Binomial Theorem · NDA previous year questions

2018 11 questions

1. Q162018 · 9 Sept 2018

   What is the coefficient of the middle term in the binomial expansion of $(2+3x{)}^4$?

   1. A.6
   2. B.12
   3. C.108
   4. D.216
   Show answer

   Answer: D

2. Q172018 · 9 Sept 2018

   Let the coefficient of the middle term of the binomial expansion of $(1+x{)}^{2n}$ be $\alpha$ and those of two middle terms of the binomial expansion of $(1+x{)}^{2n-1}$ be $\beta$ and $\gamma$. Which one of the following relations is correct?

   1. A.$\alpha >\beta +\gamma$
   2. B.$\alpha <\beta +\gamma$
   3. C.$\alpha =\beta +\gamma$
   4. D.$\alpha =\beta \gamma$
   Show answer

   Answer: C

3. Q182018 · 9 Sept 2018

   What is the value of ${\log }_7{\log }_7\sqrt{7\sqrt{7\sqrt{7}}}$ equal to?

   1. A.$3{\log }_{2}7$
   2. B.$1-3{\log }_{2}7$
   3. C.$1-3{\log }_{7}2$
   4. D.$\frac{7}{8}$
   Show answer

   Answer: C

4. Q192018 · 9 Sept 2018

   What is the value of ${\log }_{9}27+{\log }_{8}32$?

   1. A.$\frac{7}{2}$
   2. B.$\frac{19}{6}$
   3. C.4
   4. D.7
   Show answer

   Answer: B

5. Q202018 · 9 Sept 2018

   If $(0.2{)}^x=2$ and ${\log }_{10}2=0.3010$, then what is the value of x to the nearest tenth?

   1. A.$-10.0$
   2. B.$-0.5$
   3. C.$-0.4$
   4. D.$-0.2$
   Show answer

   Answer: C

6. Q232018 · 22 Apr 2018

   In the expansion of $(1+x{)}^{43}$, if the coefficients of $(2r+1{)}^{\text{th}}$ and $(r+2{)}^{\text{th}}$ terms are equal, then what is the value of $r$ ($r\ne 1$) ?

   1. A.5
   2. B.14
   3. C.21
   4. D.22
   Show answer

   Answer: B

7. Q242018 · 22 Apr 2018

   If the coefficients of $a^m$ and $a^n$ in the expansion of $(1+a{)}^{m+n}$ are $\alpha$ and $\beta$, then which one of the following is correct ?

   1. A.$\alpha =2\beta$
   2. B.$\alpha =\beta$
   3. C.$2\alpha =\beta$
   4. D.$\alpha =(m+n)\beta$
   Show answer

   Answer: B

8. Q252018 · 22 Apr 2018

   What is the number of non-zero terms in the expansion of $(1+2\sqrt{3}x{)}^{11}+(1-2\sqrt{3}x{)}^{11}$ (after simplification) ?

   1. A.4
   2. B.5
   3. C.6
   4. D.11
   Show answer

   Answer: C

9. Q262018 · 22 Apr 2018

   If $n=(2017)!$, then what is $$\frac{1}{{\log }_{2}n}+\frac{1}{{\log }_{3}n}+\frac{1}{{\log }_{4}n}+\cdots +\frac{1}{{\log }_{2017}n}$$ equal to ?

   1. A.0
   2. B.1
   3. C.$\frac{n}{2}$
   4. D.$n$
   Show answer

   Answer: B

10. Q272018 · 22 Apr 2018

    If $x+{\log }_{15}(1+3^x)=x{\log }_{15}5+{\log }_{15}12$, where x is an integer, then what is x equal to ?

    1. A.$-3$
    2. B.2
    3. C.1
    4. D.3
    Show answer

    Answer: C

11. Q282018 · 22 Apr 2018

    If $0<a<1$, the value of ${\log }_{10}a$ is negative. This is justified by

    1. A.Negative power of 10 is less than 1
    2. B.Negative power of 10 is between 0 and 1
    3. C.Negative power of 10 is positive
    4. D.Negative power of 10 is negative
    Show answer

    Answer: B