1. If A and B are two events, then which one of the
following is not always true

a) \[P \left(A \cap B\right)\leq P\left(A\right)+P\left(B\right)-1\]

b) \[P \left(A \cap B\right)\leq P\left(A\right)\]

c) \[P \left(A' \cap B'\right)\leq P\left(A'\right)+P\left(B'\right)-1\]

d) \[P \left(A \cap B\right)= P\left(A\right)P\left(B\right)\]

Explanation: (d) is true if and only if A and B are independent

2. A sum of money is rounded off to the nearest rupee.
The probability that the round off error is at most
10 paise is

a) 1/10

b) 11/100

c) 3/25

d) 21/100

Explanation:

3. The probability that an electric bulb will last 150
days or more is 0.7 and that it will last at most 160
days is 0.8. The probability that the bulb will last
150 to 160 days is

a) 0.5

b) 1/3

c) 0.56

d) 0.59

Explanation:

4. A bag contains three tickets numbered 1, 2 and 3. A
ticket is drawn at random and put back in the bag,
and this is done four times. The probability that the
sum of the numbers drawn is even is

a) 40/81

b) 41/81

c) 14/27

d) 13/81

Explanation:

5. Two numbers x and y are selected at random from
the set {1, 2, 3,…, 3N}. The probability that x^{2} – y^{2}
is divisible by 3 is

a) (3N – 1)/3N

b) (N – 1)/N

c) (5N – 3)/(9N – 3)

d) (N – 1)/2N

Explanation:

6. Three persons A, B and C are to speak at a function
along with 7 other persons. The probability that A
speaks before B and B speaks before C is

a) 3/70

b) 1/6

c) 3/7

d) 1/9

Explanation:

7. m men and n women are seated at round table in
random order. The probalility that they can be
divided into n non-interrecting pairs so that each
pair consists of a man and a woman is

a) 1/2n

b) \[2\left(2^{n}-1\right)/^{2n}C_{n}\]

c) \[2n/^{2n}C_{n}\]

d) \[1/\left(^{n}C_{n}\right)^{2}\]

Explanation:

8. If a is an integer lying in [– 5, 30], then the
probability that the graph of \[y = x^{2} + 2 \left(a + 4\right) x
–5a + 64\] is strictly above the x – axis is

a) 1/6

b) 7/36

c) 2/9

d) 3/5

Explanation:

9. Two numbers X and Y are chosen at random
(without replacement) from the set {1, 2, 5N}.
The probability that \[ X^{4} -Y^{4}\] is divisible by 5 is

a) \[\frac{N-1}{5N-1}\]

b) \[\frac{4\left(4N-1\right)}{5\left(5N-1\right)}\]

c) \[\frac{17N-5}{5\left(5N-1\right)}\]

d) \[\frac{3N-5}{5\left(5N-1\right)}\]

Explanation:

10. There is a five -volume dictionary among 50 books arranged on a shelf in random order. The probability
that these volumes stand in increasing order from
left to right (the volumes are not necessarily kept
side-by-side) is

a) 1/5

b) \[1/5^{50}\]

c) \[1/50^{5}\]

d) 1/120

Explanation: