Sequences & Series · NDA previous year questions

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2024 14 questions

Q72024 · 1 Sept 2024
If p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to?
1. A.0
2. B.p + q
3. C.pq
4. D.pq(p + q)
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Answer: A
Q82024 · 1 Sept 2024
Let $p = ln (x), q = ln (x^{3})$ and $r = ln (x^{5})$ , where $x > 1$ . Which of the following statements is/are correct? I. p, q and r are in AP. II. p, q and r can never be in GP. Select the answer using the code given below.
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
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Answer: C
Q112024 · 1 Sept 2024
Let $x > 1, y > 1, z > 1$ be in GP. Then $\frac{1}{1 + l n x}$ , $\frac{1}{1 + l n y}$ , $\frac{1}{1 + l n z}$ are
1. A.in AP
2. B.in GP
3. C.in HP
4. D.neither in AP nor in GP nor in HP
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Answer: C
Q132024 · 1 Sept 2024
If the sum of the first n terms of a series is n(2n+1), then what is the nth term?
1. A.4n - 1
2. B.4n
3. C.4n + 1
4. D.4n + 3
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Answer: A
Q382024 · 1 Sept 2024
In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is $p^{2} : q^{2}$ . Which one of the following is correct?
1. A.The first term is equal to the common difference
2. B.The first term is equal to twice the common difference
3. C.The common difference is equal to twice the first term
4. D.The first term is equal to square of the common difference
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Answer: C
Q432024 · 1 Sept 2024
Direction : Consider the following for the items that follow : The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. What is the common difference?
1. A.3
2. B.4
3. C.5
4. D.6
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Answer: D
Q442024 · 1 Sept 2024
What is the sum of all five terms?
1. A.60
2. B.65
3. C.75
4. D.80
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Answer: C
Q452024 · 1 Sept 2024
Directions
Direction : Consider the following for the items that follow : Let (8 + 3√7) 20 = U + V and (8 - 3√7) 20
= W, where U is an integer and 0 < V < 1. What is V + W equal to?
1. A.8
2. B.4
3. C.2
4. D.1
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Answer: D
Q462024 · 1 Sept 2024
Directions
Direction : Consider the following for the items that follow : Let (8 + 3√7) 20 = U + V and (8 - 3√7) 20
What is the value of (U + V)W?
1. A.1/2
2. B.1
3. C.3/2
4. D.2
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Answer: B
Q472024 · 1 Sept 2024
Directions
Direction : Consider the following for the items that follow : The roots of the quadratic equation $a^{2} (b^{2} - c^{2}) x^{2} + b^{2} (c^{2} - a^{2}) x + c^{2} (a^{2} - b^{2}) = 0$ are equal $(a^{2} \neq = b^{2} \neq = c^{2})$ .
$a^{2} (b^{2} - c^{2}) x^{2} + b^{2} (c^{2} - a^{2}) x + c^{2} (a^{2} - b^{2}) = 0$ are equal $(a^{2} \neq = b^{2} \neq = c^{2})$ . Which one of the following statements is correct?
1. A. $a^{2}$ , $b^{2}$ , $c^{2}$ are in AP.
2. B. $a^{2}$ , $b^{2}$ , $c^{2}$ are in GP.
3. C. $a^{2}$ , $b^{2}$ , $c^{2}$ are in HP.
4. D. $a^{2}$ , $b^{2}$ , $c^{2}$ are neither in AP nor in GP nor in HP.
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Answer: C
Q262024 · 21 Apr 2024
If $a, b, c$ are in AP; $b, c, d$ are in GP; $c, d, e$ are in HP, then which of the following is/are correct? 1. $a, c,$ and $e$ are in GP 2. $\frac{1}{a}, \frac{1}{c}, \frac{1}{e}$ are in GP Select the correct answer using the code given below:
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
Q272024 · 21 Apr 2024
What is the number of solutions of $lo g_{4} (x - 1) = lo g_{2} (x - 3)$ ?
1. A.Zero
2. B.One
3. C.Two
4. D.Three
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Answer: B
Q282024 · 21 Apr 2024
For $x \geq y > 1$ , let $lo g_{x} (\frac{x}{y}) + lo g_{y} (\frac{y}{x}) = k$ , then the value of $k$ can never be equal to :
1. A. $- 1$
2. B. $- \frac{1}{2}$
3. C.0
4. D.1
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Answer: D
Q1052024 · 21 Apr 2024
If $a, b, c$ are in HP, then what is $\frac{1}{b - a} + \frac{1}{b - c}$ equal to? 1. $\frac{2}{b}$ 2. $\frac{1}{a} + \frac{1}{c}$ 3. $\frac{1}{2} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$ Select the correct answer using the code given below:
1. A.1 only
2. B.1 and 2 only
3. C.3 only
4. D.1, 2 and 3
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Answer: B