Discrete Structures Subject Wise UGC NET Question Analysis Part-1

Discrete Math PYQ Part-2

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Explanation:
Formula,
Conditional Probability

Calculation,
The probability of a toothache, given evidence of a cavity,

P(toothache Ո cavity ) = 0.108 + 0.012 = 0.12

P(cavity ) = 0.108 + 0.012 + 0.072 + 0.008 = 0.2

So,Option(IV) is correct.

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Explanation:
Formula,
P(A U B) = P(A) + P(B) – P(A Ո B)
Calculation,
P(cavity U toothache) = P(cavity) + P(toothache) – P(cavity Ո toothache)

P(cavity ) = 0.108 + 0.012 + 0.072 + 0.008 = 0.2

P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2

P(cavity Ո toothache) = 0.108 + 0.012 = 0.12

P(cavity U toothache) = P(cavity) + P(toothache) – P(cavity Ո toothache)
P(cavity U toothache) = 0.2 + 0.2 – 0.12 = 0.28
So, Option(III) is correct.

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Explanation:
Formula,

Calculation,

P(cavity Ո (toothache U catch)) = 0.108 + 0.012 + 0.072 = 0.192

P(toothache U cavity) = 0.108 + 0.012 + 0.072 + 0.016 + 0.064 + 0.144 = 0.416

= 0.4615
So, Option(I) is correct.

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Explanation:
Calculation,

P(cavity ) = 0.108 + 0.012 + 0.072 + 0.008 = 0.2

So, Option(III) is correct.

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Explanation:
Formula,
Conditional Probability

Calculation,
The probability of a cavity, given evidence of a toothache,

P(cavity Ո toothache ) = 0.108 + 0.012 = 0.12

P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2

= 0.6
So,Option(IV) is correct.

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Explanation:
Statement I: n5 – n
Example : Take n = 2 , 25- 2 = 32 – 2 = 30 , which is divided by 5.
Take n = 3 , 35 – 3 = 243 – 3 = 240 , which is divided by 5.
Statement I is true.
Statement II: n3 – n
Example : Take n = 2 , 23- 2 = 8 – 2 = 6 , which is divided by 6.
Take n = 3 , 33 – 3 = 27 – 3 = 24 , which is divided by 6.
Statement II is true.

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Explanation:
Lexicographically means sorting in natural order, dictionary order.
The lexicographic order of the given bit strings will be:
0001<001<010<0101<011
Take 0001 & 001 for comparing. Compare each bit of 1st string with the corresponding bit of 2nd string.

It is clear that 0001< 001.

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Explanation:
Edge set consists of edge from i to j , if and only if
either j=i+1
or j=3i
since, we to find the minimum number of edge from vertex 1 to vertex 100.so, we have to think about how we can reach an edge 100 from an edge 1 with minimum path.
1 ->3 ->9 -> 10 -> 11 -> 33 -> 99 -> 100.
We need minimum 7 edges.

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Answer: I,II Both (Marks to all)