Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2022 · Mathematics · Binomial Theorem

Paragraph: Consider the binomial expansion of (p+q x)^9 : Question:...

Paragraph: Consider the binomial expansion of (p+qx)9(p+q x)^9 :Question: Under what condition the coefficients of x2x^2 and x4x^4 are equal?

Options

  1. Ap:q=7:2p: q=7: 2
  2. Bp2:q=7:2p^2: q=7: 2
  3. Cp:q=2:7p: q=2: 7
  4. Dp2:q2=2:7p^2: q^2=2: 7

Correct answer

B. p2:q=7:2p^2: q=7: 2

Step-by-step solution

coefficient of x2=x^2= coefficient of x4x^49C2p7q2=9C4p5q49.82.1p2=9.8.7.64.3.2.1q2p2q2=72\begin{aligned} & { }^9 C_2 p^7 q^2={ }^9 C_4 p^5 q^4 \\ & \frac{9.8}{2.1} p^2=\frac{9.8.7.6}{4.3.2.1} q^2 \\ & \frac{p^2}{q^2}=\frac{7}{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 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026What is the greatest value of r satisfying the inequality 15 r+1 > 2× ^ 15 C_r ? NDA 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 .… NDA 2026If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the… NDA 2025If k < ( 2 +1)^3 < k+2 , where k is a natural number, then what is the value of k ? NDA 2025What is the remainder when 5^ 99 is divided by 13 ? NDA 2025What is the number of rational terms in the expansion of (3^ (1)/(2) + 5^ (1)/(4) )^ 12 ? NDA 2025Which one of the following is the greatest coefficient in the expansion of (1 + x)^ 100 ? NDA 2025In the expansion of (1+x)^p(1+x)^q , if the coefficient of x^3 is 35 , then what is the… NDA 2024What is the remainder when 7^n-6 n is divided by 36 for n=100 ? NDA 2024Paragraph: Let (8+3 7 )^ 20 =U+V and (8-3 7 )^ 20 =W , where U is an integer and 0… NDA 2024Paragraph: 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 PYQsJEE Mathematics PYQs All NDA PYQs