Modern Math Previous Year Questions (CAT)  Set 0003

Previous years`s CAT questions: Modern Math
Post your solutions as reply to respective questions below.

Question 1
For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is
a. 3
b. 4
c. 6
d. 5 (CAT 1999)

Answer: Option a

Question 2
In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?
a. 10
b. 12
c. 17
d. 22 (CAT 1999)

Answer: Option c

Question 3
Abraham, Border, Charlie, Dennis and Elmer, and their respective wives recently dined together and were seated at a circular table. The seats were so arranged that men and women alternated and each woman was three places away from her husband. Mrs Charlie sat to the left of Mr Abraham. Mrs Elmer sat two places to the right of Mrs Border. Who sat to the right of Mr Abraham?
a. Mrs Dennis
b. Mrs Elmer
c. Mrs Border
d. Mrs Border or Mrs DennisÂ Â Â (CAT 1999)

Answer: Option d

Question 4
How many numbers can be formed from 1, 2, 3, 4, 5, without repetition, when the digit at the unit’s place must be greater than that in the ten’s place?
a. 54
b. 60
c. 17
d. 2 × 4! (CAT 1998 )

Answer: Option b

Question 5
P, Q, R and S are four statements. Relation between these statements is as follows.
I. If P is true, then Q must be true.
II. If Q is true, then R must be true.
III. If S is true, then either Q is false or R is false.
Which of the following must be true?
a. If P is true, then S is false
b. If S is false, then Q must be true
c. If Q is true, then P must be true
d. If R is true, then Q must be trueÂ Â (CAT 1998 )

Answer: Option a

Question 6
(CAT 2001)
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Answer: Option 2

Question 7
Twentyseven persons attend a party. Which one of the following statements can never be true?
(1) There is a person in the party who is acquainted with all the twentysix others.
(2) Each person in the party has a different number of acquaintances.
(3) There is a person in the party who has an odd number of acquaintances.
(4) In the party, there is no set of three mutual acquaintances.Â (CAT 2003 Leaked)Â

Answer: Option 4

Question 8
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) 60Â Â (CAT 2003 Leaked)

Answer: Option 2

Question 9
In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a director?
a. 9! × 2b. 2 × 8!
c. 2 × 7!
d. None of these (CAT 1997)

Answer: Option b