# GATE CSE 2016 SET-2

 Question 1
Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) $P\vee Q$
(v) $\neg Q \vee P$
The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ________.
 A 2 B 3 C 4 D 5
Discrete Mathematics   Propositional Logic
Question 1 Explanation:
 Question 2
Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x)+ f(-x)) is 10, then the degree of (g(x)-g(-x)) is ________.
 A 10 B 9 C 11 D 8
Engineering Mathematics   Calculus
Question 2 Explanation:

 Question 3
The minimum number of colours that is sufficient to vertex-colour any planar graph is _________.
 A 2 B 3 C 4 D 5
Discrete Mathematics   Graph Theory
Question 3 Explanation:
 Question 4
Consider the systems,each consisting of m linear equations in n variables.
I. If m $\lt$ n, then all such systems have a solution
II. If m $\gt$ n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution
Which one of the following is CORRECT?
 A I, II and III are true B Only II and III are true C Only III is true D None of them is true
Engineering Mathematics   Linear Algebra
Question 4 Explanation:
 Question 5
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.
 A 0.25 B 0.55 C 0.65 D 0.75
Discrete Mathematics   Probability Theory
Question 5 Explanation:

There are 5 questions to complete.