GATE CSE 2020 National Champion Quiz: Discrete Maths (App update required to attempt this test)

How many of the following is/are not Tautology?

1)

2)

3)

4)

Consider the following statements about Bipartite graph.

(a) The maximum number of edges in a bipartite graph with 10 vertices is 28. 

(b) The maximum number of edges in a bipartite graph with 24 vertices is 143.

(c) The minimum number of edges in a complete bipartite graph with 10 vertices is 9.

(d) Every bipartite graph is 2 colorable.

The number of correct statements is _______________?

If set A is empty set then n [P [P [P [A]]]?

How many solutions are there to the equation x1 + x2 + x3 + x4 = 10? Where 1 <= x1 <= x3, 2 <= x2 <= 4, 3 <= x3 <= 5 is ____________?

There were 4 red scarves, 5 yellow Umbrellas and 6 Suits in a shop. Ted, Barney, Lily, Marshal and Robin came to the shop to buy the items. How many different results could have been recorded if all of the items were sold ________

Shyam visited Ram during his brief vacation. In the mornings they both would go for Yoga. In the evening they would play tennis. To have more fun , they indulge only in one activity per day i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed at home all day long. There were 24 mornings when they did nothing , 14 evenings when they stayed at home and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram ___________

Consider the following statements

Statement 1. G is bipartite and G is a 2 colorable and every cycle in G is even cycle. All these statements are equivalent.

Statement 2. If Dirac’s theorem and ore’s theorem is initially satisfied in graph then it is not hamiltonion graph.

Statement 3. Cycle graph do not contain articulation points.

Number of statement which are correct.

Number of perfect matching in a complete graph K₉ is ______.

Consider the first order predicate formula 𝜑:

∀𝑥 [(∀𝑧 𝑧|𝑥⇒((𝑧=𝑥)∨(𝑧=1)))⇒∃𝑤 (𝑤>𝑥)∧(∀𝑧 𝑧|𝑤⇒((𝑤=𝑧)∨(𝑧=1)))]

Here ‘a|b’ denotes that ‘a divides b’, where a and b are integers. Consider the following sets:

S1 {1,2,3,…,100}

S2 Set of all positive integers

S3 Set of all integers

Which of the above sets satisfy 𝜑?

The value of 3^51 mod 5 is ________.