Gate : Computer Science, Objective Type Questions and Answers

(1)The number of different permutations of the word BANANA is

(a) 720
(b) 60
(c) 120
(d) 360

Ans : 60

(2) 7 Women and 7 Men are to sit round a circular table such that there is a man on either side of every women; the number of seating arrangements is

(a) (7!)2
(b) (6!)2
(c) 6! x 7!
(d) 7!

Ans : C, 6! x 7!

(3) The number of diagonals that can be drawn by joining the vertices of an octagon is

(a) 28
(b) 48
(c) 20
(d) none of these

Ans : 20

(4) In an examination there are three multiple choice Questions and each questions has 4 choices. Number of ways in which a student can fail to get all answers correct is

(a) 11
(b) 12
(c) 27
(d) 63

Ans : D, 63

(5) Raman has 6 friends. In how many ways can be invite one or more of them at a dinner?

(a) 61
(b) 62
(c) 63
(d) 64

Ans : 63

(6) Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

(a) 60
(b) 120
(c) 7200
(d) 7600

Ans  : C, 7200

(7) In how many ways can 5 prizes be distributed among 4 boys when every boys can take one or more prizes?

(a) 1024
(b) 625
(c) 120
(d) 600

Ans : 1024

(8) The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is

(a) 1958
(b) 1956
(c) 16
(d) 64

Ans : 1956

(9) A student can take one of four Mathematics sections and one of five English sections. The number n of ways he can register for the two courses, is

(a) 4
(b) 5
(c) 20
(d) 30

Ans : C, 20

Explanation : Then four choices of Mathematics and Five choices for English. 
Hence       :    n = 4 x 5 =20

(10) There are four bus lines between A and B; and three bus lines between B and C. The number of ways a person can travel

(i) by bus from A to C by way of B.
(a) 10
(b) 12
(c) 14
(d) 24

Ans : 12

Explanation : There are four ways to go from A to B and three ways to go from B to C; 
Hence there are 4 x 3 =12 

(ii) Round trip by bus from A to C by way of B.
(a) 12
(b) 48
(c) 144
(d) 264

Ans : 144

Explanation : There are twelve ways to go from A to C by way of B, and 12 ways to return.
Hence there are 12 x 12 = 144 ways.

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