If p and q satisfy 3^p + 3^q = 36 and 2 × 3^p + 3 × 3^q = 99, then match List I with List II:

List I

i.P + q

ii.Q - p

iii.P^2 + q^2

iv.Pq

List II

a.1

b.5

c.6

d.13

Ai-a, ii-b, iii-c, iv-d

Bi-d, ii-c, iii-a, iv-b

Ci-b, ii-a, iii-c, iv-d

Di-b, ii-a, iii-d, iv-c ✓ Correct

Correct answer: (D) i-b, ii-a, iii-d, iv-c

Explanation

The correct match is i-b, ii-a, iii-d, iv-c.

Let 3^p = A, 3^q = B; A + B = 36 and 2A + 3B = 99.

Solving gives B = 27, A = 9, so p = 2 and q = 3.

p + q = 5 (b) and q - p = 1 (a).

p^2 + q^2 = 4 + 9 = 13 (d) and pq = 6 (c).

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