Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2011 · Mathematics · Binomial Theorem

What is the ratio of coefficient of x^ 15 to the term independent...

What is the ratio of coefficient of x15x^{15} to the term independent of xx in (x2+2x)15\left(x^2+\frac{2}{x}\right)^{15} ?

Options

  1. A1/641 / 64
  2. B1/321 / 32
  3. C1/161 / 16
  4. D1/41 / 4

Correct answer

B. 1/321 / 32

Step-by-step solution

nc5(25)nc10(2)10=15!5!10!(25)15!(210)=3232×32=132\begin{aligned} \frac{n c_5\left(2^5\right)}{n c_{10}(2)^{10}} & =\frac{\frac{15!}{5!10!}\left(2^5\right)}{15!}\left(2^{10}\right) \\ & =\frac{32}{32 \times 32}=\frac{1}{32}\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