What is the number of terms in the given expression?

2023

What is the number of terms in the given expression?

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  1. A.

    12

  2. B.

    22

  3. C.

    11

  4. D.

    24

Attempted by 29 students.

Show answer & explanation

Correct answer: A

A binomial expansion

(a + b)ⁿ

contains n + 1 terms unless some terms merge after simplification.

Here,

(x² + 2/x)¹¹

has

11 + 1 = 12

terms.

Checking the powers:

22, 19, 16, 13, 10, 7, 4, 1, −2, −5, −8, −11

All are distinct.

Hence no terms merge.

Answer

12 (Option A) ✅

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