Exams › JEE Main › Maths

In a triangle, the exradii opposite to vertices A, B, C are r1 = 4, r2 = 2*sqrt(k), and r3 = 15 respectively. Given k > 0, find the value of k.

1. 15
2. 12
3. 10
4. 20

Correct answer: 15

Solution

If the exradii satisfy r2² = r1 * r3 (geometric mean condition implied by the figure context), then (2*sqrt(k))² = 4*15, so 4k = 60, giving k = 15.

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 →