Modern Math Previous Year Questions (CAT)  Set 0002

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

Question 1
There are 12 towns grouped into fourzones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?
1. 72
2. 90
3. 96
4. 144 (CAT 2003)

Answer: Option 2

Question 2
A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows — were already installed. The survey found:
15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options.
What is the number of cars that had none of the options?
1. 4
2. 3
3. 1
4. 2 (CAT 2003)

Answer: Option 2

Question 3
n1, n2, n3 ... n10 are 10 numbers such that n1 > 0 and the numbers are given in ascending order. How many triplets can be formed using these numbers such that in each triplet, the first number is less than the second number, and the second number is less than the third number?
(1) 109
(2) 27
(3) 36
(4) None of these (CAT 2002)

Answer: Option 4

Question 4
Shyam visited Ram on vacation. In the mornings, they both would go for yoga. In the evenings they Would play tennis. To have more fun, they indulge only in one actively per day, i.e., either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?
1. 32
2. 24
3. 30
4. None of these (CAT 2002)

Answer: Option 3

Question 5
How many numbers between 0 and one million can be formed using 0, 7 and 8?
(1) 486
(2) 1086
(3) 728
(4) None of these (CAT 2002)

Answer: Option 3

Question 6
In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column?
(1) 32
(2) 96
(3) 24
(4) None of these (CAT 2002)

Answer: Option 4

Question 7
There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets.
How many fourlettered passwords can be formed by using symmetrical letters only?
(repetitions not allowed)(1) 1086
(2) 255
(3) 7920
(4) None of these
How many threelettered words can be formed such that at least one symmetrical letter is there? (repetitions not allowed)
(1) 12870
(2) 18330
(3) 16420
(4) None of these (CAT 2002)

Answer: Option 3 Option 1

Question 8
One red flag, three white flags and two blue flags are arranged in a line such that,
(A) no two adjacent flags are of the same colour.
(B ) the flags at the two ends of the line are of different colours.
In how many different ways can the flags be arranged?(1) 6
(2) 4
(3) 10
(4) 2 (CAT 2000)

Answer: Option 1

Question 9
There are three cities A, B and C, each of these cities is connected with the other two cities by at least one direct road. If a traveller wants to go from one city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?
(1) 6
(2) 3
(3) 5
(4) 10 (CAT 2000)

Answer: Option 1

Question 10
The set of all positive integers is the union of two disjoint subsets {f(1), f(2) ....f(n),......} and
{g(1), g(2),......,g(n),......}, where f(1) < f(2) < ... < f(n) ....., and g(1) < g(2) < ... < g(n) .......,
and g(n) = f(f(n)) + 1 for all n ≥ 1. What is the value of g(1)?(1) Zero
(2) Two
(3) One
(4) Cannot be determined (CAT 2000)