If the positive integers are formed using any number of digits from 0,1,2,3,4,5 but using each digit not more than once in any number, then find how many of these integers are greater than 3000?
Answer: A The number of 4 digit number greater than 3000 and the number of all possible 5-digit and 6 digit number are listed below:- 4 digit ----> (3) (5) (4) (3)-----> 180 5 digit----->(5) (5) (4) (3) (1)-----> 600 6 digit-----> (5) (5) (4) (3) (2) (1)----> 600 In total= 180+ 600+ 600 = 1380.
Q. No. 26:
How many three digit positive integers, are there whose hundreds digit is greater than the tens digit, which in turn, is greater than the unit digit?
Answer: A Let HTU be the three digit number where H>T>U So, H not equal to zero. Of the ten digits (i.e 0 to 9) any combination of three digits will have exactly one arrangement where H>T>U. So, every combination of three distinct digits will give exactly one number satisfying the given condition. The number of three-digit numbers possible =10C3 = 120.
Q. No. 27:
In how many ways can twelve girls be arranged in a row if two particular girls must occupy the end places?
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. the number of choices available to him is
Answer: B Considering all vowels--- a,e,i,o,u as one unit the eight letters can be arranged in 8P8=8!ways The four vowels can be arranged themselves in 4P4 = 4!ways Total number of arrangements = 8! * 4!