Self Studies

Permutations an...

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  • Question 1
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    A school committee consists of 22 teachers and 44 students. The number of different committees that can be formed from 55 teachers and 1010 students is

  • Question 2
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    Number of cyphers at the end of 2002^{2002} C1001_{1001} is

  • Question 3
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    If r=0n{nCr1nCr+nCr1 } =2\displaystyle \sum _{ r=0 }^{ n }{ \left\{ \dfrac { { n{ C }_{ r-1 } } }{ n{ C }_{ r }+n{ C }_{ r-1 } }  \right\}  } =2 then n is equal to

  • Question 4
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    If $$\frac{3^{3 n} \cdot 2^{n}}{108}+\frac{3^{3 n}}{729}+\frac{3^{3 n} \cdot 2^{2 n}}{48}+\frac{2^{3 n} \cdot 3^{3 n}}{64}=37^{3} \cdot 3^{6}$$
    , then find the value of n ?

  • Question 5
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    The number of all the possible selection which a student can make for answering one or more questions out of eight given question in a paper, which each question has an alternative is 

  • Question 6
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    nCr+nCr+1^{n }{ C }_{ r }+^{ n }{ C }_{ r+1 } is equal to______________.

  • Question 7
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    If nC3+nC4>n+1C3^{n}C_{3} + ^{n}C_{4} > ^{n + 1}C_{3}, then

  • Question 8
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    r=0mn+rCn\displaystyle\sum^{m}_{r=0}{^{n+r}C_n} is equal to?

  • Question 9
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    The number of permutations which can be formed out of the letters of the word "SERIES" three letters together, is:

  • Question 10
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    If α=mC2\alpha = ^{m}C_{2}, then αC2^{\alpha}C_{2} is equal to

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