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` `S(10)` equals

A

3

B

6

C

9

D

12

Text Solution

Verified by Experts

The correct Answer is:
C

`because 10^(2)=2^(2)*5^(2)`
`thereforeS(10)=3xx3=9`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n,ngt1 ,x,y,n in N S(10) equals

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 f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5. i.e., 4=1+1+1+1 =1+1+2=1+2+1=2+1+1=2+2 Q. The number of solutions of the equation f(n)=n , where n in N is

lf f is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I , then

Let S_(n) denote the sum of the cubes of the first n natural numbers and S'_(n) denote the sum of the first n natural numbers, then underset(r=1)overset(n)Sigma ((S_(r))/(S'_(r))) equals to

The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the bth triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . If (m+1) is the nth triangular number, then (n-m) is

The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the bth triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . The value of t_(50) is

The number of positive integers satisfying the inequality .^(n+1)C(n-2)-.^(n+1)C(n-1)<=100 is

Let P_n denotes the number of ways in which three people can be selected out of 'n' people sitting in a row, if no two of them are consecutive. If P_(n+1)- P_n=15 then the value of 'n is____.

Let an denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_n = the number of such n-digit integers ending with digit 1 and c_n = the number of such n-digit integers ending with digit 0. The value of b_6 , is