PARAGRAPH 2 Let p, q be integers and let be the roots of t…

Maths JEE - Advanced Previous Year Paper JEE-Advanced-2017-Paper-2 Single Correct MCQ

Published on: August 13, 2026

PARAGRAPH 2

Let p, q be integers and let be the roots of the equation, x 2 - x - 1 = 0, where . For n = 0, 1,2, ... ,let a n = p n + q n .

FACT : If a and b are rational numbers and , then a = 0 = b.

(i) a 12 =

a 11 -a 10 21

a 11 + a 10 14

2a 11 +a 10 7

a 11 +2a 10 (ii) If a 4 = 28, then p + 2q = 12

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(i)

As a n+1 -a n -a n-1 = 0

So a 12 = a 11 + a 10

(ii)

a 4 = 2a 0 + 3a 1

a 4 = (q-p)(3 ) + 5p + 2q = 28

p = q = 4.

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