Exams › JEE Main › Maths

Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]² + 2[x + 2] - 7 = 0 has: (1) exactly two solutions. (2) exactly four integral solutions. (3) infinitely many solutions. (4) no integral solution.

1. exactly two solutions.
2. exactly four integral solutions.
3. infinitely many solutions.
4. no integral solution.

Correct answer: infinitely many solutions.

Solution

Let n=[x]. n^2 + 2(n+2) - 7 = 0 -> n^2 + 2n - 3 = 0 -> n = 1 or n = -3. Then x in [1,2) or x in [-3,-2), each containing infinitely many x, so there are infinitely many solutions.

Related JEE Main Maths questions

• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?
• Let X and Y be two non-empty sets, and let A be a non-empty set such that X ∩ A = Y ∩ A = A and X ∪ A = Y ∪ A. Which of the following must be true?
• If A and B are non-empty sets with A containing B, then which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →