Modern Math Previous Year Questions (CAT)  Set 0001

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

Question 1
There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
(1) 144
(2) 180
(3) 192
(4) 360
(5) 716 (CAT 2006)

Answer: Option 1

Question 2
A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:
Only September: 18
September but not August: 23
September and July: 8
September: 28
July: 48
July and August: 10
None of the three months: 24What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?
(1) 7
(2) 9
(3) 12
(4) 14
(5) 17 (CAT 2006)

Answer: Option 2

Question 3
Let S be the set of all pairs (i, j) where 1 ≤ i ≤ j < n and n ≥ 4. Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.
Q1) For general n, how many enemies will each member of S have?
(1) n – 3
(2) 1/2 (n^{2} – 3n – 2)
(3) 2n – 7
(4) 1/2 (n^{2} – 5n + 6)
(5) 1/2 (n^{2} – 7n + 14)Q2) For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?
(1) 1/2 (n^{2} 5n + 8 )
(2) 2n – 6
(3) 1/2 *n (n – 3)
(4) n – 2
(5) 1/2 (n^{2}– 7n + 16) (CAT 2007)

Question 4
Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17
(2) 16
(3) 18
(4) 15
(5) 19 (CAT 2007)

Answer: Option 3

Question 5
The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.
Q1) Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 60
(2) 75
(3) 45
(4) 90
(5) 72Q2) Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 1170
(2) 630
(3) 792
(4) 1200
(5) 936 (CAT 2008 )

Answer: Option 4 Option 1

Question 6
What is the number of distinct terms in the expansion of (a +b + c)^{20}
(1) 231
(2) 253
(3) 242
(4) 210
(5) 228 (CAT 2008 )

Answer: Option 1

Question 7
In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is
(1) 200
(2) 216
(3) 235
(4) 256 (CAT 2005)

Answer: Option 1

Question 8
A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is
1. 12 × 81
2. 16 × 192
3. 20 × 125
4. 24 × 216 (CAT 2004)

Answer: Option 1

Question 9
A string of three English letters is formed as per the following rules:
a) The first letter is any vowel.
b) The second letter is m, n or p.
c) If the second letter is m then the third letter is any vowel which is different from the first letter.
d) If the second letter is n then the third letter is e or u.
e) If the second letter is p then the third letter is the same as the first letter.
How many strings of letters can possibly be formed using the above rules?
1. 40
2. 45
3. 30
4. 35
How many strings of letters can possibly be formed using the above rules such that the third letter of the string is e?
1. 8
2. 9
3. 10
4. 11 (CAT 2003)

Answer: Option 3 Option 3

@mbatious option 4 option 3

@mbatious explanation