Permutations & Combinations · NDA previous year questions

2010 5 questions

1. Q32010 · 22 Aug 2010

   What is the number of words that can be formed from the letters of the word 'UNIVERSAL', the vowels remaining always together?

   1. A.720
   2. B.1440
   3. C.17280
   4. D.21540
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   Answer: C

2. Q982010 · 22 Aug 2010

   In how many ways can a committee consisting of $3$ men and $2$ women be formed from $7$ men and $5$ women?

   1. A.$45$
   2. B.$350$
   3. C.$700$
   4. D.$4200$
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   Answer: B

3. Q992010 · 22 Aug 2010

   If $\vec{a}=\hat{i}-\hat{k},\vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k},\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$, then $\vec{a}\cdot \left(\vec{b}\times \vec{c}\right)$ depends on

   1. A.$x$ only
   2. B.$y$ only
   3. C.both $x$ and $y$
   4. D.neither $x$ nor $y$
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   Answer: D

4. Q222010 · 18 Apr 2010

   A team of 8 players is to be chosen from a group of 12 players. Out of the eight players one is to be elected as captain and another as vice-captain. In how many ways can this be done?

   1. A.27720
   2. B.13860
   3. C.6930
   4. D.495
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   Answer: A

5. Q312010 · 18 Apr 2010

   What is the number of ways of arranging the letters of the word 'BANANA' so that no two N's appear together?

   1. A.40
   2. B.60
   3. C.80
   4. D.100
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   Answer: A