Sequences & Series · NDA previous year questions

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2021 14 questions

Q12021 · 14 Nov 2021
If $x^{2} + x + 1 = 0$ , then what is the value of $x^{199} + x^{200} + x^{201}$ ?
1. A.-1
2. B.0
3. C.1
4. D.3
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Answer: B
Q22021 · 14 Nov 2021
If x, y, z are in GP, then which of the following is/are correct? 1. ln(3x), ln(3y), ln(3z) are in AP 2. xyz + ln(x), xyz + ln(y), xyz + ln(z) are in HP 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: A
Q32021 · 14 Nov 2021
If $lo g_{10} 2$ , $lo g_{10} (2^{x} - 1)$ , $lo g_{10} (2^{x} + 3)$ are in AP, then what is x equal to?
1. A.0
2. B.1
3. C. $lo g_{2} 5$
4. D. $lo g_{5} 2$
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Answer: C
Q42021 · 14 Nov 2021
Let S = {2, 3, 4, 5, 6, 7, 9}. How many different 3-digit numbers (with all digits different) from S can be made which are less than 500?
1. A.30
2. B.49
3. C.90
4. D.147
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Answer: C
Q52021 · 14 Nov 2021
If $p = (1111 \dots up to n digits)$ , then what is the value of $9 p^{2} + p$ ?
1. A. $1 0^{n} p$
2. B. $2 p \cdot 1 0^{n}$
3. C. $1 0^{n} p - 1$
4. D. $1 0^{n} p + 1$
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Answer: A
Q102021 · 14 Nov 2021
$\frac{1}{b + c}, \frac{1}{c + a}, \frac{1}{a + b}$ are in HP, then which of the following is/are correct? 1. a, b, c are in AP 2. $(b + c)^{2}, (c + a)^{2}, (a + b)^{2}$ 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: A
Q172021 · 14 Nov 2021
If C(n, 4), C(n, 5) and C(n, 6) are in AP, then what is the value of n?
1. A.7
2. B.8
3. C.9
4. D.10
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Answer: A
Q182021 · 14 Nov 2021
How many 4 - letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?
1. A.240
2. B.200
3. C.150
4. D.120
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Answer: A
Q442021 · 14 Nov 2021
Let $S_{k}$ denote the sum of first k terms of an AP. What is $\frac{S _{30}}{S _{20} - S _{10}}$ equal to?
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: C
Q32021 · 18 Apr 2021
If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?
1. A.-500
2. B.-250
3. C.500
4. D.250
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Answer: B
Q42021 · 18 Apr 2021
Consider the following statements: 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP. 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
Q52021 · 18 Apr 2021
How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
1. A.5
2. B.4
3. C.3
4. D.0
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Answer: D
Q62021 · 18 Apr 2021
If $f (x + 1) = x^{2} - 3 x + 2$ , then what is $f (x)$ equal to?
1. A. $x^{2} - 5 x + 4$
2. B. $x^{2} - 5 x + 6$
3. C. $x^{2} + 3 x + 3$
4. D. $x^{2} - 3 x + 1$
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Answer: B
Q72021 · 18 Apr 2021
If $x^{2}$ , $x$ , $- 8$ are in AP, then which one of the following is correct?
1. A. $x \in {- 2}$
2. B. $x \in {4}$
3. C. $x \in {- 2, 4}$
4. D. $x \in {- 4, 2}$
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Answer: C