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Permutation Test - 11
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Permutation Test - 11
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  • Question 1/6
    1 / -0

    The greatest integer, which divides n! + 1, n ∈ N, n ≥ 3 is

    Solutions

    n! = 1.2.3........................n

    ∴ n! is divisible by any number from 2 to n.

    Consequently n! +1. when divided by any number between 2 and n leaves 1 as remainder. Hence

    n! + 1 is not divisible by any of the numbers from 2 to 'n' .

    The correct answer is: n

  • Question 2/6
    1 / -0

    A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is

    Solutions

    Number of selection with no complete pair = total number of ways of choosing 4 shoes - number of ways in which there is at lest one complete pair.

    = 10C4 - [5C1 × 8C2 - 5C2]

    = 210 - [140 - 10] = 80

    The correct answer is: 80

     

  • Question 3/6
    1 / -0

    Number of ways of selecting n things out of 3n things of which n are of one kind and alike and n are alike of 2nd kind and rest are unlike is

    Solutions

    Number of ways coefficient of xn in 

    (1 + x + x2 + x3 + ......+ xn)2 (1 + x)n

    = coefficient of xn in (1- xn+1)2(1 - x)-2(1 - x)

    = coefficient of xn in (1 - x)-2[(2 - (1 - x))]n

    = coefficient of xn in 2n (1 - x)-2) - 2n-1.nC1 (1 - x)-1 + 2n-2.nC2 - 2n-3.nC3 (1 - x) + ......

    = 2n(n + 1) - 2n-1.n 

    = 2n-1(n + 2).

    The correct answer is: (n + 2) 2(n–1)

     

  • Question 4/6
    1 / -0

    How many different 5 letter sequences can be made using the letters A,B,C,D with repetition such that the sequence does not include the word BAD?

    Solutions

    Number of sequences can be formed = 45

    Number of sequences including BAD = 3.42

    Total number of sequences not of having BAD = 45 - 3.42 = 976.

    The correct answer is: 976

  • Question 5/6
    1 / -0

    The number of ways in which the sequence of a 8×8 chess board can be painted red or blue so that each 2×2 squares has two red and two blue squares is

    Solutions

    Number of ways when the squares are alternating colour in first column is 28.

    Number of ways when the squares in the first column are not alternating colour = 28 – 2

    ⇒ total number of ways = 28 + 28 – 2 = 29 – 2

    The correct answer is: 29 – 2

  • Question 6/6
    1 / -0

    Statement-1 : Number of permutations of "n" dissimilar things taken "n" at a time is npn.

    Statement-2 :  n(A) = n(B) = n then the total number of functions from A to B are n!

    Solutions

    nPn = n!; 

    But number of function from A to B is nn

    The correct answer is: Both Statements-1 and Statement-2 are true and Statement-2 is the correct explanation of Statement-1

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