Binomial Theorem · NDA previous year questions

2022 12 questions

1. Q222022 · 4 Sept 2022

   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.$p^2$
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   Answer: A

2. Q232022 · 4 Sept 2022

   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)
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   Answer: B

3. Q242022 · 4 Sept 2022
   
   1. A.$p:q=7:2$
   2. B.$p^2:q^2=7:2$
   3. C.$p:q=2:7$
   4. D.$p^2:q^2=2:7$
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   Answer: B

4. Q252022 · 4 Sept 2022

   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
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   Answer: D

5. Q262022 · 4 Sept 2022

   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
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   Answer: C

6. Q272022 · 4 Sept 2022

   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
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   Answer: B

7. Q112022 · 10 Apr 2022

   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
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   Answer: B

8. Q122022 · 10 Apr 2022

   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
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   Answer: C

9. Q132022 · 10 Apr 2022

   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
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   Answer: D

10. Q142022 · 10 Apr 2022

    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)
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    Answer: C

11. Q152022 · 10 Apr 2022

    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
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    Answer: A

12. Q502022 · 10 Apr 2022

    In the expansion of ${\left(x+\frac{1}{x}\right)}^{2n}$, what is the $(n+1)$th term from the end (when arranged in descending powers of x)?

    1. A.$C(2n,n)x$
    2. B.$C(2n,n-1)x$
    3. C.$C(2n,n)$
    4. D.$C(2n,n-1)$
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    Answer: C