How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

a) 7

b)

c)

d)

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in a dictionary, then the word SACHIN appears at serial number

a) 602

b) 603

c) 600

d) 601

Range of function  is

a) {1, 2, 3}

b) {1, 2, 3, 4, 5, 6}

c) {1, 2, 3, 6}

d) {1, 2, 3, 4, 5}

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order

a) 120

b) 240

c) 360

d) 480

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first 5 questions. The number of choices available to him is

a) 140

b) 196

c) 280

d) 346

The number of ways 6 men and 5 women can dine at a round table, if no two women are to sit together is given by

a)

b)

c)

d)

If  denotes the number of combinations of n things taken r at a time, then the expression  equals

a)

b)

c)

d)

Three boys and three girls are to be seated around a table in a circle. Among them a boy X does not want any girl neighbor and a girl Y does not want any boy neighbor. The number of such arrangements possible is

a) 6

b) 4

c) 5

d) 9

Out of 18 points in a plane no three are in a straight line except five points which are collinear. The number of straight lines that can be formed joining them is

a) 144

b) 143

c) 153

d) None of these

The total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times is

a)

b)

c)

d)

The letters of the word ‘MODESTY’ are written in all possible orders and these words are arranged as in a dictionary, then the rank of the word ‘MODESTY’ is

a) 720

b) 1681

c) 2520

d) 5040

In how many ways can the letters of the word PERSON be placed in the squares of the adjoining figure so that no row remains empty

a) 18700

b) 18720

c) 8!

d) 6!

Different words are formed by arranging the letters of the word “ARRANGE”. All these words are written in the form of a dictionary. The rank of the word “ARRANGE” in the dictionary is

a) 340

b) 360

c) 342

d) 343

Different words are formed by arranging the letters of the word “ARRANGE”. All these words are written in the form of a dictionary. The number of words in which at least one vowel is in between two consonants is

a) 18

b) 36

c) 624

d) 836

There are two urns. Urn A has 3 distinct red balls and Urn B has 9 distinct blue balls. From each urn 2 balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

a) 3

b) 36

c) 66

d) 108

From 9 different novels and 3 different dictionaries 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

a) At least 500 but less than 750

b) At least 750 but less than 1000

c) At least 1000

d) Less than 500

Ten different letters of an alphabet are given. Words with five letters are formed from the given letters. Then the number of words which have at least one letter repeated is

a) 69760

b) 30240

c) 99748

d) None of these

The value of  is equal to

a)

b)

c)

d) None of these

Eight chairs are numbered one to eight. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 then the men select the chairs from amongst the remaining. The number of possible arrangements is

a)

b)

c)

d) None of these

An n digit number is a positive number with exactly n–digits. Nine hundred distinct n–digit numbers are to be formed with only the three digits 2, 5 and 7. The smallest value of n for which this is possible is

a) 6

b) 7

c) 8

d) 9

How many different 9 digit numbers can be formed from the numbers 223355888 by rearranging its digits so that the odd digits occupy even positions

a) 16

b) 36

c) 60

d) 180

If

a)

b) [2, ∞)

c)

d)

The number of arrangements of two letters of the word BANANA in which two N’s do not appear adjacently is

a) 40

b) 60

c) 80

d) 100