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Match the LIST-I with LIST-II If p and q satisfy 3p + 3q = 36 and 2 × 3p + 3 × 3q = 99, then match the following: LIST-I LIST-II A. p +
Question

Match the LIST-I with LIST-II
If p and q satisfy 3p + 3q = 36 and 2 × 3p + 3 × 3q = 99, then match the following:

LIST-I

LIST-II
A. p + q
I.
1
B. q − p
II.
5
C. p² + q²
III.
6
D. pq
IV.
13

Choose the correct answer from the options given below:

A.

A-I, B-II, C-III, D-IV

B.

A-IV, B-III, C-I, D-II

C.

A-II, B-I, C-III, D-IV

D.

A-II, B-I, C-IV, D-III

Correct option is D

Given:
3p + 3q = 36 and 2 × 3p + 3 × 3q = 99,​
Solution:
Let:
3ᵖ = a and 3q = b
Then,
a + b = 36 ...(1)
2a + 3b = 99 ...(2)
Multiplying equation (1) by 2:
2a + 2b = 72 ...(3)
Subtracting equation (3) from equation (2):
b = 99 − 72
b = 27
Therefore,
3q= 27 = 3³
Hence,
q = 3
From equation (1):
a + 27 = 36
a = 9
Therefore,
3ᵖ = 9 = 3²
Hence,
p = 2
Now,
A. p + q = 2 + 3 = 5
Therefore, A → II.
B. q − p = 3 − 2 = 1
Therefore, B → I.
C. p² + q² = 2² + 3²
= 4 + 9
= 13
Therefore, C → IV.
D. pq = 2 × 3
= 6
Therefore, D → III.
Hence, the correct matching is:
A-II, B-I, C-IV, D-III
Correct Answer: (d)

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