Q19 / 98 · NTA Abhyas (JEE Main) 2020 · Mathematics · Permutation Combination

The number of ordered pairs of positive integers $(a, b),$ such that their Least Common Multiple is the given positive integer $7^{2} \times 1 1^{3} \times 1 9^{4},$ is equal to

Correct answer: 315

Solution

Required number of ordered pairs

= (2 \times 2 + 1) (2 \times 3 + 1) (2 \times 4 + 1)

= 5 \times 7 \times 9 = 315

Hence, the correct answer is 315.

More Permutation Combination Questions

If n objects are arranged in a row, then the number of ways of selecting three objects such that no two of them are next to each other is
If there are nine straight lines of which five are concurrent at a point and the other four are concurrent at another point and no two of th
There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrically situated (that is each room
The number of ways in which 2 n distinct letters (addressed) can be distributed in N distinct mail boxes such that there are exactly K lette
The number of words of 4 letters which can be formed with the letters of the word M A T H E M A T I C S is α , then α 300 is
A shopkeeper has 10 copies each of nine different books, then the number of ways in which atleast one book can be selected is