Home
Class 12
MATHS
Let S(n) denotes the number of ordered p...

Let `S(n)` denotes the number of ordered pairs `(x,y)` satisfying `1/x+1/y=1/n,AA ,n in N` , then find `S(10)` .

A

S(3)+S(4)

B

S(5)+S(6)

C

S(8)+S(9)

D

S(1)+S(11)

Text Solution

Verified by Experts

The correct Answer is:
C
`because 6^(2)=2^(2)*3^(2)`
`impliesS(6)=3xx3=9 and 7^(2)impliesS(7)=3`
`thereforeS(6)+S(7)=12`
also, `8^(2)=2^(6)`
`impliesS(8)=7 and 9^(2)=3^(4) impliesS(9)=5`
`thereforeS(8)+S(9)=12`
`impliesS(6)+S(7)=S(8)+S(9)=12`.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Matching Type Questions)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|54 Videos

Similar Questions

Explore conceptually related problems

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n, " where " n gt 1 " and " x,y,n in N . " " (i) Find the value of S(6). " " (ii) Show that, if n is prime, then S(n)=3, always.

Let (S) denotes the number of ordered pairs (x,y) satisfying (1)/(x)+(1)/(y)=(1)/(n),x,y,n in N . Q. sum_(r=1)^(10)S(r) equals

Find the number ordered pairs (x ,y)ifx ,y in {0,1,2,3, , 10}a n dif|x-y|> 5.

Find the number ordered pairs (x ,y)ifx ,y in {0,1,2,3, , 10}a n dif|x-y|> 5.

The number of ordered pairs (x,y) , where x , y in N for which 4 , x , y are in H.P. , is equal to

Let ' n ' is the number of ordered pair (x ,y) satisfying the system of equations {x^2y^2-2x+y^2=0 2x^2-4x+3+y^2=0(x , y in R) and ' S ' is the sum of all the values of xa n dy satisfying the given system of equations then (a) n > S (b) n < S (c) n-2 = S (d) S/n=2

The number of ordered pair(s) (x, y) of real numbers satisfying the equation 1+x^(2)+2x sin(cos^(-1)y)=0 , is :

Find the number of ordered pairs (m,n)epsilon {1,2,…..20} such that 3^(m)+7^(n) is divisible by 10.

Find the number of ordered pairs of natural numbers (x, y) satisfying the equation: (xy-1)^(2) = (x+1)^(2) + (y+1)^(2)

Find the number of ordered pair of real numbers (x, y) satisfying the equation: 5x(1+1/(x^(2)+y^(2)))=12 & 5y(1-1/(x^(2) + y^(2))) =4