Binomial Theorem · NDA previous year questions

2015 7 questions

1. Q202015 · 27 Sept 2015

   In the expansion of ${\left(\sqrt{x}+\frac{1}{3x^2}\right)}^{10}$ the value of constant term (independent of $x$) is

   1. A.5
   2. B.8
   3. C.45
   4. D.90
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   Answer: A

2. Q212015 · 27 Sept 2015

   For the next three (03) items that follow: Consider the expansion of $(1+x{)}^{2n+1}$ If the coefficients of $x^r$ and $x^{r+1}$ are equal in the expansion, then $r$ is equal to

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

3. Q222015 · 27 Sept 2015

   Consider the expansion of $(1+x{)}^{2n+1}$ The average of the coefficients of the two middle terms in the expansion is

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

4. Q232015 · 27 Sept 2015

   Consider the expansion of $(1+x{)}^{2n+1}$ The sum of the coefficients of all the terms in the expansion is

   1. A.$2^{2n-1}$
   2. B.$4^{n-1}$
   3. C.$2\times 4^n$
   4. D.None of the above
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   Answer: C

5. Q242015 · 27 Sept 2015

   The coefficient of $x^{99}$ in the expansion of $(x-1)(x-2)(x-3)\dots (x-100)$ is

   1. A.5050
   2. B.5000
   3. C.-5050
   4. D.-5000
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   Answer: C

6. Q252015 · 27 Sept 2015

   If ${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3}$, then $m$ is equal to

   1. A.24
   2. B.18
   3. C.12
   4. D.4
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   Answer: A

7. Q142015 · 19 Apr 2015

   In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds $-9$ and $-1$ for roots. The correct equation is

   1. A.$x^2-10x+9=0$
   2. B.$x^2+10x+9=0$
   3. C.$x^2-10x+16=0$
   4. D.$x^2-8x-9=0$
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   Answer: A