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Gate Latest Exam Pattern - Gate Sample Question with Solutions Page 72

(#M40021715) GATE QUESTION MATHS Keep an EYE

We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

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(#M40021714) GATE QUESTION MATHS Keep an EYE

Four matrices M1, M2, M3 and M4 are dimensions p × q, q × r, r × s and s × t respectively can be multiplied in several ways with different number of total scalar multiplications. For example When multiplied as (( ) ( )) 1 2 3 4 M ×M × M ×M the total number of scalar multiplications is pqr+rst+prt. When multiplied as ((( ) ) ) 1 2 3 4 M ×M ×M ×M , the total number of scalar multiplications is pqr+prs+pst.
If p=10, q=100, r=20, s=5 and t=80, then the minimum number of scalar
multiplications needed is??

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(#M40021713) GATE QUESTION MATHS Keep an EYE

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

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(#M40021712) GATE QUESTION MATHS Keep an EYE

5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall
in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6
semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Asked In Gate MAN (12 years ago)

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(#M40021711) GATE QUESTION MATHS Keep an EYE

What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this
graph such that P contains at most 3 edges?

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(#M40021710) GATE QUESTION MATHS Keep an EYE

What is the minimum possible weight of a spanning tree T in this graph such that
vertex 0 is a leaf node in the tree T?

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(#M40021709) GATE QUESTION MATHS Keep an EYE

Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula "x y t(F (x, y, t))?
option
(A) Everyone can fool some person at some time
(B) No one can fool everyone all the time
(C) Everyone cannot fool some person all the time
(D) No one can fool some person at some time

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(#M40021707) GATE QUESTION MATHS Keep an EYE

The degree sequence of a simple graph is the sequence of the degrees of the
nodes in the graph in decreasing order. Which of the following sequences can not
be the degree sequence of any graph?

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(#M40021706) GATE QUESTION MATHS Keep an EYE

What is the probability that divisor of 1099 is a multiple of 1096?

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(#M40021705) GATE QUESTION MATHS Keep an EYE

Consider a company that assembles computers. The probability of a faulty
assembly of any computer is p. The company therefore subjects each
computer to a testing process. This testing process gives the correct result for
any computer with a probability of q. What is the probability of a computer
being declared faulty?

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