Math for Computer science
Questions 71 to 80
71.

If P(A’)
= 3/8, P(B’) =1/2 and P(A∩ B) = 1 / 4, then P(A/B) = .
(a) 1/2 (b) 1/8 (c) 1 / 4 (d) 2/5 (e) 2/8.


72.

Suppose a
coin is flipped three times. Let X(t) be the random variable that equals the
number of tails that appears and t is the outcome, then X(HTT) = _____.
(a) 3 (b) 2 (c) 1 (d) 0 (e) 4.


73.

A coin is
tossed and a single 6sided die is rolled. What is the probability of landing
on the head side of the coin and rolling a 3 on the die?
(a) ½ (b) 1/12 (c) 1/3 (d) 1/6 (e) 2/3.


74.

How many
functions are there from a set with m elements to one with n
elements?
(a) nm (b) n^{m+1 }(c)
m^{n }(d)
m^{n+1 }(e)
m + n.


75.

The
values of n and r, if P(n,r) = 7920, are
(a) 10 , 3 (b) 12, 4 (c) 11, 4 (d) 10 , 4 (e) 11, 8.


76.

An
integer s is an inverse of a modulo m if
(a) a ≡ s (mod m) (b) s
≡ a (mod m)
(c) s.a ≡ 1 (mod m) (d) m.s ≡
1 (mod a)
(e) m.a ≡ 1 (mod s).


77.

A drawer
contains a dozen brown socks and a dozen black socks, all unmatched. A man
takes out socks at random in the dark. How many socks must he take to be sure
that he has at least two socks of the same color?
(a) 3 (b) 13 (c) 14 (d) 12 (e) 2.


78.

A finite
state machine with output, where the output is determined only by the state,
is
(a) Kleene machine (b) Mealy
machine
(c) Moore machine (d)
Deterministic Finite state automata.
(e) Nondeterministic
Finite state automata.


79.

The
grammar which has no restrictions on its productions is
(a) Type 0 Grammar (b) Type 1
Grammar
(c) Type 2 Grammar (d) Type 3
Grammar (e) Type 4 Grammar.


80.

Let A = {F, {F}} then which of the following
statement is true?

Answers
71.

Answer : (a)
Reason : The student can select the three projects
from three lists one after the other in 23+15+19 = 57 ways (Sum rule).


72.

Answer : (a)
Reason : P(A/B) = P(A∩B) / P(B) = (1/4) / (1–1/2) =
1/2


73.

Answer : (b)
Reason : A random variable is a function from the
sample space of an experiment to the set of real numbers.


74.

Answer : (a)
Reason : A function corresponds to a choice of one of
the n elements in the codomain for each of the m elements in the domain. Henc
tby the product rule there are n.×n×….×n = nm functions from a set with m
elements to one with n elements.


75.

Answer : (c)
Reason : P(n,r) = 7920; 7920 = 792 * 10 = 11*10*72 = 11*10*9*8 = P(11, 4)
Therefore , n= 11,r = 4.


76.

Answer : (c)
Reason : no explanation.


77.

Answer : (b)
Reason : Let us suppose the man picks black sock first
and then brown sock. In the 3rd attempt he has to either pick black or brown
so he is having two socks of same color. So according to pigeon hole
principle he has to pick a minimum number of three socks to have at least two
socks of the same color. pigeon hole principle explains worst case scenario.


78.

Answer : (c)
Reason : The finite state machine with output, where
the output is determined only by the state is Moore machine.


79.

Answer : (a)
Reason : The grammar which has no restrictions on its
productions is Type 0 Grammar


80.

Answer : (c)
Reason: By definition of power set of a set.

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