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.