Now, "OP+OQ =|8-(2)/(m)| + |2 -8m|`
`= 10+(2)/(-m) + (-8m)`
`ge 10+2sqrt((2)/(-m) xx(-8m)) ge 18`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (JEE MAIN)|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (JEE ADVANCED)|3 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MATRIX MATCH TYPE)|8 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Total number of relations that can be defined on set A = {1,2,3,4} is

Show that number of equivalence relation in the set {1,2,3} containing (1,2) and (2,1) is two.

Knowledge Check

  • Total number of relations that can be defined on set A={1,2,3,4} is

    A
    `2^(4)`
    B
    `2^(8)`
    C
    `2^(12)`
    D
    `2^(16)`

    • Similar Questions

    Explore conceptually related problems

    Find the number of permutations of the letters of the words 'FORECAST' and 'MILKY' taking 5 at a time of which 3 letters from the first word and 2 from the second.

    Find the number of permutations of the letters of the words FORECAST and MILKY taking 5 at a time of which 3 letters from the first word and 2 from the second .

    Find the numbers of positive integers from 1 to 1000, which are divisible by at least 2, 3, or 5.

    There are 720 permutations of the digits 1, 2, 3, ,4 ,5, 6. Suppose these permutations are arranged from smallest to largest numerical values, beginning from 123456 and ending with 654321. Then the digit in unit place of number at 267th position is________.

    Among the 8! [permutations of the digits 1, 2, 3..., 8, consider those arrangements which have the following property. If we take any five consecutive positions the product of the digits in these positions is divisible by 5. The number of such arrangements is equal to a. 7! b. 2.(7!) c. 7C_4 d. none of these

    Find the total number of n -digit number (n >1) having property that no two consecutive digits are same.

    Find two consecutive positive odd integers, sum of whose squares is 290.

    Home
    Profile