Probability

JEE Main 2024 (Online) 8th April Morning ShiftMCQMedium📈 Topic in 36% papers+4−1

Ques. 1JEE Main 2024, 8 April (Morning Shift)

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

Answer

(1) 10

Solution

Integers: a and 24 - a, a = 1, 2, , 23 23 equally likely cases

By AM GM, the greatest product = 12 12 = 144

Need a(24 - a) 34 144 = 108

a2 - 24a + 108 0 (a - 6)(a - 18) 0 6 a 18

[figure]

So there are 13 favourable cases and mn = 1323

n - m = 23 - 13 = 10

Answer: (1)

Keep practising — Probability

Ques. 2JEE Main 2024, 6 April (Evening Shift)

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 :

1825
1225
625
425

Ques. 3JEE Main 2024, 5 April (Morning Shift)

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 :

1128
164
3256
3128

Ques. 4JEE Main 2024, 5 April (Evening Shift)

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 :

Ques. 5JEE Main 2024, 1 February (Evening Shift)

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 :

935
335
2435
1835

Ques. 6JEE Main 2024, 30 January (Morning Shift)

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 :

31121
60121
62121
30121

Ques. 7JEE Main 2024, 29 January (Evening Shift)

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

825
950
1425
2150

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All JEE Main Mathematics chapters

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