Sequences & Series · NDA previous year questions

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2016 16 questions

Q112016 · 18 Sept 2016
How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms ?
1. A.One
2. B.Two
3. C.Four
4. D.Infinitely many
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Answer: D
Q122016 · 18 Sept 2016
Consider the following for the next three (03) items that follow : Let a, x, y, z, b be in AP, where $x + y + z = 15$ . Let a, p, q, r, b be in HP, where $p^{- 1} + q^{- 1} + r^{- 1} = 5/3$ . What is the value of ab ?
1. A.10
2. B.9
3. C.8
4. D.6
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Answer: B
Q132016 · 18 Sept 2016
Consider the following for the next three (03) items that follow : Let a, x, y, z, b be in AP, where $x + y + z = 15$ . Let a, p, q, r, b be in HP, where $p^{- 1} + q^{- 1} + r^{- 1} = 5/3$ . What is the value of xyz ?
1. A.120
2. B.105
3. C.90
4. D.Cannot be determined
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Answer: B
Q142016 · 18 Sept 2016
Consider the following for the next three (03) items that follow : Let a, x, y, z, b be in AP, where $x + y + z = 15$ . Let a, p, q, r, b be in HP, where $p^{- 1} + q^{- 1} + r^{- 1} = 5/3$ . What is the value of pqr ?
1. A.35/243
2. B.81/35
3. C.243/35
4. D.Cannot be determined
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Answer: C
Q152016 · 18 Sept 2016
Passage
Consider the following for the next two (02) items that follow : The sixth term of an AP is 2 and its common difference is greater than 1.
What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest ?
1. A.8/5
2. B.9/5
3. C.2
4. D.11/5
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Answer: A
Q162016 · 18 Sept 2016
Passage
Consider the following for the next two (02) items that follow : The sixth term of an AP is 2 and its common difference is greater than 1.
What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest ?
1. A.-4
2. B.-6
3. C.-8
4. D.-10
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Answer: B
Q172016 · 18 Sept 2016
Passage
Consider the following for the next two (02) items that follow : The sixth term of an AP is 2 and its common difference is greater than 1.
The interior angles of a polygon of n sides are in AP. The smallest angle is $12 0^{\circ}$ and the common difference is $5^{\circ}$ . How many possible values can n have ?
1. A.One
2. B.Two
3. C.Three
4. D.Infinitely many
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Answer: A
Q182016 · 18 Sept 2016
Passage
Consider the following for the next two (02) items that follow : The sixth term of an AP is 2 and its common difference is greater than 1.
What is the largest interior angle of the polygon ?
1. A. $16 0^{\circ}$ only
2. B. $19 5^{\circ}$ only
3. C.Either $16 0^{\circ}$ or $19 5^{\circ}$
4. D.Neither $16 0^{\circ}$ nor $19 5^{\circ}$
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Answer: A
Q192016 · 18 Sept 2016
If $x^{l n (\frac{y}{z})} \cdot y^{l n (x z)^{2}} \cdot z^{l n (\frac{x}{y})} = y^{4 l n y}$ for any $x > 1$ , $y > 1$ and $z > 1$ , then which one of the following is correct ?
1. A. $ln y$ is the GM of $ln x$ , $ln x$ , $ln x$ and $ln z$
2. B. $ln y$ is the AM of $ln x$ , $ln x$ , $ln x$ and $ln z$
3. C. $ln y$ is the HM of $ln x$ , $ln x$ , $ln x$ and $ln z$
4. D. $ln y$ is the AM of $ln x$ , $ln x$ , $ln z$ and $ln z$
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Answer: B
Q232016 · 18 Sept 2016
Consider the following for the next two (02) items that follow : $2 x^{2} + 3 x - α = 0$ has roots $- 2$ and $β$ while the equation $x^{2} - 3 m x + 2 m^{2} = 0$ has both roots positive, where $α > 0$ and $β > 0$ . If $β$ , 2, 2m are in GP, then what is the value of $β m$ ?
1. A.1
2. B.2
3. C.4
4. D.6
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Answer: A
Q242016 · 18 Sept 2016
If $c > 0$ and $4 a + c < 2 b$ , then $a x^{2} - b x + c = 0$ has a root in which one of the following intervals ?
1. A.(0, 2)
2. B.(2, 3)
3. C.(3, 4)
4. D.(-2, 0)
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Answer: A
Q252016 · 18 Sept 2016
What is the number of odd integers between 1000 and 9999 with no digit repeated ?
1. A.2100
2. B.2120
3. C.2240
4. D.3331
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Answer: C
Q82016 · 17 Apr 2016
For the next two (2) items that follow : Given that $lo g_{x} y, lo g_{z} x, lo g_{y} z$ are in GP, $x y z = 64$ and $x^{3}, y^{3}, z^{3}$ are in AP. Which one of the following is correct? $x, y$ and $z$ are
1. A.in AP only
2. B.in GP only
3. C.in both AP and GP
4. D.neither in AP nor in GP
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Answer: C
Q92016 · 17 Apr 2016
For the next two (2) items that follow : Given that $lo g_{x} y, lo g_{z} x, lo g_{y} z$ are in GP, $x y z = 64$ and $x^{3}, y^{3}, z^{3}$ are in AP. Which one of the following is correct? $x y, y z$ and $z x$ are
1. A.in AP only
2. B.in GP only
3. C.in both AP and GP
4. D.neither in AP nor in GP
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Answer: C
Q732016 · 17 Apr 2016
For the next two (2) items that follow : Given that $a_{n} = \int_{0}^{π} \frac{sin ^{2} {( n + 1 ) x }}{sin 2 x} d x$ Consider the following statements : 1. The sequence ${a_{2 n}}$ is in AP with common difference zero. 2. The sequence ${a_{2 n - 1}}$ is in AP with common difference zero. Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q742016 · 17 Apr 2016
For the next two (2) items that follow : Given that $a_{n} = \int_{0}^{π} \frac{sin ^{2} {( n + 1 ) x }}{sin 2 x} d x$ What is $a_{n - 1} - a_{n - 4}$ equal to?
1. A. $- 1$
2. B.0
3. C.1
4. D.2
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Answer: B