CAT Sample Questions

Quantitative Section : Quantitative Sample Questions

Permutation and Combination

161. How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
     1. 16C7 * 7!
     2. 12C4 * 4C3 * 7!
     3. 12C3 * 4C4
     4. 12C4 * 4C3

     Ans : B

162. In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
     1. 5C3
     2. 5P3
     3. 53
     4. 35

     Ans : D

163. How many number of times will the digit '7' be written when listing the integers from 1 to 1000?
     1. 271
     2. 300
     3. 252
     4. 304

     Ans : B

164. There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
     1. 5
     2. 21
     3. 33
     4. 60

     Ans : B

165. What is the value of 1*1! + 2*2! + 3!*3! + ............ n*n!, where n! means n factorial or n(n-A(n-2)...1
     1. n(n-A(n-A!))
     2. (n+A!)/(n(n-A))
     3. (n+A! - n!)
     4. (n + A! - 1!)

     Ans : D

166. There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?
     1. 15624
     2. 16384
     3. 6144
     4. 240

     Ans : A

167. In how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?
     1. 10! - 2!
     2. 9! - 2!
     3. 10! - 9!
     4. None of these

     Ans : D

168. How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 which are divisible by 3, without repeating the digits?
     1. 15
     2. 96
     3. 216
     4. 120

     Ans : C

169. How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively?
     1. 8! / 2!
     2. 8! - 2!
     3. 6!
     4. 8! - 2*7!

     Ans : C

170. Four dice are rolled simultaneously. What is the number of possible outcomes in which at least one of the die shows 6?
     1. 6! / 4!
     2. 625
     3. 671
     4. 1296

     Ans : C