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Probability

JEE Main 2024 (Online) 5th April Morning ShiftMCQMedium📈 Topic in 36% papers+4−1
Ques. 1JEE 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 :

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

Answer

(2) 164

Solution

Total cases = 83 = 512

Repeated roots ⇒ b2 = 4ac ⇒ b even, ac = b24

b = 2: ac = 1 → (1, 1) ⇒ 1 way

b = 4: ac = 4 → (1, 4), (2, 2), (4, 1) ⇒ 3 ways

b = 6: ac = 9 → (3, 3) ⇒ 1 way

b = 8: ac = 16 → (2, 8), (4, 4), (8, 2) ⇒ 3 ways

P = 8512 = 164

Answer: (2)

Keep practising — Probability

Ques. 2JEE 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 :

  1. 38
  2. 76
  3. 57
  4. 19
Ques. 3JEE 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 :

  1. 935
  2. 335
  3. 2435
  4. 1835
Ques. 4JEE 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 :

  1. 31121
  2. 60121
  3. 62121
  4. 30121
Ques. 5JEE 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

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

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