Probability

A board has 16 squares as shown in the figure : [figure] Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

1. 35
2. 45
3. 2330
4. 710

Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4. If the probability that ax2 + bx + c = 0 has all real roots is mn, (m, n) = 1, then m + n is equal to .

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the ith roll than the number obtained in the (i - 1)th roll, i = 2, 3, is equal to

1. 5/54
2. 2/54
3. 1/54
4. 3/54

Let the sum of two positive integers be 24. If the probability, that their product is not less than 34 times their greatest possible product, is mn, where (m, n) = 1, then n - m equals

1. 10
2. 11
3. 9
4. 8

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :

1. 1825
2. 1225
3. 625
4. 425

The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are chosen from the set \1, 2, 3, 4, 5, 6, 7, 8\. The probability of this equation having repeated roots is :

1. 1128
2. 164
3. 3256
4. 3128

The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are from the set \1, 2, 3, 4, 5, 6\. If the probability of this equation having one real root bigger than the other is p, then 216p equals :

1. 38
2. 76
3. 57
4. 19

Let Ajay will not appear in JEE exam with probability p= 27, while both Ajay and Vijay will appear in the exam with probability q= 15. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

1. 935
2. 335
3. 2435
4. 1835

Two integers x and y are chosen with replacement from the set \0,1,2,3, ,10\. Then the probability that |x-y|>5, is :

1. 31121
2. 60121
3. 62121
4. 30121

An integer is chosen at random from the integers 1,2,3, ,50. The probability that the chosen integer is a multiple of at least one of 4, 6 and 7 is

1. 825
2. 950
3. 1425
4. 2150