Consider the expansion of (1+x)^n . Let p, q, r and s be the coefficients of first, second, n^ th and (n+1)^ th terms respectively. What is (p s+q r ) equal to?

Correct answer: C. 1+n^2 According to question aligned & p= ^n C_0=1, q= ^n C_1=n & r= ^n C_ n-1 = ^n C_1=n and S= ^n C_n=1 & p s+q r=1 × 1+n × n=1+n^2 aligned

NDA 2021

Exam: NDA
Year: 2021
Subject: Mathematics
Chapter: Binomial Theorem

NDA 2021 · Mathematics · Binomial Theorem

Consider the expansion of (1+x)^n . Let p, q, r and s be the...

Consider the expansion of

(1+x)^n

. Let

p, q, r

and

s

be the coefficients of first, second,

n^{\text{th }}

and

(n+1)^{\text{th }}

terms respectively. What is (p s+q r

) equal to?

Options

A $1+2 n$
B $1+2 n^2$
C $1+n^2$
D $1+4 n$

Correct answer

C. $1+n^2$

Step-by-step solution

According to

question

\begin{aligned} & p={ }^n C_0=1, q={ }^n C_1=n \\ & r={ }^n C_{n-1}={ }^n C_1=n \text{ and } S={ }^n C_n=1 \\ & \therefore p s+q r=1 \times 1+n \times n=1+n^2 \end{aligned}

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

A set S contains (2n+1) elements. If the number of subsets of S which contain at most n… NDA 2026 Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026 Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026 What is the greatest value of r satisfying the inequality 15 r+1 > 2× ^ 15 C_r ? NDA 2026 Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026 Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026 Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026 If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the… NDA 2025 If k < ( 2 +1)^3 < k+2 , where k is a natural number, then what is the value of k ? NDA 2025 What is the remainder when 5^ 99 is divided by 13 ? NDA 2025 What is the number of rational terms in the expansion of (3^ (1)/(2) + 5^ (1)/(4) )^ 12 ? NDA 2025 Which one of the following is the greatest coefficient in the expansion of (1 + x)^ 100 ? NDA 2025 In the expansion of (1+x)^p(1+x)^q , if the coefficient of x^3 is 35 , then what is the… NDA 2024 What is the remainder when 7^n-6 n is divided by 36 for n=100 ? NDA 2024 Paragraph: Let (8+3 7 )^ 20 =U+V and (8-3 7 )^ 20 =W , where U is an integer and 0… NDA 2024 Paragraph: Let (8+3 7 )^ 20 =U+V and (8-3 7 )^ 20 =W , where U is an integer and 0… NDA 2024 Full Binomial Theorem list Binomial Theorem JEE Maths PYQs JEE Mathematics PYQs All NDA PYQs