CS GATE 2014 PAPER 03 - Online Test

Q1. Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions?
Answer : Option A
Explaination / Solution:



Q2. With respect to the numerical evaluation of the definite integral,  where a and b are given, which of the following statements is/are TRUE?
(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral. 
(II) The value of K obtained using the Simpson’s rule is always equal to the exact value of the definite integral.
Answer : Option C
Explaination / Solution:




Q3. The value of the integral given below is 
Answer : Option A
Explaination / Solution:



Q4. Consider the set of all functions f : {0,1,...,2014} → {0,1...,2014} such that f (f (i)) = i for 0 ≤ i ≤ 2014. Consider the following statements.
P. For each such function it must be the case that for every i, f(i) = i,
Q. For each such function it must be the case that for some i,f(i) = i,
R. Each such function must be onto.
Which one of the following is CORRECT?
Answer : Option B
Explaination / Solution:
No Explaination.


Q5. Let δ denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with δ ≥3, which one of the following is TRUE?
Answer : Option A
Explaination / Solution:

We know that v + r = e+2 ⇒ e=n+r-2......(1)
Where V=  n (number of vertices); r = number of faces and
e = number of edges
Given, δ ≥ 3 then 3n ≤ 2e

Number of faces is atleast (n/2) + 2

Q6. The CORECT formula for the sentence, “not all rainy days are cold” is
Answer : Option D
Explaination / Solution:

Given statement is 
 
(Since p→q ≡~ p∨q and let r(d) be rainy day, c(d) be cold day)