MATHEMATICS_Q51_JEE_Advanced_2012_S2 - Competishun – Live JEE & NEET Courses and Exam Prep

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JEE Advance 2012

paper 2

Question

Let $\mathrm{a}_{\mathrm{n}}$ 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 $\mathrm{b}_{\mathrm{n}}=$ the number of such n -digit integers ending with digit 1 and $\mathrm{c}_{\mathrm{n}}=$ the number of such $n$-digit integers ending with digit 0 .
Which of the following is correct ?

Select the correct option:

A

$a_{17}=a_{16}+a_{15}$

B

$\mathrm{c}_{17} \neq \mathrm{c}_{16}+\mathrm{c}_{15}$

C

$\mathrm{b}_{17} \neq \mathrm{b}_{16}+\mathrm{c}_{16}$

D

$a_{17}=c_{17}+b_{16}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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