Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2020 · Mathematics · Binomial Theorem

The term independent of x in the binomial expansion of ((2)/(x^2)-...

The term independent of xx in the binomial expansion of (2x2−x)10\left(\frac{2}{x^2}-\sqrt{x}\right)^{10} is equal to

Options

  1. A180
  2. B120
  3. C90
  4. D72

Correct answer

A. 180

Step-by-step solution

Let (r+1)th(r+1)^{\mathrm{th}} term is independent of xx. (r+1)th term =10Cr⋅(2x2)10−r⋅(−x)r(r+1)^{\mathrm{th}} \text{ term }={ }^{10} C_r \cdot\left(\frac{2}{x^2}\right)^{10-r} \cdot(-\sqrt{x})^r Exponent of xx in independent term =0=0 i.e. r2−2(10−r)=0r−4(10−r)=0⇒5r−40=0⇒r=8\frac{r}{2}-2(10-r)=0r-4(10-r)=0 \Rightarrow 5 r-40=0 \Rightarrow r=8 Thus, 9th term is independent of xx.  9th term =10C8(2)10−8⋅(−1)8=10C8(2)2=10×92×4=180\begin{aligned} \text{ 9th term } & ={ }^{10} C_8(2)^{10-8} \cdot(-1)^8={ }^{10} C_8(2)^2 \\ & =\frac{10 \times 9}{2} \times 4=180 \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