Binomial Theorem · NDA previous year questions

2024 4 questions

1. Q62024 · 1 Sept 2024

   In the expansion of $(1+x{)}^p(1+x{)}^q$, if the coefficient of $x^3$ is 35, then what is the value of $(p+q)$?

   1. A.5
   2. B.6
   3. C.7
   4. D.8
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   Answer: C

2. Q302024 · 21 Apr 2024

   What is the coefficient of $x^{10}$ in the expansion of $(1-x^2{)}^{20}{\left(2-x^2-\frac{1}{x^2}\right)}^{-5}$?

   1. A.-1
   2. B.1
   3. C.10
   4. D.Coefficient of $x^{10}$ does not exist
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   Answer: A

3. Q312024 · 21 Apr 2024

   If the 4th term in the expansion of ${\left(mx+\frac{1}{x}\right)}^n$ is $\frac{5}{2}$, then what is the value of $mn$?

   1. A.-3
   2. B.3
   3. C.6
   4. D.12
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   Answer: B

4. Q342024 · 21 Apr 2024

   In a binomial expansion of $(x+y{)}^{2n+1}(x-y{)}^{2n+1}$, the sum of middle terms is zero. What is the value of $\left(\frac{x^2}{y^2}\right)$ ?

   1. A.1
   2. B.2
   3. C.4
   4. D.8
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   Answer: A