Binomial Theorem · NDA previous year questions

2021 7 questions

1. Q202021 · 14 Nov 2021

   How many terms are there in the expansion of ${\left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)}^{21}$ where $a\ne 0,b\ne 0$?

   1. A.21
   2. B.22
   3. C.42
   4. D.43
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   Answer: D

2. Q212021 · 14 Nov 2021

   For what values of k is the system of equations $2k^{2}x+3y-1=0,7x-2y+3=0,6kx+y+1=0$ consistent?

   1. A.$\frac{3\pm \sqrt{11}}{10}$
   2. B.$\frac{21\pm \sqrt{161}}{10}$
   3. C.$\frac{3\pm \sqrt{7}}{10}$
   4. D.$\frac{4\pm \sqrt{11}}{10}$
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   Answer: B

3. Q272021 · 14 Nov 2021

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

   1. A.$1+2n$
   2. B.$1+2n^2$
   3. C.$1+n^2$
   4. D.$1+4n$
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   Answer: C

4. Q12021 · 18 Apr 2021

   What is C(n, 1) + C(n, 2) + _ _ _ _  _ + C(n, n) equal to

   1. A.$2+2^2+2^3+\cdots +2^n$
   2. B.$1+2+2^2+2^3+\cdots +2^n$
   3. C.$1+2+2^2+2^3+\cdots +2^{n-1}$
   4. D.$2+2^2+2^3+\cdots +2^{n-1}$
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   Answer: C

5. Q22021 · 18 Apr 2021

   What is the sum of the coefficients of first and last terms in the expansion of $(1+x{)}^{2n}$, where n is a natural number?

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

6. Q302021 · 18 Apr 2021

   What is the coefficient of the middle term in the expansion of $(1+4x+4x^2{)}^5$?

   1. A.8064
   2. B.4032
   3. C.2016
   4. D.1008
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   Answer: A

7. Q492021 · 18 Apr 2021

   If $C_0$, $C_1$, $C_2$, $\dots$, $C_n$ are the coefficients in the expansion of $(1+x{)}^n$, then what is the value of $C_1+C_2+C_3+\dots +C_n$?

   1. A.$2^n$
   2. B.$2^n-1$
   3. C.$2^{n-1}$
   4. D.$2^n-2$
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   Answer: B