Binomial Theorem · NDA previous year questions

2017 5 questions

1. Q192017 · 10 Sept 2017

   The number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$ after simplification is

   1. A.202
   2. B.101
   3. C.51
   4. D.50
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   Answer: C

2. Q202017 · 10 Sept 2017

   In the expansion of $(1+x{)}^{50}$, the sum of the coefficients of odd powers of $x$ is

   1. A.$2^{26}$
   2. B.$2^{49}$
   3. C.$2^{50}$
   4. D.$2^{51}$
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   Answer: B

3. Q212017 · 10 Sept 2017

   If $x+{\log }_{10}(1+2^x)=x{\log }_{10}5+{\log }_{10}6$ then $x$ is equal to

   1. A.$2,-3$
   2. B.2 only
   3. C.1
   4. D.3
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   Answer: C

4. Q222017 · 10 Sept 2017

   If $A=\left(\begin{array}{cc}-2& 2\\ 2& -2\end{array}\right)$, then which one of the following is correct?

   1. A.$A^2=-2A$
   2. B.$A^2=-4A$
   3. C.$A^2=-3A$
   4. D.$A^2=4A$
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   Answer: B

5. Q242017 · 23 Apr 2017

   The expansion of $(x-y{)}^n,n\ge 5$ is done in the descending powers of $x$. If the sum of the fifth and sixth terms is zero, then $\frac{x}{y}$ is equal to

   1. A.$\frac{n-5}{6}$
   2. B.$\frac{n-4}{5}$
   3. C.$\frac{5}{n-4}$
   4. D.$\frac{6}{n-5}$
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   Answer: B