1
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, is the same expression as that of $$F$$ with $$+$$ and $$ \cdot $$ swapped. $$F$$ is said to be self-dual if $$F = {F^D} \cdot $$. The number of self-dual functions with $$n$$ Boolean variables is
A
$${2^n}$$
B
$${2^{n - 1}}$$
C
$${2^{{2^n}}}$$
D
$${2^{{2^{n - 1}}}}$$
2
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Let $$k = {2^n}.$$ A circuit is built by giving the output of an ݊$$n$$-bit binary counter as input to an $$n$$-to-$${2^n}$$ bit decoder. This circuit is equivalent to a
A
$$k$$-bit binary up counter.
B
$$k$$-bit binary down counter.
C
$$k$$-bit ring counter.
D
$$k$$-bit Johnson counter.
3
GATE CSE 2014 Set 2
Numerical
+1
-0
The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functinal be denoted by p. Then 100p = __________________.
Your input ____
4
GATE CSE 2014 Set 2
Numerical
+1
-0
Each of the nine words in the sentence "The Quick brown fox jumps over the lazy dog" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is ______________. (Then answer should be rounded to one decimal place.)
Your input ____
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