Sequences & Series · NDA previous year questions

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2017 13 questions

Q82017 · 10 Sept 2017
A person is to count 4500 notes. Let $a_{n}$ denote the number of notes he counts in the $n th$ minute. If $a_{1} = a_{2} = a_{3} = \dots = a_{10} = 150$ , and $a_{10}, a_{11}, a_{12}, \dots$ are in AP with the common difference $- 2$ , then the time taken by him to count all the notes is
1. A.24 minutes
2. B.34 minutes
3. C.125 minutes
4. D.135 minutes
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Answer: B
Q92017 · 10 Sept 2017
If $y = x + x^{2} + x^{3} + \dots$ up to infinite terms, where $x < 1$ , then which one of the following is correct?
1. A. $x = \frac{y}{1 + y}$
2. B. $x = \frac{y}{1 - y}$
3. C. $x = \frac{1 + y}{y}$
4. D. $x = \frac{1 - y}{y}$
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Answer: A
Q102017 · 10 Sept 2017
The value of $\frac{1}{l o g _{3} e} + \frac{1}{l o g _{3} e ^{2}} + \frac{1}{l o g _{3} e ^{4}} + \dots$ up to infinite terms is
1. A. $lo g_{e} 9$
2. B.0
3. C.1
4. D. $lo g_{e} 3$
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Answer: A
Q112017 · 10 Sept 2017
If $1.3 + 2. 3^{2} + 3. 3^{3} + \dots + n . 3^{n} = \frac{( 2 n - 1 ) 3 ^{a} + b}{4}$ then $a$ and $b$ are respectively
1. A. $n, 2$
2. B. $n, 3$
3. C. $n + 1, 2$
4. D. $n + 1, 3$
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Answer: D
Q122017 · 10 Sept 2017
If $S_{n} = n P + \frac{n ( n - 1 ) Q}{2}$ , where $S_{n}$ denotes the sum of the first $n$ terms of an AP, then the common difference is
1. A. $P + Q$
2. B. $2 P + 3 Q$
3. C. $2 Q$
4. D. $Q$
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Answer: D
Q92017 · 23 Apr 2017
What is the sum of the series $0.3 + 0.33 + 0.333 + \dots n$ terms?
1. A. $\frac{1}{3} [n - \frac{1}{9} (1 - \frac{1}{1 0 ^{n}})]$
2. B. $\frac{1}{3} [n - \frac{2}{9} (1 - \frac{1}{1 0 ^{n}})]$
3. C. $\frac{1}{3} [n - \frac{1}{3} (1 - \frac{1}{1 0 ^{n}})]$
4. D. $\frac{1}{3} [n - \frac{1}{9} (1 + \frac{1}{1 0 ^{n}})]$
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Answer: A
Q102017 · 23 Apr 2017
If the sum of $m$ terms of an AP is $n$ and the sum of $n$ terms is $m$ , then the sum of $(m + n)$ terms is
1. A. $mn$
2. B. $m + n$
3. C. $2 (m + n)$
4. D. $- (m + n)$
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Answer: D
Q112017 · 23 Apr 2017
The fifth term of an AP of $n$ terms, whose sum is $n^{2} - 2 n$ , is
1. A.5
2. B.7
3. C.8
4. D.15
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Answer: B
Q122017 · 23 Apr 2017
The sum of all the two-digit odd numbers is
1. A.2475
2. B.2530
3. C.4905
4. D.5049
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Answer: A
Q132017 · 23 Apr 2017
The sum of the first $n$ terms of the series $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \dots$ is equal to
1. A. $2^{n} - n - 1$
2. B. $1 - 2^{- n}$
3. C. $2^{- n} + n - 1$
4. D. $2^{n} - 1$
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Answer: C
Q172017 · 23 Apr 2017
The sum of the roots of the equation $x^{2} + b x + c = 0$ (where $b$ and $c$ are non-zero) is equal to the sum of the reciprocals of their squares. Then $\frac{1}{c}, b, \frac{c}{b}$ are in
1. A.AP
2. B.GP
3. C.HP
4. D.None of the above
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Answer: C
Q182017 · 23 Apr 2017
The sum of the roots of the equation $a x^{2} + x + c = 0$ (where $a$ and $c$ are non-zero) is equal to the sum of the reciprocals of their squares. Then $a, c a^{2}, c^{2}$ are in
1. A.AP
2. B.GP
3. C.HP
4. D.None of the above
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Answer: A
Q482017 · 23 Apr 2017
Let $x, y, z$ be positive real numbers such that $x, y, z$ are in GP and $tan^{- 1} x$ , $tan^{- 1} y$ and $tan^{- 1} z$ are in AP. Then which one of the following is correct?
1. A. $x = y = z$
2. B. $x z = 1$
3. C. $x \neq = y$ and $y = z$
4. D. $x = y$ and $y \neq = z$
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Answer: Dropped in the final answer key (full marks to everyone)