Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Which of the following is not true about (a + x)ⁿ, where n is a positive integer?
Options
A \( (a + x)^n = a^n + na^{n-1}x + \frac{n(n-1)}{2!}a^{n-2}x^2 + ... \)
B The index of a decreases from n to zero while that of n increases from zero to n.
C The coefficients of terms equidistant from the ends are equal.
D None of these.
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

Option A is the correct binomial expansion. Option B: the index of a decreases from n to 0, and the index of x increases from 0 to n. This is correct. Option C: binomial coefficients are symmetric, so coefficients equidistant from ends are equal. All statements are true, so "none of these" (D) is the answer to "which is not true".

Hint

Recall the properties of binomial expansion: symmetry of coefficients, pattern of indices.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 547 of 696
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