Home
Class 12
MATHS
How many ordered pairs of (m,n) integers...

How many ordered pairs of (m,n) integers satisfy `(m)/(12)=(12)/(n)`?

A

`30`

B

`15`

C

`12`

D

`10`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `(m)/(12)=(12)/(n)`
`impliesmn=144impliesn=(144)/(m)`
We want to find here total number of divisors of `144`
`144=2^(4)3^(2)`
Total divisors are `(4+1)(2+1)=15`
But negative pairs are also possible hence `=30`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|9 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

Similar Questions

Explore conceptually related problems

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

Find q and r for the following pairs of integers a and b satisfying a = bq + r . a = - 32, b = - 12

Show that the mutual inductance between a pair of coils is same (M_(12) = M_(21))

The number of ordered pairs (m,n) where m , n in {1,2,3,…,50} , such that 6^(m)+9^(n) is a multiple of 5 is

For any positive integer (m,n) (with ngeqm ), Let ((n),(m)) =.^nC_m Prove that ((n),(m)) + 2((n-1),(m))+3((n-2),(m))+....+(n-m+1)((m),(m))

If m , n are positive integers and m+nsqrt(2)=sqrt(41+24sqrt(2)) , then (m+n) is equal to

For non-negative integers m and n a function is defined as follows f(m,n) = {n+1 if m=0; f(m-1,1) if m!=0, n=0} Then the value of f(1,1) is

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi