Let a be A Factor Of 120, Then The Number Of Integral Solution Of x1x2x3 = a is 

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.



Let a be a factor of 120, then the number of integral solution of x1x2x3 = a is 


Correct option is


Let x4 be such that x4 = 120/a. then, the number of positive integral solutions of x1x2x3 = a is same as that of number of positive integral solutions of x1x2x3x4 = 120 = 23 × 3 × 5.     

We can assign 3 and 5 to unknown quantities in 4 × 4 ways. We can assign all 2 to one unknown in 4C1 ways, to two unknowns in (4C2)(2) and to three unknown in 4C3 ways. Hence, the number of required solutions  

          = 4 × 4 × [4C1 + (4C2)(2) + 4C3]   

          = 4 × 4 × 20 = 320.



The number of ways of arranging letters of the word RACHIT so that the vowels are in alphabetical order is


A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is


The number of ways in which a mixed double game can be arranged from amongst 9 married couple if no husband and wife play in the same game is 


The number of times the digit 3 will be written when listing the integers from 1 to 1000 is


The number of positive integers n such that 2n divides n! is


A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is    


The sum of the factors of 9! Which are odd and are of the form 3m + 2, where m is a natural number is 


Sum of all three digit numbers (no digit being zero) having the property that all digit are perfect squares, is


Let S = {1, 2, 3, ... n}. if X denote the set of all subsets of S containing exactly two elements, then the value of   


There are 15 points in a plane of which exactly 8 are collinear. Find the number of straight lines obtained by joining there points.