Chapter 5

There are 4 balls of different colours and 4 boxes of colours same as those of the balls, The number of ways in which the balls, one in each box could be placed such that a ball does not go to a box of its own colour is (a) 5 (b) 6 (c) 9 (d) 12

Let \(\mathrm{T}_{\mathrm{n}}\) denote the no of triangles which can be formed using the vertices of regular polygon of \(\mathrm{n}\) sides if \(\mathrm{T}_{(\mathrm{n}+1)}-\mathrm{T}_{\mathrm{n}}=21\) then \(\mathrm{n}=\) is (a) 4 (b) 5 (c) 6 (d) 7

The number of 9 digit numbers formed using the digit 223355888 such that odd digits occupy even places is (a) 16 (b) 36 (c) 60 (d) 80

Five digit numbers divisible by 3 are formed using the digits \(0,1,2,3,4,5,6,7\) without repetition. The no, of such numbers are (a) 936 (b) 480 (c) 600 (d) 216

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 choice available to him is (a) 140 (b) 196 (c) 180 (d) 346

The number of ways of distributing 8 identical balls in 3 distinct boxes so that no box is empty is (a) 5 (b) \({ }^{8} \mathrm{C}_{3}\) (c) 38 (d) 21

The number of positive integer solution of the equation \((\mathrm{x} / 99)=[\mathrm{x} /(101)]\) is (a) 2500 (b) 2499 (c) 1729 (d) 1440

If the letters of the word SACHIN are arranged in all possible ways and these words are written in dictionary order then the word SACHIN appears at serial number (a) 600 (b) 601 (c) 602 (d) 603

The product of n natural number \(\mathrm{n} \geq 2\) is (a) not divisible by n (b) divisible by \(\mathrm{n}\), but not by \(2 \mathrm{n}\) (c) divisible by \(2 \mathrm{n}\), but not by n! (d) divisible by n!

Nine hundred distinct n digit numbers are to be formed using only the 3 digits \(2,5,7 .\) The smallest value of \(\mathrm{n}\) for which this is possible is (a) 6 (b) 7 (c) 8 (d) 9