1
GATE CSE 2018
Numerical
+2
-0
Consider the minterm list form of a Boolean function ๐น given below. $$F\left( {P,Q,R,S} \right) = $$ $$\sum {m\left( {0,2,5,7,9,11} \right)} $$ $$ + \,\,d\left( {3,8,10,12,14} \right)$$

Here, $$m$$ denotes a minterm and $$d$$ denotes a donโ€™t care term. The number of essential prime implicants of the function $$F$$ is ______.

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2
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following is a closed form expression for the generating function of the sequence $$\left\{ {{a_n}} \right\},$$ where $${a_n} = 2n + 3$$ for all $$n = 0,1,2,....?$$
A
$${3 \over {{{\left( {1 - x} \right)}^2}}}$$
B
$${{3x} \over {{{\left( {1 - x} \right)}^2}}}$$
C
$${\left( {1 - x} \right)}$$
D
$${{3 - x} \over {{{\left( {1 - x} \right)}^2}}}$$
3
GATE CSE 2018
Numerical
+2
-0
Two people, $$P$$ and $$Q,$$ decide to independently roll two identical dice, each with $$6$$ faces, numbered $$1$$ to $$6.$$ The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by $$P$$ and $$Q.$$ Assume that all $$6$$ numbers on each dice are equi-probable and that all trials are independent. The probability (rounded to $$3$$ decimal places) that one of them wins on the third trial is _____.
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4
GATE CSE 2018
Numerical
+1
-0
Consider a matrix $$A = u{v^T}$$ where $$u = \left( {\matrix{ 1 \cr 2 \cr } } \right),v = \left( {\matrix{ 1 \cr 1 \cr } } \right).$$ Note that $${v^T}$$ denotes the transpose of $$v.$$ The largest eigenvalue of $$A$$ is _____.
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