Sequences & Series · NDA previous year questions

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2025 13 questions

Q12025 · 14 Sept 2025
If $p^{x} = q^{y} = r^{z}$ where x, y and z are in GP, then consider the following statements: I. p, q and r are in AP. II. $ln p, ln q$ and $ln r$ are in GP. Which of the statements given above is/are correct?
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: B
Q52025 · 14 Sept 2025
If $(10 + lo g_{10} x), (10 + lo g_{10} y)$ and $(10 + lo g_{10} z)$ are in AP, then consider the following statements: I. The GM of x and z is $y^{2}$ II. The AM of $lo g_{10} x$ and $lo g_{10} z$ is $lo g_{10} y$ Which of the statements given above is/are correct?
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: B
Q62025 · 14 Sept 2025
How many terms of the series 1 + 3 + 5 + 7 +... amount to a sum equal to 12345678987654321?
1. A.11111111
2. B.110000011
3. C.111101111
4. D.111111111
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Answer: D
Q72025 · 14 Sept 2025
How many terms are identical in the two APs 19, 21, 23,... up to 110 terms and 19, 22, 25, 28,... up to 75 terms?
1. A.35
2. B.36
3. C.37
4. D.38
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Answer: C
Q82025 · 14 Sept 2025
If $α = \frac{- 1 + - 3}{2}$ then what is the value of $(1 + α^{19} - α^{35})^{100} - (1 - 3 α^{25} + α^{38})^{50}$ ?
1. A.-2
2. B.-1
3. C.0
4. D.2
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Answer: C
Q92025 · 14 Sept 2025
What is the remainder when $5^{99}$ is divided by 13?
1. A.10
2. B.9
3. C.8
4. D.6
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Answer: C
Q322025 · 14 Sept 2025
Passage
For the following two (02) items: Consider the equation abx² + bcx + ca = cax² + abx + bc
If the roots of the equation are equal, then a, b, c are in
1. A.AP
2. B.GP
3. C.HP
4. D.None of the above
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Answer: C
Q12025 · 13 Apr 2025
The sum of the first k terms of a series S is $3 k^{2} + 5 k$ . Which one of the following is correct?
1. A.The terms of S form an arithmetic progression with common difference 14.
2. B.The terms of S form an arithmetic progression with common difference 6.
3. C.The terms of S form a geometric progression with common ratio 10/7.
4. D.The terms of S form a geometric progression with common ratio 11/4.
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Answer: B
Q22025 · 13 Apr 2025
The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r≠1 is the common ratio, then what is the number of possible real values of r?
1. A.One
2. B.Two
3. C.Three
4. D.More than three
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Answer: C
Q52025 · 13 Apr 2025
If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?
1. A.-3
2. B.-2
3. C.2
4. D.3
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Answer: A
Q62025 · 13 Apr 2025
If p, 1, q are in AP and p, 2, q are in GP, then which of the following statements is/are correct? I. p, 4, q are in HP. II. (1/p), (1/4), (1/q) are in AP. 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
Q72025 · 13 Apr 2025
If $x = (1111)_{2}$ , $y = (1001)_{2}$ and $z = (110)_{2}$ , then what is $x^{3} - y^{3} - z^{3} - 3 x y z$ equal to?
1. A. $(111001)_{2}$
2. B. $(100111)_{2}$
3. C. $(1)_{2}$
4. D. $(0)_{2}$
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Answer: D
Q82025 · 13 Apr 2025
1. A.0
2. B.1
3. C.Δ
4. D.−Δ
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Answer: A