Chapter 5

Let \(\mathrm{A}\) be a set with \(\mathrm{n}\) elements. The number of onto functions from \(\mathrm{A}\) to \(\mathrm{A}\) is (a) \(n^{n}\) (b) \(\mathrm{n}^{\mathrm{n}}-\mathrm{n} !\) (c) \(\left(\mathrm{n}^{\mathrm{n}} / \mathrm{n} !\right)\) (d) \(\mathrm{n} !\)

10 person are to be arranged around a round table. 3 persons wish to sit as a group number of ways the arrangement can be made is (a) \(9 ! \times 3 !\) (b) \(8 ! \times 3 !\) (c) \(7 ! \times{ }^{8} \mathrm{P}_{3}\) (d) \(7 ! \times 3 !\)

How many number greater than 10 lac be formed from \(2,3,0,3,4,2,3\) (a) 420 (b) 360 (c) 400 (d) 300

The average of the four digits numbers that can be formed by using each of the digits \(3,5,7\), and 9 exactly once in each number is (a) 4444 (b) 5555 (c) 6666 (d) 7777

In an examination a question paper consists of 10 questions which is divided into two parts. i.e. part \(i\) and part ii containing 5 and 7 questions respectively. A student is required to attempt 8 question in all selecting at least 3 from each part. In how many ways can a student select the questions (a) \({ }^{5} \mathrm{C}_{2} \cdot{ }^{7} \mathrm{C}_{2}+{ }^{5} \mathrm{C}_{1} \cdot{ }^{7} \mathrm{C}_{3}+{ }^{5} \mathrm{C}_{0} \cdot{ }^{7} \mathrm{C}_{4}\) (b) \({ }^{12} \mathrm{C}_{5} \cdot{ }^{12} \mathrm{C}_{7}\) (c) \({ }^{5} \mathrm{C}_{3} \cdot{ }^{7} \mathrm{C}_{5}\) (d) \({ }^{12} \mathrm{C}_{8}\)

Three boys and three girls are to be seated around a round table in a circle. Among them the boy \(\mathrm{X}\) does not want any girl neighbour and the girl \(\mathrm{Y}\) does not want any boy neighbour then the no. of arrangement is (a) 2 (b) 4 (c) 23 (d) 33

4 boys picked up 30 mangoes. In how many ways can they divide them, if all mangoes be identical (a) \({ }^{33} \mathrm{C}_{4}\) (b) \({ }^{33} \mathrm{C}_{2}\) (c) 5456 (d) 6554 .

The number of ways of dividing 15 men and 15 women into 15 couples each consisting of a man and a woman is (a) 1240 (b) 1840 (c) 1820 (d) 2005

The number of times the digits 3 will be written when listing the integers from 1 to 1000 is (a) 269 (b) 300 (c) 271 (d) 302

The number of ways of distributing 52 cards among four players so that three players have 17 cards each and the fourth player has just one card is (a) \(\left[(52 !) /(17 !)^{3}\right]\) (b) \(52 !\) (c) \((17 !)\) (d) \(\left[(52 !) /(17 !)^{2}\right]\)