JEE Advanced2012MathematicsPermutation and CombinationActual
Let a_ n denote the number of all n -digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let b_ n = the number of such n -digit integers ending with digit 1 and c_ n = the number of such n -digit integers ending with digit 0 . Question: Which of the following is correct?
Options
- Aa₁₇=a₁₆+a₁₅
- Bc₁₇ c₁₆+c₁₅
- Cb₁₇ b₁₆+c₁₆
- Da₁₇=c₁₇+b₁₆
Correct answer
A. a₁₇=a₁₆+a₁₅
Step-by-step solution
By recurring formula, a₁₇=a₁₆+a₁₅ is correct Also c₁₇ c₁₆+c₁₅ a₁₅ a₁₄+a₁₃ ( c_ n =a_ n-2 ) Incorrect Similarly, other parts are also incorrect.