Binomial Theorem · NDA previous year questions

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2010 7 questions

Q212010 · 22 Aug 2010
What is the sum of all the coefficients in the expansion of $(1 + x)^{n}$ ?
1. A. $2^{n}$
2. B. $2^{n} - 1$
3. C. $2^{n - 1}$
4. D. $2 (n - 1)$
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Answer: A
Q242010 · 22 Aug 2010
What is the coefficient of $x^{4}$ in the expansion of $(\frac{1 - x}{1 + x})^{2}$ ?
1. A.-16
2. B.16
3. C.8
4. D.-8
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Answer: B
Q862010 · 22 Aug 2010
What is the coefficient of $x^{17}$ in the expansion of $(3 x - \frac{x ^{3}}{6})^{9}$ ?
1. A. $189/8$
2. B. $567/2$
3. C. $21/16$
4. D.None of the above
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Answer: A
Q962010 · 22 Aug 2010
What is the number of terms in the expansion of $(a + b + c)^{n}, n \in N$ ?
1. A. $n + 1$
2. B. $n + 2$
3. C. $n (n + 1)$
4. D. $(n + 1) (n + 2) /2$
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Answer: D
Q972010 · 22 Aug 2010
What is the number of signals that can be sent by $6$ flags of different colours taking one or more at a time?
1. A. $21$
2. B. $63$
3. C. $720$
4. D. $1956$
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Answer: D
Q242010 · 18 Apr 2010
What is the sum of the coefficients of all the terms in the expansion of $(45 x - 49)^{4}$ ?
1. A. $- 256$
2. B. $- 100$
3. C.100
4. D.256
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Answer: D
Q302010 · 18 Apr 2010
Consider the following statements related to a variable X having a binomial distribution $b_{X} (n, p)$ : 1. If $p = \frac{1}{2}$ , then the distribution is symmetrical. 2. p remaining constant, $P (X = r)$ increases as n increases. Which of the statements given above 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: A