(Q). How many natural numbers less than 1000 will have exactly 3 factors?Solution:-Only square of a prime number has three factors, So the number are:2², 3², 5², 7², 11², 13², 17², 19², 23², 29², 31² above numbers are less than 1000 & each one has 3 factorsHence...
(Q). How many 2 digit numbers exist whose number of factors is 8?Solution:- If N = aᵖbᑫcʳ…..then number of factors = (p+1)(q+1)(r+1)………we are given that number of factors = 8∴ (p+1)(q+1)(r+1)……. = 8we have following cases:-...
(Q). In how many ways can a mixed double game in Tennis be arranged from 20 married couples, if no husband and wife play in the same game.Solution:-2 men can be selected in ²⁰C₂...
(Q). In how many ways two numbers can be selected from 100, 101, 102, ……… 199 such that when these selected numbers are multiplied then the product is divisible by 3?Solution:- Numbers divisible by 3...
(Q). Out of 8 men and 4 women a committee of 5 is to be formed. In how many ways this can be done:(i). So as to include at least 1 woman in the committee(ii). So as to include at least 1 woman in the comittee & exclude at least 1 man from the...
(Q). A question paper is divided into two parts A & B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part...
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