Binomial Theorem · NDA previous year questions

2025 7 questions

1. Q42025 · 14 Sept 2025

   Let n be a natural number. The number of consecutive zeros at the end of the expansion of n! is exactly 2. How many values of n are possible?

   1. A.3
   2. B.4
   3. C.5
   4. D.More than 5
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   Answer: C

2. Q202025 · 14 Sept 2025

   Which one of the following is the greatest coefficient in the expansion of $(1+x{)}^{100}$ ?

   1. A.The coefficient of $x^{100}$
   2. B.The coefficient of $x^{99}$
   3. C.The coefficient of $x^{51}$
   4. D.The coefficient of $x^{50}$
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   Answer: D

3. Q1062025 · 14 Sept 2025

   Under which of the following conditions may binomial distribution be used? I. The number of trials is infinite and not fixed. II. The trials are independent. III. Each trial has two possible outcomes. Select the correct answer using the code given below.

   1. A.II only
   2. B.III only
   3. C.I and II
   4. D.II and III
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   Answer: D

4. Q202025 · 13 Apr 2025

   What is the number of rational terms in the expansion of $(\sqrt{3}+5^{\frac{1}{4}}{)}^{12}$

   1. A.2
   2. B.3
   3. C.4
   4. D.6
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   Answer: C

5. Q212025 · 13 Apr 2025

   If the sum of binomial coefficients in the expansion of $(x+y{)}^n$ is 256, then the greatest binomial coefficient occurs in which one of the following terms?

   1. A.Third
   2. B.Fourth
   3. C.Fifth
   4. D.Ninth
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   Answer: C

6. Q222025 · 13 Apr 2025

   If $k<(\sqrt{2}+1{)}^3<k+2$, where k is a natural number, the value of k?

   1. A.11
   2. B.13
   3. C.15
   4. D.17
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   Answer: B

7. Q232025 · 13 Apr 2025

   If then which one of the following is a value of x?

   
   1. A.-2
   2. B.-1
   3. C.0
   4. D.1
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   Answer: D