Binomial Theorem · NDA previous year questions

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

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 $x^{50}$

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

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

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

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

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

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

In the expansion of $(1+x{)}^p(1+x{)}^q$, if the coefficient of $x^3$ is 35, then what is the value of $(p+q)$?

1. A.5
2. B.6
3. C.7
4. D.8

What is the coefficient of $x^{10}$ in the expansion of $(1-x^2{)}^{20}{\left(2-x^2-\frac{1}{x^2}\right)}^{-5}$?

1. A.-1
2. B.1
3. C.10
4. D.Coefficient of $x^{10}$ does not exist

If the 4th term in the expansion of ${\left(mx+\frac{1}{x}\right)}^n$ is $\frac{5}{2}$, then what is the value of $mn$?

1. A.-3
2. B.3
3. C.6
4. D.12

In a binomial expansion of $(x+y{)}^{2n+1}(x-y{)}^{2n+1}$, the sum of middle terms is zero. What is the value of $\left(\frac{x^2}{y^2}\right)$ ?

1. A.1
2. B.2
3. C.4
4. D.8

In a Binomial distribution B(n, p), n = 6 and 9P(X = 4) = P(X = 2). What is p equal to ?

1. A.$\frac{1}{4}$
2. B.$\frac{1}{2}$
3. C.$\frac{3}{4}$
4. D.$\frac{4}{5}$

If the sixth term in the binomial expansion of ${\left(x^{-\frac{8}{3}}+x^2{\log }_{10}x\right)}^8$ is 5600, then what is the value of x ?

1. A.6
2. B.8
3. C.9
4. D.10

How many terms are there in the expansion of $(3x-y{)}^4(x+3y{)}^4$ ?

1. A.9
2. B.12
3. C.15
4. D.17

Consider the binomial expansion of $(p+qx{)}^9$ : What is the value of q if the coefficients of $x^3$ and $x^6$ are equal ?

1. A.p
2. B.9p
3. C.$\frac{1}{p}$
4. D.$p^2$

What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?

1. A.pq
2. B.p/q
3. C.4p/5q
4. D.1/(pq)

1. A.$p:q=7:2$
2. B.$p^2:q^2=7:2$
3. C.$p:q=2:7$
4. D.$p^2:q^2=2:7$

Consider the word 'QUESTION' : How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?

1. A.36
2. B.144
3. C.576
4. D.864 p

How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

1. A.288
2. B.576
3. C.1152
4. D.2304

How many 8-letter words with or without meaning, can be formed so that all consonants are together?

1. A.5760
2. B.2880
3. C.1440
4. D.720

How many terms are there in the expansion of ${\left(1+\frac{2}{x}\right)}^9{\left(1-\frac{2}{x}\right)}^9$?

1. A.9
2. B.10
3. C.19
4. D.20

Consider the following statements in respect of the expansion of $(x+y{)}^{10}$ 1. Among all the coefficients of the terms, the coefficient of the 6th term has the highest value 2. The coefficient of the 3rd term is equal to coefficient of the 9th term 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

If C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5)?

1. A.42
2. B.35
3. C.28
4. D.21

What is the value of C(51, 21) - C(51, 22) + C(51, 23) - C(51, 24) + C(51, 25) - C(51, 26) + C(51, 27) - C(51, 28) + C(51, 29) - C(51, 30) ?

1. A.C(51, 25)
2. B.C(51, 27)
3. C.C(51, 51) - C(51, 0)
4. D.C(51, 25) - C(51, 27)

How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?

1. A.32
2. B.36
3. C.40
4. D.45