**1. The remainder when 2 ^{60 }is divided by 5 equals? **

- (a) 0
- (b) 1
- (c) 2
- (d) None of these

**2. Let a, b be any positive integers and x = 0 or 1, then**

- (a) a
^{x}b^{(1-x)}= xa+(1-x)b - (b) a
^{x}b^{(1-x)}=(1-x)a+xb - (c) a
^{x}b^{(1-x)}=a(1-x)bx - (d) None of the above is necessarily true

**3. There are six boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a white ball or a black ball in such a manner that at least one box contains a black ball and all the boxes containing black balls are consecutively numbered. The total number of ways in which this can be done equals?**

- (a) 15
- (b) 21
- (c) 63
- (d) 64

**4. In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?**

- (a) 3%
- (b) 5%
- (c) 2.5%
- (d) 4%

**5. Consider a function f(k) defined for positive integers k = 1,2,... ; the function satisfies the condition f(1) + f(2) + ... = p/(p-1) where p is fraction i.e. 0 < p < 1. Then f(k) is given by**

- (a) p(-p)
^{k-1} - (b) p(1-p)
^{k-1} - (c) {p(1-p)}
^{k-1} - (d) None of these

**6. 116 people participated in a singles tennis tournament of knock out format. The players are paired up in the first round, the winners of the first round are paired up in second round, and so on till the final is played between two players. If after any round, there is odd number of players, one player is given a bye, i.e. he skips that round and plays the next round with the winners. Find the total number of matches played in the tournament.**

- (a) 115
- (b) 53
- (c) 232
- (d) 116

**7. If n is any positive integer, then n ^{3} - n is divisible**

- (a) Always by 12
- (b) Never by 12
- (c) Always by 6
- (d) Never by 6

**8. The value of (1-d ^{3})/(1-d) is**

- (a) > 1 if d > -1
- (b) > 3 if d > 1
- (c) > 2 if 0 < d < 0.5
- (d) < 2 if d < -2

**9. Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is**

- (a) 25
- (b) 18
- (c) 20
- (d) None of these

**10. The roots of the equation ax ^{2}+ 3x + 6 = 0 will be reciprocal to each other if the value of a is**

- (a) 3
- (b) 4
- (c) 5
- (d) 6

*(Above questions were asked in CAT 1990 Paper)*

### Answers

- (b)
- (a)
- (b)
- (a)
- (a)
- (a)
- (c)
- (b)
- (c)
- (d)