If the constant term in the expansion of  is 405, then what can be the values of k?

This question was previously asked in
NDA (Held On: 17 Nov 2019) Maths Previous Year paper
View all NDA Papers >
  1. ±2
  2. ±3
  3. ±5
  4. ±9

Answer (Detailed Solution Below)

Option 2 : ±3
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Concept:

In the binomial expansion of (a + b)n, the term which does not involve any variable is said to be an independent term.

The general term in the binomial expansion of (a + b)n is given by:

Calculation:

Given: The constant term in the expansion of  is 405

i.e the independent term of  is 405.

Let (r + 1)th term be the independent term.

∵ (r + 1)th term is the independent term

⇒ k = ± 3

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Hot Links: teen patti game - 3patti poker teen patti gold download all teen patti game