Sign in
Please select an account to continue using cracku.in
↓ →
JEE WhatsApp Group
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
How many three-digit positive integers are there if the digits are the side lengths of some isosceles or equilateral triangle?
No digit can be 0, and at least two digits must be equal. Equilateral cases give 9 numbers. For a pair $$(x, x, y)$$ with $$y \neq x$$ the triangle inequality needs $$y < 2x$$, and counting valid $$y$$ for $$x = 1$$ to $$9$$ gives $$0+2+4+6+8+8+8+8+8 = 52$$ multisets, each arrangeable in 3 ways. The total is $$9 + 3 \times 52 = 165$$.
_1.webp)
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
91- 6303239042
