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CS GATE 2014 PAPER 03 - Online Test
cs gate 2014 paper 03
TEST : 5
# Engineering Mathematics
# CS GATE 2014 PAPER 03
Prepare / Learn
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?
A.
(97 × 97 × 97)/100
3
B.
(99 × 98 × 97)/100
3
C.
(97 × 96 × 95)/100
3
D.
(97 × 96 × 95)/(3! × 100
3
)
View Solution
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Answer :
Option A
Explaination / Solution:
# Engineering Mathematics
# CS GATE 2014 PAPER 03
Prepare / Learn
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.
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
View Solution
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Answer :
Option C
Explaination / Solution:
# Engineering Mathematics
# CS GATE 2014 PAPER 03
Prepare / Learn
Q3.
The value of the integral given below is
A.
− 2π
B.
π
C.
−π
D.
2π
View Solution
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Answer :
Option A
Explaination / Solution:
# Engineering Mathematics
# CS GATE 2014 PAPER 03
Prepare / Learn
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?
A.
P, Q and R are true
B.
Only Q and R are true
C.
Only P and Q are true
D.
Only R is true
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
No Explaination.
# Engineering Mathematics
# CS GATE 2014 PAPER 03
Prepare / Learn
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?
A.
In any planar embedding, the number of faces is at least (n/2) + 2
B.
In any planar embedding, the number of faces is less than (n/2) + 2
C.
There is a planar embedding in which the number of faces is less than (n/2) + 2
D.
There is a planar embedding in which the number of faces is at most n/(δ+1)
View Solution
Add Work Space
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
# Engineering Mathematics
# CS GATE 2014 PAPER 03
Prepare / Learn
Q6.
The CORECT formula for the sentence, “not all rainy days are cold” is
A.
∀d (Rainy (d)∧∼Cold(d))
B.
∀d (~Rainy (d)→Cold(d))
C.
∃d (~Rainy (d)→Cold(d))
D.
∃d (Rainy (d)∧∼Cold(d))
View Solution
Add Work Space
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)
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