Sequences & Series · NDA previous year questions

2018 9 questions

1. Q72018 · 9 Sept 2018

   If an infinite GP has the first term x and the sum 5, then which one of the following is correct?

   1. A.$x<-10$
   2. B.$-10<x<0$
   3. C.$0<x<10$
   4. D.$x>10$
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   Answer: C

2. Q82018 · 9 Sept 2018

   The sum of the series $3-1+\frac{1}{3}-\frac{1}{9}+\dots$ is equal to

   1. A.$\frac{20}{9}$
   2. B.$\frac{9}{20}$
   3. C.$\frac{9}{4}$
   4. D.$\frac{4}{9}$
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   Answer: C

3. Q92018 · 9 Sept 2018

   Let $T_r$ be the $r^{th}$ term of an AP for $r=1,2,3,\dots$. If for some distinct positive integers m and n we have $T_m=1/n$ and $T_n=1/m$, then what is $T_{mn}$ equal to?

   1. A.$(mn{)}^{-1}$
   2. B.$m^{-1}+n^{-1}$
   3. C.1
   4. D.0
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   Answer: C

4. Q102018 · 9 Sept 2018

   If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is

   1. A.$8,2,\frac{1}{2},\frac{1}{8},\dots$
   2. B.$10,2,\frac{2}{5},\frac{2}{25},\dots$
   3. C.$4,2,1,\frac{1}{2},\frac{1}{2^2},\dots$
   4. D.$6,3,\frac{3}{2},\frac{3}{4},\dots$
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   Answer: C

5. Q112018 · 9 Sept 2018

   If a, b, c are in AP or GP or HP, then $\frac{a-b}{b-c}$ is equal to

   1. A.$\frac{b}{a}$ or 1 or $\frac{b}{c}$
   2. B.$\frac{c}{a}$ or $\frac{c}{b}$ or 1
   3. C.1 or $\frac{a}{b}$ or $\frac{a}{c}$
   4. D.1 or $\frac{a}{b}$ or $\frac{c}{a}$
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   Answer: C

6. Q362018 · 9 Sept 2018

   If $\sec (\theta -\alpha )$, $\sec \theta$ and $\sec (\theta +\alpha )$ are in AP, where $\cos \alpha \ne 1$, then what is the value of ${\sin }^2\theta +\cos \alpha$?

   1. A.$0$
   2. B.$1$
   3. C.$-1$
   4. D.$\frac{1}{2}$
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   Answer: A

7. Q372018 · 9 Sept 2018

   If $A+B+C=180^{\circ }$, then what is $\sin 2A-\sin 2B-\sin 2C$ equal to?

   1. A.$-4\sin A\sin B\sin C$
   2. B.$-4\cos A\sin B\cos C$
   3. C.$-4\cos A\cos B\sin C$
   4. D.$-4\sin A\cos B\cos C$
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   Answer: D

8. Q152018 · 22 Apr 2018

   If x, 3/2, z are in AP; x, 3, z are in GP; then which one of the following will be in HP ?

   1. A.x, 6, z
   2. B.x, 4, z
   3. C.x, 2, z
   4. D.x, 1, z
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   Answer: A

9. Q332018 · 22 Apr 2018

   If $x$, $x-y$ and $x+y$ are the angles of a triangle (not an equilateral triangle) such that $\tan (x-y)$, $\tan x$ and $\tan (x+y)$ are in GP, then what is $x$ equal to?

   1. A.$\pi /4$
   2. B.$\pi /3$
   3. C.$\pi /6$
   4. D.$\pi /2$
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   Answer: Dropped in the final answer key (full marks to everyone)