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Which of the following is the sum of $6 p + 4 q – r + 3, 2 r - 5 p – 6, 11 q - 7 p + 2 r – 1 and 2 q – 3 r + 4$ ?

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- 6 p + 17 q - 6

- 6 p - 17 q + 6

- 6 p + 17 q + 6

- 6 p - 17 q - 6

answer is C.

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Detailed Solution

Given,

6 p + 4 q – r + 3, 2 r - 5 p – 6, 11 q - 7 p + 2 r – 1 and 2 q – 3 r + 4

Add each term of given expression,

⇒ (6 p + 4 q − r + 3) + (2 r − 5 p − 6) + (11 q − 7 p + 2 r − 1) + (2 q − 3 r + 4)

⇒ 6 p + 4 q − r + 3 + 2 r − 5 p − 6 + 11 q − 7 p + 2 r − 1 + 2 q − 3 r + 4

Separate each term of p, q and r.

⇒ (6 p − 5 p − 7 p) + (4 q + 11 q + 2 q) + (− r + 2 r + 2 r − 3 r) + (3 − 1 + 4)

Take p, q and r common.
We get,

⇒ p (6 − 5 − 7) + q (4 + 11 + 2) + r (− 1 + 2 + 2 − 3) + (3 − 1 + 4)

⇒ p (6 − 12) + q (17) + r (4 − 4) + (7 − 1)

⇒ p (− 6) + q (17) + r (0) + (6)

⇒ − 6 p + 17 q + 6

Hence, the addition of

6 p + 4 q − r + 3, 2 r − 5 p − 6, 11 q − 7 p + 2 r − 1

and

2 q − 3 r + 4

− 6 p + 17 q + 6

Therefore, option 3 is correct.

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