Math for Computer science
Questions 151 to 160
151.
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Let A = {a, b}
and B be the set of all strings over A. The function g: B →Z is defined
as g(S) = the number of a’s
in S, for each string S ∈B. Then g (ababb) =
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How many
different permutations can be formed out of all the letters of the word
“MATHS”?
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How many
different permutations can be formed out of the letters of the word
“MISSISSIPPI”?
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How many groups
of 4 people can be formed from 6 people?
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How many ways
can 5 persons arrange themselves around a circular table?
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Ten balls
numbered 0, 1, 2, ….., 9 are put in a box and two balls are taken at random
without replacement. The probability
that both numbers are odd is equal to
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A box contains 4
red balls and 2 white balls. Another box contains 5 red balls and 3 white
balls. Abox is selected at random and then a ball is drawn at random. The
probability that the ball is white is equal to
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If A and B be
two events with P(A) = , P(B) = and P(A È B) = , then P(A/B) =
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If A and B be
two events with P(A) = , P(B) = and P(A Ç B) = , then P(Ac Ç Bc) =
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It is given that
p → q, q → r and r → s are true. Which of the following must be necessarily
true?
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Answers
151.
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Answer : (b)
Reason : by
the definition of function the number of a’s are in the given string is 2
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Answer : (d)
Reason : by
the definition of permutations the number of ways are (5!)
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Answer : (c)
Reason : by
the definition of permutations with indistinguishable objects the number of ways are (11!) / (2! 4! 4!)
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Answer : (a)
Reason : 4
people has to be selected from 6 people which can be done in C(6,4) ways = 15
ways
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Answer : (b)
Reason : by
circular permutation the number of
ways are (5-1)! = 4! = 2456
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Answer : (d)
Reason : The
no. of ways choosing 2 balls is C (52,2 ).
The first odd number can be drawn in C(5,2 ) ways and that of second
odd number in C(4,2 ) ways . the probability is given by 4/9 ( after simplification of [C(5,2 )x C(4,2 )] / C (52,2 ) )
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Answer : (d)
Reason : The
probability of choosing a box is ½.
The white ball choosing from 1 box is 2/6 and
The white ball choosing from 2 box is 3/6 so the required probability
is 1/6+3/16
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Answer : (c)
Reason : P(AÇB)
= 0 so
P(A/B) = 0
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Answer : (b)
Reason : By
the Addition theorem on
probability , P(Ac Ç
Bc) = 1- P (AÈ B )
= 1 – (7/9)
=2/9
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Answer : (d)
Reason : By
the definition of Hypothetical
syllogism
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incomplete answer choice
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