# 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:
 Question 6
Suppose that the eigen values of matrix A are 1, 2, 4. The determinant of $(A^{-1})^{T}$ is _________.
 A 0 B 0.125 C 0.25 D 0.75
Engineering Mathematics   Linear Algebra
Question 6 Explanation:
 Question 7
Consider an eight-bit ripple-carry Combinational Circuit for computing the sum of A and B, where A and B are integers represented in 2's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ________.
 A 0 B 1 C -1 D 2
Digital Logic   Combinational Circuit
Question 7 Explanation:
 Question 8
Let, $x_{1} \oplus x_{2} \oplus x_{3} \oplus x_{4}=0$ where $x_{1}, x_{2} , x_{3} , x_{4}$ are Boolean variables, and $\oplus$ is the XOR operator. Which one of the following must always be TRUE?
 A $x_{1} x_{2} x_{3} x_{4}=0$ B $x_{1} x_{3}+ x_{2}=0$ C $\bar{x}_{1}\oplus \bar{x}_{3}=\bar{x}_{2}\oplus \bar{x}_{4}$ D $x_{1} +x_{2}+ x_{3}+ x_{4}=0$
Digital Logic   Boolean Algebra
Question 8 Explanation:
 Question 9
Let X be the number of distinct 16-bit integers in 2's complement representation. Let Y be the number of distinct 16 bit integers in sign magnitude representation. Then X-Y is ________.
 A 0 B 1 C 2 D 16
Digital Logic   Number System
Question 9 Explanation:
 Question 10
A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is _______ .
 A 14 B 16 C 18 D 20
Computer Organization   Machine Instruction
Question 10 Explanation:
There are 10 questions to complete.